{"id":133,"date":"2024-03-12T00:01:05","date_gmt":"2024-03-11T16:01:05","guid":{"rendered":"https:\/\/ultserver.com\/blog\/?p=133"},"modified":"2024-03-20T17:38:19","modified_gmt":"2024-03-20T09:38:19","slug":"%e4%b9%b0%e5%8d%96%e8%82%a1%e7%a5%a8%e7%9a%84%e6%9c%80%e4%bd%b3%e6%97%b6%e6%9c%baiv","status":"publish","type":"post","link":"https:\/\/ultserver.com\/blog\/programming-problems\/%e4%b9%b0%e5%8d%96%e8%82%a1%e7%a5%a8%e7%9a%84%e6%9c%80%e4%bd%b3%e6%97%b6%e6%9c%baiv\/","title":{"rendered":"\u4e70\u5356\u80a1\u7968\u7684\u6700\u4f73\u65f6\u673aIV"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u63cf\u8ff0<\/h2>\n\n\n\n<p>\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 prices \u548c\u4e00\u4e2a\u6574\u6570 k \uff0c\u5176\u4e2d prices[i] \u662f\u67d0\u652f\u7ed9\u5b9a\u7684\u80a1\u7968\u5728\u7b2c i \u5929\u7684\u4ef7\u683c\u3002<\/p>\n\n\n\n<p>\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u8ba1\u7b97\u4f60\u6240\u80fd\u83b7\u53d6\u7684\u6700\u5927\u5229\u6da6\u3002\u4f60\u6700\u591a\u53ef\u4ee5\u5b8c\u6210 k \u7b14\u4ea4\u6613\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u6700\u591a\u53ef\u4ee5\u4e70 k \u6b21\uff0c\u5356 k \u6b21\u3002<\/p>\n\n\n\n<p>\u6ce8\u610f\uff1a\u4f60\u4e0d\u80fd\u540c\u65f6\u53c2\u4e0e\u591a\u7b14\u4ea4\u6613\uff08\u4f60\u5fc5\u987b\u5728\u518d\u6b21\u8d2d\u4e70\u524d\u51fa\u552e\u6389\u4e4b\u524d\u7684\u80a1\u7968\uff09\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u601d\u8def<\/h2>\n\n\n\n<p>\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u6c42\u89e3\u8be5\u9898\u3002<\/p>\n\n\n\n<p>\u9996\u5148\u53ef\u4ee5\u5c06\u6bcf\u5929\u7684\u4ea4\u6613\u72b6\u6001\u5206\u4e3a\u4e0b\u8ff0\u60c5\u51b5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6ca1\u6709\u8fc7\u4efb\u4f55\u4ea4\u6613<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2c1\u6b21\u4e70\u5165<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2c1\u6b21\u5356\u51fa<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2c2\u6b21\u4e70\u5165<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2c2\u6b21\u5356\u51fa<\/li>\n\n\n\n<li>\u2026\u2026<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2cn\u6b21\u4e70\u5165<\/li>\n\n\n\n<li>\u8fdb\u884c\u8fc7\u7b2cn\u6b21\u5356\u51fa<br>\u5171\u6709 $2k+1$ \u4e2a\u72b6\u6001\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u800c\u6bcf\u4e2a\u72b6\u6001\u4e4b\u95f4\u5b58\u5728\u4e0b\u8ff0\u8f6c\u79fb\u5173\u7cfb\uff1a<\/p>\n\n\n\n<p>$$<br>\u672c\u65e5\u8fdb\u884c\u8fc7\u7b2ci\u6b21\u4e70\u5165\u7684\u603b\u5229\u6da6= max\\left( \\begin{aligned} \u6628\u65e5\u8fdb\u884c\u8fc7\u7b2c[i-1]\u6b21\u5356\u51fa\u7684\u603b\u5229\u6da6 &#8211; \u672c\u65e5\u80a1\u4ef7 \\\\ \u6628\u65e5\u8fdb\u884c\u8fc7\u7b2ci\u6b21\u4e70\u5165\u7684\u603b\u5229\u6da6 \\ \\end{aligned} \\right)<br>$$<\/p>\n\n\n\n<p>$$<br>\u672c\u65e5\u8fdb\u884c\u8fc7\u7b2ci\u6b21\u5356\u51fa\u7684\u603b\u5229\u6da6= max\\left( \\begin{aligned} \u6628\u65e5\u8fdb\u884c\u8fc7\u7b2ci\u6b21\u4e70\u5165\u7684\u603b\u5229\u6da6 + \u672c\u65e5\u80a1\u4ef7 \\\\ \u6628\u65e5\u8fdb\u884c\u8fc7\u7b2ci\u6b21\u5356\u51fa\u7684\u603b\u5229\u6da6 \\ \\end{aligned} \\right)<br>$$<\/p>\n\n\n\n<p>\u901a\u8fc7\u52a8\u6001\u89c4\u5212\u6309\u7167\u4e0a\u8ff0\u72b6\u6001\u4e0e\u72b6\u6001\u8f6c\u79fb\u8fdb\u884c\u6c42\u89e3\u5373\u53ef\uff0c\u6700\u7ec8\u83b7\u5f97\u7684\u6700\u5927\u5229\u6da6\u5373\u4e3a\u6700\u540e\u4e00\u5929\u6240\u6709\u72b6\u6001\u4e2d\u7684\u6700\u5927\u503c\u3002<\/p>\n\n\n\n<p>\u4e0a\u8ff0\u65b9\u6cd5\u540c\u6837\u9002\u7528\u4e8e<a href=\"https:\/\/leetcode.cn\/problems\/best-time-to-buy-and-sell-stock-iii\/?envType=study-plan-v2&amp;envId=top-interview-150\">\u4e70\u5356\u80a1\u7968\u7684\u6700\u4f73\u65f6\u673aIII<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4ee3\u7801<\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:flex;align-items:center;padding:10px 0px 10px 16px;margin-bottom:-2px;width:100%;text-align:left;background-color:#2b2b2b;color:#c7c7c7\">C++<\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution {\npublic:\n    int maxProfit(int k, vector&lt;int&gt;&amp; prices) {\n        vector&lt;vector&lt;int&gt;&gt; dp;\n\n\n        for (const auto&amp; price: prices) {\n            dp.emplace_back(vector&lt;int&gt;(k * 2 + 1));\n        }\n\n\n        dp[0][0] = 0;\n        for (size_t idx = 1; idx &lt;= 2 * k; idx += 2) {\n            dp[0][idx] = -prices[0];\n            dp[0][idx + 1] = 0;\n        }\n\n\n        for (size_t day = 1; day &lt; prices.size(); day++) {\n            dp[day][0] = dp[day - 1][0];\n\n\n            for (size_t idx = 1; idx &lt;= 2 * k; idx += 2) {\n                dp[day][idx] = max(dp[day - 1][idx - 1] - prices[day], dp[day - 1][idx]);\n                dp[day][idx + 1] = max(dp[day - 1][idx] + prices[day], dp[day - 1][idx + 1]);\n            }\n        }\n\n\n        return *max_element(dp.back().begin(), dp.back().end());\n    }\n};\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M4.5 12.75l6 6 9-13.5\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M16.5 8.25V6a2.25 2.25 0 00-2.25-2.25H6A2.25 2.25 0 003.75 6v8.25A2.25 2.25 0 006 16.5h2.25m8.25-8.25H18a2.25 2.25 0 012.25 2.25V18A2.25 2.25 0 0118 20.25h-7.5A2.25 2.25 0 018.25 18v-1.5m8.25-8.25h-6a2.25 2.25 0 00-2.25 2.25v6\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\"> {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">public:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">maxProfit<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">k<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #4EC9B0\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;<\/span><span style=\"color: #569CD6\">&amp;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">prices<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        vector&lt;vector&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;&gt; dp;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #569CD6\">const<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">auto<\/span><span style=\"color: #D4D4D4\">&amp; price: prices) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">emplace_back<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #DCDCAA\">vector<\/span><span style=\"color: #D4D4D4\">&lt;<\/span><span style=\"color: #569CD6\">int<\/span><span style=\"color: #D4D4D4\">&gt;(k * <\/span><span style=\"color: #B5CEA8\">2<\/span><span style=\"color: #D4D4D4\"> + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">));<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">][<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">] = <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #569CD6\">size_t<\/span><span style=\"color: #D4D4D4\"> idx = <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">; idx &lt;= <\/span><span style=\"color: #B5CEA8\">2<\/span><span style=\"color: #D4D4D4\"> * k; idx += <\/span><span style=\"color: #B5CEA8\">2<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">][idx] = -<\/span><span style=\"color: #9CDCFE\">prices<\/span><span style=\"color: #D4D4D4\">[<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">];<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">][idx + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">] = <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #569CD6\">size_t<\/span><span style=\"color: #D4D4D4\"> day = <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">; day &lt; <\/span><span style=\"color: #9CDCFE\">prices<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">size<\/span><span style=\"color: #D4D4D4\">(); day++) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day][<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">] = <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">][<\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">];<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #569CD6\">size_t<\/span><span style=\"color: #D4D4D4\"> idx = <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">; idx &lt;= <\/span><span style=\"color: #B5CEA8\">2<\/span><span style=\"color: #D4D4D4\"> * k; idx += <\/span><span style=\"color: #B5CEA8\">2<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day][idx] = <\/span><span style=\"color: #DCDCAA\">max<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">][idx - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">] - <\/span><span style=\"color: #9CDCFE\">prices<\/span><span style=\"color: #D4D4D4\">[day], <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">][idx]);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day][idx + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">] = <\/span><span style=\"color: #DCDCAA\">max<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">][idx] + <\/span><span style=\"color: #9CDCFE\">prices<\/span><span style=\"color: #D4D4D4\">[day], <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">[day - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">][idx + <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> *<\/span><span style=\"color: #DCDCAA\">max_element<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">back<\/span><span style=\"color: #D4D4D4\">().<\/span><span style=\"color: #DCDCAA\">begin<\/span><span style=\"color: #D4D4D4\">(), <\/span><span style=\"color: #9CDCFE\">dp<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">back<\/span><span style=\"color: #D4D4D4\">().<\/span><span style=\"color: #DCDCAA\">end<\/span><span style=\"color: #D4D4D4\">());<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">};<\/span><\/span><\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u529b\u6263\u9898\u76ee\uff1a\u4e70\u5356\u80a1\u7968\u7684\u6700\u4f73\u65f6\u673aIVhttps:\/\/leetcode.cn\/problems\/best-time-to-buy-and-sell-stock-iv\/description\/<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","wikipediapreview_detectlinks":true,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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