+
+ Read the Docs
+ v: ${config.versions.current.slug}
+
+
+
+
+ ${renderLanguages(config)}
+ ${renderVersions(config)}
+ ${renderDownloads(config)}
+
+ - 托管于 Read the Docs
+ -
+ 项目主页
+
+ -
+ 构建
+
+ -
+ 下载
+
+
+
+ - 搜索
+ -
+
+
+
+
+
+ Hosted by Read the Docs
+
+
+
+ `;
+
+ // Inject the generated flyout into the body HTML element.
+ document.body.insertAdjacentHTML("beforeend", flyout);
+
+ // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout.
+ document
+ .querySelector("#flyout-search-form")
+ .addEventListener("focusin", () => {
+ const event = new CustomEvent("readthedocs-search-show");
+ document.dispatchEvent(event);
+ });
+ })
+}
+
+if (themeLanguageSelector || themeVersionSelector) {
+ function onSelectorSwitch(event) {
+ const option = event.target.selectedIndex;
+ const item = event.target.options[option];
+ window.location.href = item.dataset.url;
+ }
+
+ document.addEventListener("readthedocs-addons-data-ready", function (event) {
+ const config = event.detail.data();
+
+ const versionSwitch = document.querySelector(
+ "div.switch-menus > div.version-switch",
+ );
+ if (themeVersionSelector) {
+ let versions = config.versions.active;
+ if (config.versions.current.hidden || config.versions.current.type === "external") {
+ versions.unshift(config.versions.current);
+ }
+ const versionSelect = `
+
+ `;
+
+ versionSwitch.innerHTML = versionSelect;
+ versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch);
+ }
+
+ const languageSwitch = document.querySelector(
+ "div.switch-menus > div.language-switch",
+ );
+
+ if (themeLanguageSelector) {
+ if (config.projects.translations.length) {
+ // Add the current language to the options on the selector
+ let languages = config.projects.translations.concat(
+ config.projects.current,
+ );
+ languages = languages.sort((a, b) =>
+ a.language.name.localeCompare(b.language.name),
+ );
+
+ const languageSelect = `
+
+ `;
+
+ languageSwitch.innerHTML = languageSelect;
+ languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch);
+ }
+ else {
+ languageSwitch.remove();
+ }
+ }
+ });
+}
+
+document.addEventListener("readthedocs-addons-data-ready", function (event) {
+ // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav.
+ document
+ .querySelector("[role='search'] input")
+ .addEventListener("focusin", () => {
+ const event = new CustomEvent("readthedocs-search-show");
+ document.dispatchEvent(event);
+ });
+});
\ No newline at end of file
diff --git a/_static/language_data.js b/_static/language_data.js
new file mode 100644
index 0000000..c7fe6c6
--- /dev/null
+++ b/_static/language_data.js
@@ -0,0 +1,192 @@
+/*
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ */
+
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
+
+
+/* Non-minified version is copied as a separate JS file, if available */
+
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+ var step2list = {
+ ational: 'ate',
+ tional: 'tion',
+ enci: 'ence',
+ anci: 'ance',
+ izer: 'ize',
+ bli: 'ble',
+ alli: 'al',
+ entli: 'ent',
+ eli: 'e',
+ ousli: 'ous',
+ ization: 'ize',
+ ation: 'ate',
+ ator: 'ate',
+ alism: 'al',
+ iveness: 'ive',
+ fulness: 'ful',
+ ousness: 'ous',
+ aliti: 'al',
+ iviti: 'ive',
+ biliti: 'ble',
+ logi: 'log'
+ };
+
+ var step3list = {
+ icate: 'ic',
+ ative: '',
+ alize: 'al',
+ iciti: 'ic',
+ ical: 'ic',
+ ful: '',
+ ness: ''
+ };
+
+ var c = "[^aeiou]"; // consonant
+ var v = "[aeiouy]"; // vowel
+ var C = c + "[^aeiouy]*"; // consonant sequence
+ var V = v + "[aeiou]*"; // vowel sequence
+
+ var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
+ var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
+ var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
+ var s_v = "^(" + C + ")?" + v; // vowel in stem
+
+ this.stemWord = function (w) {
+ var stem;
+ var suffix;
+ var firstch;
+ var origword = w;
+
+ if (w.length < 3)
+ return w;
+
+ var re;
+ var re2;
+ var re3;
+ var re4;
+
+ firstch = w.substr(0,1);
+ if (firstch == "y")
+ w = firstch.toUpperCase() + w.substr(1);
+
+ // Step 1a
+ re = /^(.+?)(ss|i)es$/;
+ re2 = /^(.+?)([^s])s$/;
+
+ if (re.test(w))
+ w = w.replace(re,"$1$2");
+ else if (re2.test(w))
+ w = w.replace(re2,"$1$2");
+
+ // Step 1b
+ re = /^(.+?)eed$/;
+ re2 = /^(.+?)(ed|ing)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ re = new RegExp(mgr0);
+ if (re.test(fp[1])) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+ }
+ else if (re2.test(w)) {
+ var fp = re2.exec(w);
+ stem = fp[1];
+ re2 = new RegExp(s_v);
+ if (re2.test(stem)) {
+ w = stem;
+ re2 = /(at|bl|iz)$/;
+ re3 = new RegExp("([^aeiouylsz])\\1$");
+ re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+ if (re2.test(w))
+ w = w + "e";
+ else if (re3.test(w)) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+ else if (re4.test(w))
+ w = w + "e";
+ }
+ }
+
+ // Step 1c
+ re = /^(.+?)y$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(s_v);
+ if (re.test(stem))
+ w = stem + "i";
+ }
+
+ // Step 2
+ re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ suffix = fp[2];
+ re = new RegExp(mgr0);
+ if (re.test(stem))
+ w = stem + step2list[suffix];
+ }
+
+ // Step 3
+ re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ suffix = fp[2];
+ re = new RegExp(mgr0);
+ if (re.test(stem))
+ w = stem + step3list[suffix];
+ }
+
+ // Step 4
+ re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+ re2 = /^(.+?)(s|t)(ion)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(mgr1);
+ if (re.test(stem))
+ w = stem;
+ }
+ else if (re2.test(w)) {
+ var fp = re2.exec(w);
+ stem = fp[1] + fp[2];
+ re2 = new RegExp(mgr1);
+ if (re2.test(stem))
+ w = stem;
+ }
+
+ // Step 5
+ re = /^(.+?)e$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(mgr1);
+ re2 = new RegExp(meq1);
+ re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+ if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+ w = stem;
+ }
+ re = /ll$/;
+ re2 = new RegExp(mgr1);
+ if (re.test(w) && re2.test(w)) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+
+ // and turn initial Y back to y
+ if (firstch == "y")
+ w = firstch.toLowerCase() + w.substr(1);
+ return w;
+ }
+}
+
diff --git a/_static/minus.png b/_static/minus.png
new file mode 100644
index 0000000..d96755f
Binary files /dev/null and b/_static/minus.png differ
diff --git a/_static/plot_directive.css b/_static/plot_directive.css
new file mode 100644
index 0000000..d45593c
--- /dev/null
+++ b/_static/plot_directive.css
@@ -0,0 +1,16 @@
+/*
+ * plot_directive.css
+ * ~~~~~~~~~~~~
+ *
+ * Stylesheet controlling images created using the `plot` directive within
+ * Sphinx.
+ *
+ * :copyright: Copyright 2020-* by the Matplotlib development team.
+ * :license: Matplotlib, see LICENSE for details.
+ *
+ */
+
+img.plot-directive {
+ border: 0;
+ max-width: 100%;
+}
diff --git a/_static/plus.png b/_static/plus.png
new file mode 100644
index 0000000..7107cec
Binary files /dev/null and b/_static/plus.png differ
diff --git a/_static/pygments.css b/_static/pygments.css
new file mode 100644
index 0000000..6f8b210
--- /dev/null
+++ b/_static/pygments.css
@@ -0,0 +1,75 @@
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+.highlight .hll { background-color: #ffffcc }
+.highlight { background: #f8f8f8; }
+.highlight .c { color: #3D7B7B; font-style: italic } /* Comment */
+.highlight .err { border: 1px solid #F00 } /* Error */
+.highlight .k { color: #008000; font-weight: bold } /* Keyword */
+.highlight .o { color: #666 } /* Operator */
+.highlight .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */
+.highlight .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */
+.highlight .cp { color: #9C6500 } /* Comment.Preproc */
+.highlight .cpf { color: #3D7B7B; font-style: italic } /* Comment.PreprocFile */
+.highlight .c1 { color: #3D7B7B; font-style: italic } /* Comment.Single */
+.highlight .cs { color: #3D7B7B; font-style: italic } /* Comment.Special */
+.highlight .gd { color: #A00000 } /* Generic.Deleted */
+.highlight .ge { font-style: italic } /* Generic.Emph */
+.highlight .ges { font-weight: bold; font-style: italic } /* Generic.EmphStrong */
+.highlight .gr { color: #E40000 } /* Generic.Error */
+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
+.highlight .gi { color: #008400 } /* Generic.Inserted */
+.highlight .go { color: #717171 } /* Generic.Output */
+.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
+.highlight .gs { font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #04D } /* Generic.Traceback */
+.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #008000 } /* Keyword.Pseudo */
+.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #B00040 } /* Keyword.Type */
+.highlight .m { color: #666 } /* Literal.Number */
+.highlight .s { color: #BA2121 } /* Literal.String */
+.highlight .na { color: #687822 } /* Name.Attribute */
+.highlight .nb { color: #008000 } /* Name.Builtin */
+.highlight .nc { color: #00F; font-weight: bold } /* Name.Class */
+.highlight .no { color: #800 } /* Name.Constant */
+.highlight .nd { color: #A2F } /* Name.Decorator */
+.highlight .ni { color: #717171; font-weight: bold } /* Name.Entity */
+.highlight .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */
+.highlight .nf { color: #00F } /* Name.Function */
+.highlight .nl { color: #767600 } /* Name.Label */
+.highlight .nn { color: #00F; font-weight: bold } /* Name.Namespace */
+.highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
+.highlight .nv { color: #19177C } /* Name.Variable */
+.highlight .ow { color: #A2F; font-weight: bold } /* Operator.Word */
+.highlight .w { color: #BBB } /* Text.Whitespace */
+.highlight .mb { color: #666 } /* Literal.Number.Bin */
+.highlight .mf { color: #666 } /* Literal.Number.Float */
+.highlight .mh { color: #666 } /* Literal.Number.Hex */
+.highlight .mi { color: #666 } /* Literal.Number.Integer */
+.highlight .mo { color: #666 } /* Literal.Number.Oct */
+.highlight .sa { color: #BA2121 } /* Literal.String.Affix */
+.highlight .sb { color: #BA2121 } /* Literal.String.Backtick */
+.highlight .sc { color: #BA2121 } /* Literal.String.Char */
+.highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */
+.highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
+.highlight .s2 { color: #BA2121 } /* Literal.String.Double */
+.highlight .se { color: #AA5D1F; font-weight: bold } /* Literal.String.Escape */
+.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */
+.highlight .si { color: #A45A77; font-weight: bold } /* Literal.String.Interpol */
+.highlight .sx { color: #008000 } /* Literal.String.Other */
+.highlight .sr { color: #A45A77 } /* Literal.String.Regex */
+.highlight .s1 { color: #BA2121 } /* Literal.String.Single */
+.highlight .ss { color: #19177C } /* Literal.String.Symbol */
+.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */
+.highlight .fm { color: #00F } /* Name.Function.Magic */
+.highlight .vc { color: #19177C } /* Name.Variable.Class */
+.highlight .vg { color: #19177C } /* Name.Variable.Global */
+.highlight .vi { color: #19177C } /* Name.Variable.Instance */
+.highlight .vm { color: #19177C } /* Name.Variable.Magic */
+.highlight .il { color: #666 } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/_static/searchtools.js b/_static/searchtools.js
new file mode 100644
index 0000000..91f4be5
--- /dev/null
+++ b/_static/searchtools.js
@@ -0,0 +1,635 @@
+/*
+ * Sphinx JavaScript utilities for the full-text search.
+ */
+"use strict";
+
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
+ var Scorer = {
+ // Implement the following function to further tweak the score for each result
+ // The function takes a result array [docname, title, anchor, descr, score, filename]
+ // and returns the new score.
+ /*
+ score: result => {
+ const [docname, title, anchor, descr, score, filename, kind] = result
+ return score
+ },
+ */
+
+ // query matches the full name of an object
+ objNameMatch: 11,
+ // or matches in the last dotted part of the object name
+ objPartialMatch: 6,
+ // Additive scores depending on the priority of the object
+ objPrio: {
+ 0: 15, // used to be importantResults
+ 1: 5, // used to be objectResults
+ 2: -5, // used to be unimportantResults
+ },
+ // Used when the priority is not in the mapping.
+ objPrioDefault: 0,
+
+ // query found in title
+ title: 15,
+ partialTitle: 7,
+ // query found in terms
+ term: 5,
+ partialTerm: 2,
+ };
+}
+
+// Global search result kind enum, used by themes to style search results.
+class SearchResultKind {
+ static get index() { return "index"; }
+ static get object() { return "object"; }
+ static get text() { return "text"; }
+ static get title() { return "title"; }
+}
+
+const _removeChildren = (element) => {
+ while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+ string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, searchTerms, highlightTerms) => {
+ const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+ const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+ const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+ const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+ const contentRoot = document.documentElement.dataset.content_root;
+
+ const [docName, title, anchor, descr, score, _filename, kind] = item;
+
+ let listItem = document.createElement("li");
+ // Add a class representing the item's type:
+ // can be used by a theme's CSS selector for styling
+ // See SearchResultKind for the class names.
+ listItem.classList.add(`kind-${kind}`);
+ let requestUrl;
+ let linkUrl;
+ if (docBuilder === "dirhtml") {
+ // dirhtml builder
+ let dirname = docName + "/";
+ if (dirname.match(/\/index\/$/))
+ dirname = dirname.substring(0, dirname.length - 6);
+ else if (dirname === "index/") dirname = "";
+ requestUrl = contentRoot + dirname;
+ linkUrl = requestUrl;
+ } else {
+ // normal html builders
+ requestUrl = contentRoot + docName + docFileSuffix;
+ linkUrl = docName + docLinkSuffix;
+ }
+ let linkEl = listItem.appendChild(document.createElement("a"));
+ linkEl.href = linkUrl + anchor;
+ linkEl.dataset.score = score;
+ linkEl.innerHTML = title;
+ if (descr) {
+ listItem.appendChild(document.createElement("span")).innerHTML =
+ " (" + descr + ")";
+ // highlight search terms in the description
+ if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
+ highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
+ }
+ else if (showSearchSummary)
+ fetch(requestUrl)
+ .then((responseData) => responseData.text())
+ .then((data) => {
+ if (data)
+ listItem.appendChild(
+ Search.makeSearchSummary(data, searchTerms, anchor)
+ );
+ // highlight search terms in the summary
+ if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js
+ highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
+ });
+ Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+ Search.stopPulse();
+ Search.title.innerText = _("Search Results");
+ if (!resultCount)
+ Search.status.innerText = Documentation.gettext(
+ "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+ );
+ else
+ Search.status.innerText = Documentation.ngettext(
+ "Search finished, found one page matching the search query.",
+ "Search finished, found ${resultCount} pages matching the search query.",
+ resultCount,
+ ).replace('${resultCount}', resultCount);
+};
+const _displayNextItem = (
+ results,
+ resultCount,
+ searchTerms,
+ highlightTerms,
+) => {
+ // results left, load the summary and display it
+ // this is intended to be dynamic (don't sub resultsCount)
+ if (results.length) {
+ _displayItem(results.pop(), searchTerms, highlightTerms);
+ setTimeout(
+ () => _displayNextItem(results, resultCount, searchTerms, highlightTerms),
+ 5
+ );
+ }
+ // search finished, update title and status message
+ else _finishSearch(resultCount);
+};
+// Helper function used by query() to order search results.
+// Each input is an array of [docname, title, anchor, descr, score, filename, kind].
+// Order the results by score (in opposite order of appearance, since the
+// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically.
+const _orderResultsByScoreThenName = (a, b) => {
+ const leftScore = a[4];
+ const rightScore = b[4];
+ if (leftScore === rightScore) {
+ // same score: sort alphabetically
+ const leftTitle = a[1].toLowerCase();
+ const rightTitle = b[1].toLowerCase();
+ if (leftTitle === rightTitle) return 0;
+ return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
+ }
+ return leftScore > rightScore ? 1 : -1;
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+ var splitQuery = (query) => query
+ .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+ .filter(term => term) // remove remaining empty strings
+}
+
+/**
+ * Search Module
+ */
+const Search = {
+ _index: null,
+ _queued_query: null,
+ _pulse_status: -1,
+
+ htmlToText: (htmlString, anchor) => {
+ const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
+ for (const removalQuery of [".headerlink", "script", "style"]) {
+ htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() });
+ }
+ if (anchor) {
+ const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`);
+ if (anchorContent) return anchorContent.textContent;
+
+ console.warn(
+ `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.`
+ );
+ }
+
+ // if anchor not specified or not found, fall back to main content
+ const docContent = htmlElement.querySelector('[role="main"]');
+ if (docContent) return docContent.textContent;
+
+ console.warn(
+ "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template."
+ );
+ return "";
+ },
+
+ init: () => {
+ const query = new URLSearchParams(window.location.search).get("q");
+ document
+ .querySelectorAll('input[name="q"]')
+ .forEach((el) => (el.value = query));
+ if (query) Search.performSearch(query);
+ },
+
+ loadIndex: (url) =>
+ (document.body.appendChild(document.createElement("script")).src = url),
+
+ setIndex: (index) => {
+ Search._index = index;
+ if (Search._queued_query !== null) {
+ const query = Search._queued_query;
+ Search._queued_query = null;
+ Search.query(query);
+ }
+ },
+
+ hasIndex: () => Search._index !== null,
+
+ deferQuery: (query) => (Search._queued_query = query),
+
+ stopPulse: () => (Search._pulse_status = -1),
+
+ startPulse: () => {
+ if (Search._pulse_status >= 0) return;
+
+ const pulse = () => {
+ Search._pulse_status = (Search._pulse_status + 1) % 4;
+ Search.dots.innerText = ".".repeat(Search._pulse_status);
+ if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+ };
+ pulse();
+ },
+
+ /**
+ * perform a search for something (or wait until index is loaded)
+ */
+ performSearch: (query) => {
+ // create the required interface elements
+ const searchText = document.createElement("h2");
+ searchText.textContent = _("Searching");
+ const searchSummary = document.createElement("p");
+ searchSummary.classList.add("search-summary");
+ searchSummary.innerText = "";
+ const searchList = document.createElement("ul");
+ searchList.setAttribute("role", "list");
+ searchList.classList.add("search");
+
+ const out = document.getElementById("search-results");
+ Search.title = out.appendChild(searchText);
+ Search.dots = Search.title.appendChild(document.createElement("span"));
+ Search.status = out.appendChild(searchSummary);
+ Search.output = out.appendChild(searchList);
+
+ const searchProgress = document.getElementById("search-progress");
+ // Some themes don't use the search progress node
+ if (searchProgress) {
+ searchProgress.innerText = _("Preparing search...");
+ }
+ Search.startPulse();
+
+ // index already loaded, the browser was quick!
+ if (Search.hasIndex()) Search.query(query);
+ else Search.deferQuery(query);
+ },
+
+ _parseQuery: (query) => {
+ // stem the search terms and add them to the correct list
+ const stemmer = new Stemmer();
+ const searchTerms = new Set();
+ const excludedTerms = new Set();
+ const highlightTerms = new Set();
+ const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+ splitQuery(query.trim()).forEach((queryTerm) => {
+ const queryTermLower = queryTerm.toLowerCase();
+
+ // maybe skip this "word"
+ // stopwords array is from language_data.js
+ if (
+ stopwords.indexOf(queryTermLower) !== -1 ||
+ queryTerm.match(/^\d+$/)
+ )
+ return;
+
+ // stem the word
+ let word = stemmer.stemWord(queryTermLower);
+ // select the correct list
+ if (word[0] === "-") excludedTerms.add(word.substr(1));
+ else {
+ searchTerms.add(word);
+ highlightTerms.add(queryTermLower);
+ }
+ });
+
+ if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js
+ localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+ }
+
+ // console.debug("SEARCH: searching for:");
+ // console.info("required: ", [...searchTerms]);
+ // console.info("excluded: ", [...excludedTerms]);
+
+ return [query, searchTerms, excludedTerms, highlightTerms, objectTerms];
+ },
+
+ /**
+ * execute search (requires search index to be loaded)
+ */
+ _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => {
+ const filenames = Search._index.filenames;
+ const docNames = Search._index.docnames;
+ const titles = Search._index.titles;
+ const allTitles = Search._index.alltitles;
+ const indexEntries = Search._index.indexentries;
+
+ // Collect multiple result groups to be sorted separately and then ordered.
+ // Each is an array of [docname, title, anchor, descr, score, filename, kind].
+ const normalResults = [];
+ const nonMainIndexResults = [];
+
+ _removeChildren(document.getElementById("search-progress"));
+
+ const queryLower = query.toLowerCase().trim();
+ for (const [title, foundTitles] of Object.entries(allTitles)) {
+ if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) {
+ for (const [file, id] of foundTitles) {
+ const score = Math.round(Scorer.title * queryLower.length / title.length);
+ const boost = titles[file] === title ? 1 : 0; // add a boost for document titles
+ normalResults.push([
+ docNames[file],
+ titles[file] !== title ? `${titles[file]} > ${title}` : title,
+ id !== null ? "#" + id : "",
+ null,
+ score + boost,
+ filenames[file],
+ SearchResultKind.title,
+ ]);
+ }
+ }
+ }
+
+ // search for explicit entries in index directives
+ for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+ if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+ for (const [file, id, isMain] of foundEntries) {
+ const score = Math.round(100 * queryLower.length / entry.length);
+ const result = [
+ docNames[file],
+ titles[file],
+ id ? "#" + id : "",
+ null,
+ score,
+ filenames[file],
+ SearchResultKind.index,
+ ];
+ if (isMain) {
+ normalResults.push(result);
+ } else {
+ nonMainIndexResults.push(result);
+ }
+ }
+ }
+ }
+
+ // lookup as object
+ objectTerms.forEach((term) =>
+ normalResults.push(...Search.performObjectSearch(term, objectTerms))
+ );
+
+ // lookup as search terms in fulltext
+ normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms));
+
+ // let the scorer override scores with a custom scoring function
+ if (Scorer.score) {
+ normalResults.forEach((item) => (item[4] = Scorer.score(item)));
+ nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item)));
+ }
+
+ // Sort each group of results by score and then alphabetically by name.
+ normalResults.sort(_orderResultsByScoreThenName);
+ nonMainIndexResults.sort(_orderResultsByScoreThenName);
+
+ // Combine the result groups in (reverse) order.
+ // Non-main index entries are typically arbitrary cross-references,
+ // so display them after other results.
+ let results = [...nonMainIndexResults, ...normalResults];
+
+ // remove duplicate search results
+ // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+ let seen = new Set();
+ results = results.reverse().reduce((acc, result) => {
+ let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+ if (!seen.has(resultStr)) {
+ acc.push(result);
+ seen.add(resultStr);
+ }
+ return acc;
+ }, []);
+
+ return results.reverse();
+ },
+
+ query: (query) => {
+ const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query);
+ const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms);
+
+ // for debugging
+ //Search.lastresults = results.slice(); // a copy
+ // console.info("search results:", Search.lastresults);
+
+ // print the results
+ _displayNextItem(results, results.length, searchTerms, highlightTerms);
+ },
+
+ /**
+ * search for object names
+ */
+ performObjectSearch: (object, objectTerms) => {
+ const filenames = Search._index.filenames;
+ const docNames = Search._index.docnames;
+ const objects = Search._index.objects;
+ const objNames = Search._index.objnames;
+ const titles = Search._index.titles;
+
+ const results = [];
+
+ const objectSearchCallback = (prefix, match) => {
+ const name = match[4]
+ const fullname = (prefix ? prefix + "." : "") + name;
+ const fullnameLower = fullname.toLowerCase();
+ if (fullnameLower.indexOf(object) < 0) return;
+
+ let score = 0;
+ const parts = fullnameLower.split(".");
+
+ // check for different match types: exact matches of full name or
+ // "last name" (i.e. last dotted part)
+ if (fullnameLower === object || parts.slice(-1)[0] === object)
+ score += Scorer.objNameMatch;
+ else if (parts.slice(-1)[0].indexOf(object) > -1)
+ score += Scorer.objPartialMatch; // matches in last name
+
+ const objName = objNames[match[1]][2];
+ const title = titles[match[0]];
+
+ // If more than one term searched for, we require other words to be
+ // found in the name/title/description
+ const otherTerms = new Set(objectTerms);
+ otherTerms.delete(object);
+ if (otherTerms.size > 0) {
+ const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+ if (
+ [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+ )
+ return;
+ }
+
+ let anchor = match[3];
+ if (anchor === "") anchor = fullname;
+ else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+ const descr = objName + _(", in ") + title;
+
+ // add custom score for some objects according to scorer
+ if (Scorer.objPrio.hasOwnProperty(match[2]))
+ score += Scorer.objPrio[match[2]];
+ else score += Scorer.objPrioDefault;
+
+ results.push([
+ docNames[match[0]],
+ fullname,
+ "#" + anchor,
+ descr,
+ score,
+ filenames[match[0]],
+ SearchResultKind.object,
+ ]);
+ };
+ Object.keys(objects).forEach((prefix) =>
+ objects[prefix].forEach((array) =>
+ objectSearchCallback(prefix, array)
+ )
+ );
+ return results;
+ },
+
+ /**
+ * search for full-text terms in the index
+ */
+ performTermsSearch: (searchTerms, excludedTerms) => {
+ // prepare search
+ const terms = Search._index.terms;
+ const titleTerms = Search._index.titleterms;
+ const filenames = Search._index.filenames;
+ const docNames = Search._index.docnames;
+ const titles = Search._index.titles;
+
+ const scoreMap = new Map();
+ const fileMap = new Map();
+
+ // perform the search on the required terms
+ searchTerms.forEach((word) => {
+ const files = [];
+ // find documents, if any, containing the query word in their text/title term indices
+ // use Object.hasOwnProperty to avoid mismatching against prototype properties
+ const arr = [
+ { files: terms.hasOwnProperty(word) ? terms[word] : undefined, score: Scorer.term },
+ { files: titleTerms.hasOwnProperty(word) ? titleTerms[word] : undefined, score: Scorer.title },
+ ];
+ // add support for partial matches
+ if (word.length > 2) {
+ const escapedWord = _escapeRegExp(word);
+ if (!terms.hasOwnProperty(word)) {
+ Object.keys(terms).forEach((term) => {
+ if (term.match(escapedWord))
+ arr.push({ files: terms[term], score: Scorer.partialTerm });
+ });
+ }
+ if (!titleTerms.hasOwnProperty(word)) {
+ Object.keys(titleTerms).forEach((term) => {
+ if (term.match(escapedWord))
+ arr.push({ files: titleTerms[term], score: Scorer.partialTitle });
+ });
+ }
+ }
+
+ // no match but word was a required one
+ if (arr.every((record) => record.files === undefined)) return;
+
+ // found search word in contents
+ arr.forEach((record) => {
+ if (record.files === undefined) return;
+
+ let recordFiles = record.files;
+ if (recordFiles.length === undefined) recordFiles = [recordFiles];
+ files.push(...recordFiles);
+
+ // set score for the word in each file
+ recordFiles.forEach((file) => {
+ if (!scoreMap.has(file)) scoreMap.set(file, new Map());
+ const fileScores = scoreMap.get(file);
+ fileScores.set(word, record.score);
+ });
+ });
+
+ // create the mapping
+ files.forEach((file) => {
+ if (!fileMap.has(file)) fileMap.set(file, [word]);
+ else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word);
+ });
+ });
+
+ // now check if the files don't contain excluded terms
+ const results = [];
+ for (const [file, wordList] of fileMap) {
+ // check if all requirements are matched
+
+ // as search terms with length < 3 are discarded
+ const filteredTermCount = [...searchTerms].filter(
+ (term) => term.length > 2
+ ).length;
+ if (
+ wordList.length !== searchTerms.size &&
+ wordList.length !== filteredTermCount
+ )
+ continue;
+
+ // ensure that none of the excluded terms is in the search result
+ if (
+ [...excludedTerms].some(
+ (term) =>
+ terms[term] === file ||
+ titleTerms[term] === file ||
+ (terms[term] || []).includes(file) ||
+ (titleTerms[term] || []).includes(file)
+ )
+ )
+ break;
+
+ // select one (max) score for the file.
+ const score = Math.max(...wordList.map((w) => scoreMap.get(file).get(w)));
+ // add result to the result list
+ results.push([
+ docNames[file],
+ titles[file],
+ "",
+ null,
+ score,
+ filenames[file],
+ SearchResultKind.text,
+ ]);
+ }
+ return results;
+ },
+
+ /**
+ * helper function to return a node containing the
+ * search summary for a given text. keywords is a list
+ * of stemmed words.
+ */
+ makeSearchSummary: (htmlText, keywords, anchor) => {
+ const text = Search.htmlToText(htmlText, anchor);
+ if (text === "") return null;
+
+ const textLower = text.toLowerCase();
+ const actualStartPosition = [...keywords]
+ .map((k) => textLower.indexOf(k.toLowerCase()))
+ .filter((i) => i > -1)
+ .slice(-1)[0];
+ const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+ const top = startWithContext === 0 ? "" : "...";
+ const tail = startWithContext + 240 < text.length ? "..." : "";
+
+ let summary = document.createElement("p");
+ summary.classList.add("context");
+ summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
+
+ return summary;
+ },
+};
+
+_ready(Search.init);
diff --git a/_static/sphinx_highlight.js b/_static/sphinx_highlight.js
new file mode 100644
index 0000000..8a96c69
--- /dev/null
+++ b/_static/sphinx_highlight.js
@@ -0,0 +1,154 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+ if (node.nodeType === Node.TEXT_NODE) {
+ const val = node.nodeValue;
+ const parent = node.parentNode;
+ const pos = val.toLowerCase().indexOf(text);
+ if (
+ pos >= 0 &&
+ !parent.classList.contains(className) &&
+ !parent.classList.contains("nohighlight")
+ ) {
+ let span;
+
+ const closestNode = parent.closest("body, svg, foreignObject");
+ const isInSVG = closestNode && closestNode.matches("svg");
+ if (isInSVG) {
+ span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+ } else {
+ span = document.createElement("span");
+ span.classList.add(className);
+ }
+
+ span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+ const rest = document.createTextNode(val.substr(pos + text.length));
+ parent.insertBefore(
+ span,
+ parent.insertBefore(
+ rest,
+ node.nextSibling
+ )
+ );
+ node.nodeValue = val.substr(0, pos);
+ /* There may be more occurrences of search term in this node. So call this
+ * function recursively on the remaining fragment.
+ */
+ _highlight(rest, addItems, text, className);
+
+ if (isInSVG) {
+ const rect = document.createElementNS(
+ "http://www.w3.org/2000/svg",
+ "rect"
+ );
+ const bbox = parent.getBBox();
+ rect.x.baseVal.value = bbox.x;
+ rect.y.baseVal.value = bbox.y;
+ rect.width.baseVal.value = bbox.width;
+ rect.height.baseVal.value = bbox.height;
+ rect.setAttribute("class", className);
+ addItems.push({ parent: parent, target: rect });
+ }
+ }
+ } else if (node.matches && !node.matches("button, select, textarea")) {
+ node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+ }
+};
+const _highlightText = (thisNode, text, className) => {
+ let addItems = [];
+ _highlight(thisNode, addItems, text, className);
+ addItems.forEach((obj) =>
+ obj.parent.insertAdjacentElement("beforebegin", obj.target)
+ );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const SphinxHighlight = {
+
+ /**
+ * highlight the search words provided in localstorage in the text
+ */
+ highlightSearchWords: () => {
+ if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight
+
+ // get and clear terms from localstorage
+ const url = new URL(window.location);
+ const highlight =
+ localStorage.getItem("sphinx_highlight_terms")
+ || url.searchParams.get("highlight")
+ || "";
+ localStorage.removeItem("sphinx_highlight_terms")
+ url.searchParams.delete("highlight");
+ window.history.replaceState({}, "", url);
+
+ // get individual terms from highlight string
+ const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+ if (terms.length === 0) return; // nothing to do
+
+ // There should never be more than one element matching "div.body"
+ const divBody = document.querySelectorAll("div.body");
+ const body = divBody.length ? divBody[0] : document.querySelector("body");
+ window.setTimeout(() => {
+ terms.forEach((term) => _highlightText(body, term, "highlighted"));
+ }, 10);
+
+ const searchBox = document.getElementById("searchbox");
+ if (searchBox === null) return;
+ searchBox.appendChild(
+ document
+ .createRange()
+ .createContextualFragment(
+ '
' +
+ '' +
+ _("Hide Search Matches") +
+ "
"
+ )
+ );
+ },
+
+ /**
+ * helper function to hide the search marks again
+ */
+ hideSearchWords: () => {
+ document
+ .querySelectorAll("#searchbox .highlight-link")
+ .forEach((el) => el.remove());
+ document
+ .querySelectorAll("span.highlighted")
+ .forEach((el) => el.classList.remove("highlighted"));
+ localStorage.removeItem("sphinx_highlight_terms")
+ },
+
+ initEscapeListener: () => {
+ // only install a listener if it is really needed
+ if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
+
+ document.addEventListener("keydown", (event) => {
+ // bail for input elements
+ if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+ // bail with special keys
+ if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
+ if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
+ SphinxHighlight.hideSearchWords();
+ event.preventDefault();
+ }
+ });
+ },
+};
+
+_ready(() => {
+ /* Do not call highlightSearchWords() when we are on the search page.
+ * It will highlight words from the *previous* search query.
+ */
+ if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords();
+ SphinxHighlight.initEscapeListener();
+});
diff --git a/chiken_rabbit.html b/chiken_rabbit.html
new file mode 100644
index 0000000..f3bf452
--- /dev/null
+++ b/chiken_rabbit.html
@@ -0,0 +1,934 @@
+
+
+
+
+
+
+
+
+
鸡兔同笼问题 — Class Boru 文档
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+鸡兔同笼问题
+
+第一部分：故事引入
+农场里有一个笼子，里面关着鸡和兔。农夫数了数，发现笼子里共有 35 个头, 94 只脚。农夫很困惑：到底有多少只鸡，多少只兔呢？请你来帮忙！
+问题场景
+
+ flowchart LR
+ A[农夫观察笼子] --> B[数头: 35个]
+ A --> C[数脚: 94只]
+
求解目标
+
+ flowchart LR
+ D[? 多少只鸡] --> E[需要方法求解]
+ F[? 多少只兔] --> E
+
+
+第二部分：直观观察
+
+动物特征对比
+
+
+动物 |
+头数 |
+脚数 |
+
|---|
+
+
+鸡 |
+1 |
+2 |
+
+兔 |
+1 |
+4 |
+
+
+
+
+
+已知条件与目标
+
+ flowchart LR
+ H[头数=35] --> X[求: 鸡数x]
+ F[脚数=94] --> Y[求: 兔数y]
+
关系梳理：
+
+鸡有 2 条腿，兔有 4 条腿
头数总和: 35(每只动物一个头)
脚数总和: 94
我们需要找到鸡和兔的数量
+
+
+
+第三部分：解法一（假设法，适合低年级）
+
+核心思路
+
+ flowchart LR
+ A[假设全是鸡] --> B[计算脚数差]
+ B --> C[求出兔数]
+ C --> D[求出鸡数]
+
+
+详细步骤
+步骤1: 假设全是鸡
+
+ flowchart LR
+ A[35只全是鸡] --> B["脚数 = 35*2 = 70"]
+
+\[35 \times 2 = 70 \quad \text{只脚}\]
+步骤2: 发现差距
+
+ flowchart LR
+ A[假设: 70只脚] --> C[差额: 24只脚]
+ B[实际: 94只脚] --> C
+
实际脚数是 94, 比假设多：
+
+\[94 - 70 = 24\]
+步骤3: 修正假设
+
+ flowchart LR
+ A[差额 24 只脚] --> B[每兔多 2 只脚]
+ B --> C["兔数 = 24/2 = 12"]
+ C --> D["鸡数 = 35-12 = 23"]
+
每只兔比鸡多 2 条腿，因此兔的数量为：
+
+\[\frac{24}{2} = 12\]
+所以鸡的数量为：
+
+\[35 - 12 = 23\]
+步骤4: 验证结果
+
+ flowchart LR
+ A["鸡: 23*2 = 46脚"] --> C[总计: 94脚]
+ B["兔: 12*4 = 48脚"] --> C
+
验证: 12 * 4 + 23 * 2 = 48 + 46 = 94 (正确)
+
+
+
+第四部分：解法二（代入法，适合中年级）
+
+核心思路
+
+ flowchart LR
+ A[设鸡x, 兔y] --> B[由头数得y=35-x]
+ B --> C[代入脚数方程]
+ C --> D[求解x, y]
+
+
+详细步骤
+设鸡为 \(x\)，兔为 \(y\)。
+步骤1: 建立关系
+
+ flowchart LR
+ A["x + y = 35"] --> B["y = 35 - x"]
+ B --> C[代入方程2]
+
由头数方程：
+
+\[y = 35 - x\]
+步骤2: 代入求解
+
+ flowchart TD
+ A["2x + 4(35-x) = 94"]
+ B["-2x = -46"]
+ C["x = 23, y = 12"]
+ A --> B --> C
+
代入脚数方程：
+
+\[2x + 4(35 - x) = 94\]
+化简：
+
+\[\begin{split}-2x + 140 = 94 \\
+-2x = -46 \\
+x = 23\end{split}\]
+所以 \(y = 35 - 23 = 12\)
+
+
+
+第五部分：解法三（方程法，适合高年级）
+
+核心思路
+
+ flowchart LR
+ A[建立方程组] --> B[选择解法]
+ B --> C[代入法/消元法]
+ C --> D[求解答案]
+
+
+详细步骤
+建立方程组：
+
+\[\begin{split}\begin{cases}
+x + y = 35 \\
+2x + 4y = 94
+\end{cases}\end{split}\]
+方法一：代入法
+
+ flowchart LR
+ A["x = 35-y"] --> B["代入第二式"]
+ B --> C["y = 12, x = 23"]
+
方法二：消元法
+
+ flowchart LR
+ A["方程1 x2"] --> B["相减消元"]
+ B --> C["y = 12"]
+ C --> D["x = 23"]
+
答案：鸡 23 只，兔 12 只
+
+
+
+第六部分：方法比较
+
+方法对比
+
+
+方法 |
+特点 |
+适合年级 |
+
|---|
+
+
+假设法 |
+直观易懂 |
+低年级 |
+
+代入法 |
+步骤清晰 |
+中年级 |
+
+方程法 |
+系统严谨 |
+高年级 |
+
+
+
+
+
+殊途同归
+
+ flowchart LR
+ A[假设法] --> D[答案: 鸡23, 兔12]
+ B[代入法] --> D
+ C[方程法] --> D
+
+
+
+第七部分：互动练习
+
+题 1: 鸡兔同笼问题（变式）
+已知条件
+
+ flowchart LR
+ A[头数: 40] --> C[求: 鸡? 兔?]
+ B[脚数: 100] --> C
+
+\[\begin{split}\begin{cases}
+x + y = 40 \\
+2x + 4y = 100
+\end{cases}\end{split}\]
+(Source code, png, hires.png, pdf)
+
+
+
+答案：鸡 30 只，兔 10 只
+
+
+题 2: 桌椅问题
+已知条件
+
+ flowchart LR
+ A[桌子: 4腿] --> C[求: 桌子?]
+ B[椅子: 3腿] --> D[求: 椅子?]
+ E[总数: 30件] --> C
+ F[总腿: 100] --> D
+
+\[\begin{split}\begin{cases}
+x + y = 30 \\
+4x + 3y = 100
+\end{cases}\end{split}\]
+(Source code, png, hires.png, pdf)
+
+
+
+答案：桌子 10 张，椅子 20 把
+
+
+题 3: 铅笔和钢笔问题
+已知条件
+
+ flowchart LR
+ A[铅笔: 1元/支] --> C[求: 铅笔?]
+ B[钢笔: 3元/支] --> D[求: 钢笔?]
+ E[总数: 40支] --> C
+ F[总价: 80元] --> D
+
+\[\begin{split}\begin{cases}
+x + y = 40 \\
+x + 3y = 80
+\end{cases}\end{split}\]
+答案：铅笔 20 支，钢笔 20 支
+
+
+题 4: 公交车和小汽车问题
+已知条件
+
+ flowchart LR
+ A[公交: 40轮] --> C[求: 公交?]
+ B[汽车: 4轮] --> D[求: 汽车?]
+ E[总数: 20辆] --> C
+ F[总轮: 296] --> D
+
+\[\begin{split}\begin{cases}
+x + y = 20 \\
+40x + 4y = 296
+\end{cases}\end{split}\]
+答案：公交车 6 辆，小汽车 14 辆
+
+
+题 5: 鸡兔鸭同笼问题（进阶）
+已知条件
+
+ flowchart LR
+ A[鸡: 2腿] --> D[求: 鸡?]
+ B[兔: 4腿] --> E[求: 兔?]
+ C[鸭: 2腿] --> F[求: 鸭?]
+ G[总数: 60只] --> D
+ H[总腿: 160] --> E
+ I[鸡比鸭多10只] --> F
+
+\[\begin{split}\begin{cases}
+x + y + z = 60 \\
+2x + 4y + 2z = 160 \\
+x - z = 10
+\end{cases\end{split}\]
+答案：鸡 25 只，兔 20 只，鸭 15 只
+
+
+
+第八部分：小结
+
+知识结构
+
+ flowchart TB
+ A[鸡兔同笼问题] --> B[假设法]
+ A --> C[代入法]
+ A --> D[方程法]
+
+
+解题步骤
+
+ flowchart LR
+ A[分析问题] --> B[选择方法]
+ B --> C[求解]
+ C --> D[验证答案]
+
+
+要点总结
+
+鸡兔同笼问题是典型的应用题，核心是找到头数和腿数的关系
三种解法各有优劣
数学的魅力在于不同路径可以通向同一个答案
解题后要验证结果
+
+
+
+思考题
+如果笼子里有若干只蜘蛛（8条腿）、蜻蜓（6条腿）和蝉（6条腿），共 20 只，总共 130 条腿。已知蜘蛛比蝉多 1 只。问每种昆虫各有多少只？
+已知条件
+
+ flowchart LR
+ A[蜘蛛: 8腿] --> D[求: 蜘蛛?]
+ B[蜻蜓: 6腿] --> E[求: 蜻蜓?]
+ C[蝉: 6腿] --> F[求: 蝉?]
+ G[总数: 20只] --> D
+ H[总腿: 130] --> E
+ I[蜘蛛=蝉+1] --> F
+
解题提示
+
+ flowchart LR
+ A[设蝉为z只] --> B[蜘蛛=z+1只]
+ B --> C[蜻蜓=19-2z只]
+ C --> D[列腿数方程求解]
+
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最大公约数与最小公倍数 — Class Boru 文档
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+ - 最大公约数与最小公倍数
+ -
+ 查看页面源码
+
+
+
+
+
+
+
+
+最大公约数与最小公倍数
+
+第一部分：故事引入
+小明要给班级的图书角买书。他发现如果每6本一包，正好包完；如果每8本一包，也正好包完。小明至少买了多少本书？
+问题场景
+
+ flowchart LR
+ A[买书问题] --> B[6本一包: 正好包完]
+ A --> C[8本一包: 正好包完]
+
求解目标
+
+ flowchart LR
+ D[求: 至少买多少本?] --> E[需要方法求解]
+
+
+第二部分：直观观察
+
+基本概念
+
+
+概念 |
+定义 |
+符号 |
+
|---|
+
+
+最大公约数 |
+两个数公有的约数中最大的一个 |
+GCD |
+
+最小公倍数 |
+两个数公有的倍数中最小的一个 |
+LCM |
+
+
+
+
+
+约数与倍数关系
+
+ flowchart LR
+ A[数a] --> B[约数: 能整除a的数]
+ A --> C[倍数: a的整数倍]
+
以6和8为例：
+
+6的约数：1, 2, 3, 6
8的约数：1, 2, 4, 8
6和8的公约数：1, 2
6和8的最大公约数：2
6的倍数：6, 12, 18, 24, 30, ...
8的倍数：8, 16, 24, 32, ...
6和8的公倍数：24, 48, 72, ...
6和8的最小公倍数：24
+
+
+
+第三部分：解法一（列举法，适合低年级）
+
+核心思路
+
+ flowchart LR
+ A[列举约数/倍数] --> B[找公共的]
+ B --> C[选最大/最小]
+
+
+求最大公约数步骤
+例：求18和24的最大公约数
+步骤1: 列举约数
+
+ flowchart LR
+ A[18的约数] --> B[1, 2, 3, 6, 9, 18]
+ C[24的约数] --> D[1, 2, 3, 4, 6, 8, 12, 24]
+
步骤2: 找公约数
+
+ flowchart LR
+ A[公约数] --> B[1, 2, 3, 6]
+
步骤3: 选最大的
+
+ flowchart LR
+ A[最大公约数] --> B[GCD = 6]
+
+
+求最小公倍数步骤
+例：求18和24的最小公倍数
+步骤1: 列举倍数
+
+ flowchart LR
+ A[18的倍数] --> B[18, 36, 54, 72, 90, ...]
+ C[24的倍数] --> D[24, 48, 72, 96, ...]
+
步骤2: 找公倍数
+
+ flowchart LR
+ A[公倍数] --> B[72, 144, ...]
+
步骤3: 选最小的
+
+ flowchart LR
+ A[最小公倍数] --> B[LCM = 72]
+
+
+
+第四部分：解法二（短除法，适合中年级）
+
+核心思路
+
+ flowchart LR
+ A[用公因数连续除] --> B[直到互质为止]
+ B --> C[计算结果]
+
+
+求最大公约数
+例：求18和24的最大公约数
+
+ flowchart TD
+ A["2 | 18 24"]
+ B["3 | 9 12"]
+ C[" | 3 4"]
+ A --> B --> C
+
计算过程：
+2 | 18 24
+ ---------
+3 | 9 12
+ ---------
+ 3 4
+
+
最大公约数 = 2 × 3 = 6
+
+
+求最小公倍数
+例：求18和24的最小公倍数
+使用相同的短除过程：
+最小公倍数 = 2 × 3 × 3 × 4 = 72
+
+ flowchart LR
+ A["GCD = 所有除数的积"] --> B["GCD = 2*3 = 6"]
+ C["LCM = 所有数的积"] --> D["LCM = 2*3*3*4 = 72"]
+
+
+
+第五部分：解法三（质因数分解法，适合高年级）
+
+核心思路
+
+ flowchart LR
+ A[分解质因数] --> B[提取公共部分]
+ B --> C[计算结果]
+
+
+分解质因数
+例：求18和24的GCD和LCM
+步骤1: 分解质因数
+
+ flowchart LR
+ A["18 = 2 * 3 * 3"]
+ B["24 = 2 * 2 * 2 * 3"]
+
步骤2: 求GCD
+
+ flowchart LR
+ A[取公共质因数的最低次幂] --> B["GCD = 2^1 * 3^1 = 6"]
+
步骤3: 求LCM
+
+ flowchart LR
+ A[取所有质因数的最高次幂] --> B["LCM = 2^3 * 3^2 = 72"]
+
+
+重要关系
+
+ flowchart TD
+ A["GCD(a,b) * LCM(a,b) = a * b"]
+
+ style A fill:#e8f5e9
+
验证：GCD(18,24) × LCM(18,24) = 6 × 72 = 432 = 18 × 24 ✓
+
+
+
+第六部分：方法比较
+
+方法对比
+
+
+方法 |
+特点 |
+适合年级 |
+
|---|
+
+
+列举法 |
+直观易懂，适合小数 |
+低年级 |
+
+短除法 |
+计算简便，常用方法 |
+中年级 |
+
+质因数分解 |
+理论清晰，适合大数 |
+高年级 |
+
+
+
+
+
+方法选择
+
+ flowchart TD
+ A[求GCD/LCM] --> B{数字大小}
+ B -->|小| C[列举法]
+ B -->|中| D[短除法]
+ B -->|大| E[质因数分解]
+
+
+
+第七部分：互动练习
+
+题 1: 基础题
+已知条件
+
+ flowchart LR
+ A[求12和18] --> B[GCD = ?]
+ A --> C[LCM = ?]
+
解答过程
+
+ flowchart LR
+ A["12 = 2*2*3"] --> C["GCD = 2*3 = 6"]
+ B["18 = 2*3*3"] --> D["LCM = 2*2*3*3 = 36"]
+
答案：GCD(12,18) = 6，LCM(12,18) = 36
+
+
+题 2: 应用题（分糖果）
+题目
+小明有12颗糖果，小红有18颗糖果。要把它们分别装进袋子里，每袋数量相同且最多，每袋装几颗？
+已知条件
+
+ flowchart LR
+ A[小明: 12颗] --> C[求: 每袋最多?]
+ B[小红: 18颗] --> C
+
分析
+
+ flowchart LR
+ A[每袋数量相同] --> C[求GCD]
+ B[每袋最多] --> C
+ C --> D["GCD(12,18) = 6"]
+
答案：每袋最多装6颗
+
+
+题 3: 应用题（发车问题）
+题目
+公交A线每12分钟发一班车，公交B线每18分钟发一班车。两车同时发车后，至少多少分钟再次同时发车？
+已知条件
+
+ flowchart LR
+ A[A线: 12分钟] --> C[求: 至少多久?]
+ B[B线: 18分钟] --> C
+
分析
+
+ flowchart LR
+ A[再次同时发车] --> C[求LCM]
+ B[至少] --> C
+ C --> D["LCM(12,18) = 36"]
+
答案：至少36分钟后再次同时发车
+
+
+题 4: 进阶题
+题目
+求三个数12、18、24的最大公约数和最小公倍数。
+已知条件
+
+ flowchart LR
+ A[12, 18, 24] --> B[GCD = ?]
+ A --> C[LCM = ?]
+
解答过程
+
+ flowchart LR
+ A["12 = 2*2*3"] --> D["GCD = 2*3 = 6"]
+ B["18 = 2*3*3"] --> E["LCM = 2*2*2*3*3 = 72"]
+ C["24 = 2*2*2*3"]
+
答案：GCD(12,18,24) = 6，LCM(12,18,24) = 72
+
+
+题 5: 综合应用题
+题目
+一个长方形操场，长72米，宽48米。要在四周插彩旗，要求四角都插，且相邻两面彩旗之间的距离相等。最少需要插多少面彩旗？
+已知条件
+
+ flowchart LR
+ A[长: 72米] --> C[求: 最少几面?]
+ B[宽: 48米] --> C
+
分析
+
+ flowchart LR
+ A[距离相等] --> C[求GCD]
+ B[最少] --> C
+ C --> D["GCD(72,48) = 24"]
+ D --> E["周长/间隔 = (72+48)*2/24 = 10"]
+
答案：最少需要插10面彩旗
+
+
+
+第八部分：小结
+
+知识结构
+
+ flowchart TB
+ A[GCD与LCM] --> B[列举法]
+ A --> C[短除法]
+ A --> D[质因数分解]
+
+
+重要公式
+
+ flowchart TD
+ A["GCD(a,b) * LCM(a,b) = a * b"]
+ style A fill:#fff3e0
+
+
+解题步骤
+
+ flowchart LR
+ A[分析问题] --> B[判断求GCD还是LCM]
+ B --> C[选择方法]
+ C --> D[计算验证]
+
+
+要点总结
+
+最大公约数用于"最多"、"最长"等问题
最小公倍数用于"至少"、"最少"等问题
短除法是最常用的方法
记住重要关系：GCD × LCM = 两数之积
+
+
+
+思考题
+一个房间长240厘米，宽180厘米。要用正方形地砖铺地，要求地砖尽可能大且正好铺满。需要多少块地砖？每块地砖的面积是多少？
+已知条件
+
+ flowchart LR
+ A[长: 240厘米] --> C[求: 地砖数量?]
+ B[宽: 180厘米] --> D[求: 每块面积?]
+
解题提示
+
+ flowchart LR
+ A[正方形地砖] --> C[边长 = GCD]
+ B[尽可能大] --> C
+ C --> D["GCD(240,180) = 60"]
+ D --> E["数量 = 240*180/(60*60) = 12"]
+
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搜索 — Class Boru 文档
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