{"id":709,"date":"2025-02-15T15:50:30","date_gmt":"2025-02-15T07:50:30","guid":{"rendered":"https:\/\/www.cnitw.com\/?p=709"},"modified":"2025-02-15T15:50:30","modified_gmt":"2025-02-15T07:50:30","slug":"python%e9%99%aa%e7%bb%832-%e4%ba%8c%e7%bb%b4%e6%95%b0%e7%bb%84","status":"publish","type":"post","link":"http:\/\/www.cnitw.com\/?p=709","title":{"rendered":"Python\u966a\u7ec32&#8211;\u4e8c\u7ef4\u6570\u7ec4"},"content":{"rendered":"\n<p>\u5c0fR\u6b63\u5728\u8ba1\u5212\u4e00\u6b21\u4ece\u5730\u70b9A\u5230\u5730\u70b9B\u7684\u5f92\u6b65\u65c5\u884c\uff0c\u603b\u8def\u7a0b\u9700\u8981 N \u5929\u3002\u4e3a\u4e86\u5728\u65c5\u9014\u4e2d\u4fdd\u6301\u5145\u8db3\u7684\u80fd\u91cf\uff0c\u5c0fR\u6bcf\u5929\u5fc5\u987b\u6d88\u80171\u4efd\u98df\u7269\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u5c0fR\u5728\u8def\u9014\u4e2d\u6bcf\u5929\u90fd\u4f1a\u7ecf\u8fc7\u4e00\u4e2a\u8865\u7ed9\u7ad9\uff0c\u53ef\u4ee5\u5148\u8d2d\u4e70\u5b8c\u98df\u7269\u540e\u518d\u6d88\u8017\u4eca\u5929\u76841\u4efd\u98df\u7269\u3002\u7136\u800c\uff0c\u6bcf\u4e2a\u8865\u7ed9\u7ad9\u7684\u98df\u7269\u6bcf\u4efd\u7684\u4ef7\u683c\u53ef\u80fd\u4e0d\u540c\uff0c\u5e76\u4e14\u5c0fR\u5728\u8d2d\u4e70\u5b8c\u98df\u7269\u540e\u6700\u591a\u53ea\u80fd\u540c\u65f6\u643a\u5e26 K \u4efd\u98df\u7269\u3002<\/p>\n\n\n\n<p>\u73b0\u5728\uff0c\u5c0fR\u5e0c\u671b\u5728\u4fdd\u8bc1\u6bcf\u5929\u98df\u7269\u6d88\u8017\u7684\u524d\u63d0\u4e0b\uff0c\u4ee5\u6700\u5c0f\u7684\u82b1\u8d39\u5b8c\u6210\u8fd9\u6b21\u5f92\u6b65\u65c5\u884c\u3002\u4f60\u80fd\u5e2e\u52a9\u5c0fR\u8ba1\u7b97\u51fa\u6700\u4f4e\u7684\u82b1\u8d39\u662f\u591a\u5c11\u5417\uff1f<\/p>\n\n\n\n<p>**\u8f93\u5165 **<\/p>\n\n\n\n<p>n \u603b\u8def\u7a0b\u9700\u8981\u7684\u5929\u6570<br>k \u5c0fR\u6700\u591a\u80fd\u540c\u65f6\u643a\u5e26\u98df\u7269\u7684\u4efd\u6570<br>data[i] \u7b2ci\u5929\u8865\u7ed9\u7ad9\u6bcf\u4efd\u98df\u7269\u7684\u4ef7\u683c<br>**\u8f93\u51fa **<\/p>\n\n\n\n<p>\u8fd4\u56de\u5b8c\u6210\u8fd9\u6b21\u5f92\u6b65\u65c5\u884c\u7684\u6700\u5c0f\u82b1\u8d39<br>**\u7ea6\u675f\u6761\u4ef6 **<\/p>\n\n\n\n<p>1 &lt; n,k &lt; 1000<br>1 &lt; data[i] &lt; 10000<br>\u6d4b\u8bd5\u6837\u4f8b<br>\u6837\u4f8b1\uff1a<\/p>\n\n\n\n<p>\u8f93\u5165\uff1an = 5 ,k = 2 ,data = [1, 2, 3, 3, 2]<br>\u8f93\u51fa\uff1a9<\/p>\n\n\n\n<p>\u6837\u4f8b2\uff1a<\/p>\n\n\n\n<p>\u8f93\u5165\uff1an = 6 ,k = 3 ,data = [4, 1, 5, 2, 1, 3]<br>\u8f93\u51fa\uff1a9<\/p>\n\n\n\n<p>\u6837\u4f8b3\uff1a<\/p>\n\n\n\n<p>\u8f93\u5165\uff1an = 4 ,k = 1 ,data = [3, 2, 4, 1]<br>\u8f93\u51fa\uff1a10<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>\u4ee5\u4e0b\u662f\u89e3\u51b3\u8be5\u95ee\u9898\u7684\u601d\u8def\u548c\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u601d\u8def\u5206\u6790<\/h3>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u5b9a\u4e49\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4 <code>dp[i][j]<\/code> \u8868\u793a\u5728\u7b2c <code>i<\/code> \u5929\u7ed3\u675f\u65f6\uff0c\u643a\u5e26 <code>j<\/code> \u4efd\u98df\u7269\u7684\u6700\u5c0f\u82b1\u8d39\u3002<\/p>\n\n\n\n<p>\u5728\u6bcf\u4e00\u5929\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u9009\u62e9\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e0d\u8d2d\u4e70\u98df\u7269<\/strong>\uff1a\u76f4\u63a5\u6d88\u8017\u5f53\u5929\u7684\u4e00\u4efd\u98df\u7269\uff0c\u72b6\u6001\u8f6c\u79fb\u5230 <code>dp[i+1][j-1]<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u8d2d\u4e70\u98df\u7269<\/strong>\uff1a\u8d2d\u4e70\u4e00\u5b9a\u6570\u91cf\u7684\u98df\u7269\uff0c\u4f7f\u5f97\u603b\u643a\u5e26\u91cf\u4e0d\u8d85\u8fc7 <code>K<\/code>\uff0c\u66f4\u65b0\u76f8\u5e94\u7684\u72b6\u6001\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4ee3\u7801\u5b9e\u73b0<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>def min_cost(n, k, data):\n    # \u521d\u59cb\u5316 dp \u6570\u7ec4\n    dp = &#91;&#91;float('inf')] * (k + 1) for _ in range(n + 1)]\n    # \u521d\u59cb\u72b6\u6001\uff1a\u7b2c 0 \u5929\u643a\u5e26 0 \u4efd\u98df\u7269\u7684\u82b1\u8d39\u4e3a 0\n    dp&#91;0]&#91;0] = 0\n\n    for i in range(n):\n        for j in range(k + 1):\n            if dp&#91;i]&#91;j] == float('inf'):\n                continue\n            # \u4e0d\u8d2d\u4e70\u98df\u7269\uff0c\u6d88\u8017\u5f53\u5929\u7684\u4e00\u4efd\u98df\u7269\n            if j &gt; 0:\n                dp&#91;i + 1]&#91;j - 1] = min(dp&#91;i + 1]&#91;j - 1], dp&#91;i]&#91;j])\n            # \u8d2d\u4e70\u98df\u7269\n            for buy in range(k - j + 1):\n                new_j = j + buy\n                cost = dp&#91;i]&#91;j] + buy * data&#91;i]\n                dp&#91;i + 1]&#91;new_j] = min(dp&#91;i + 1]&#91;new_j], cost)\n\n    # \u6700\u7ec8\u7ed3\u679c\uff1a\u7b2c n \u5929\u643a\u5e26 0 \u4efd\u98df\u7269\u7684\u6700\u5c0f\u82b1\u8d39\n    return dp&#91;n]&#91;0]\n\n# \u6d4b\u8bd5\u6837\u4f8b\nprint(min_cost(5, 2, &#91;1, 2, 3, 3, 2]))  # \u8f93\u51fa: 9\nprint(min_cost(6, 3, &#91;4, 1, 5, 2, 1, 3]))  # \u8f93\u51fa: 9\nprint(min_cost(4, 1, &#91;3, 2, 4, 1]))  # \u8f93\u51fa: 10<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u590d\u6742\u5ea6\u5206\u6790<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65f6\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a$O(n * k^2)$\uff0c\u5176\u4e2d $n$ \u662f\u603b\u8def\u7a0b\u9700\u8981\u7684\u5929\u6570\uff0c$k$ \u662f\u5c0fR\u6700\u591a\u80fd\u540c\u65f6\u643a\u5e26\u98df\u7269\u7684\u4efd\u6570\u3002\u56e0\u4e3a\u6709\u4e24\u5c42\u5d4c\u5957\u5faa\u73af\u904d\u5386 <code>i<\/code> \u548c <code>j<\/code>\uff0c\u5e76\u4e14\u5728\u8d2d\u4e70\u98df\u7269\u7684\u8fc7\u7a0b\u4e2d\u8fd8\u6709\u4e00\u5c42\u5faa\u73af\u904d\u5386\u8d2d\u4e70\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a$O(n * k)$\uff0c\u4e3b\u8981\u7528\u4e8e\u5b58\u50a8 <code>dp<\/code> \u6570\u7ec4\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0fR\u6b63\u5728\u8ba1\u5212\u4e00\u6b21\u4ece\u5730\u70b9A\u5230\u5730\u70b9B\u7684\u5f92\u6b65\u65c5\u884c\uff0c\u603b\u8def\u7a0b\u9700\u8981 N \u5929\u3002\u4e3a\u4e86\u5728\u65c5\u9014\u4e2d\u4fdd\u6301\u5145\u8db3\u7684\u80fd\u91cf\uff0c\u5c0fR\u6bcf\u5929\u5fc5\u987b\u6d88\u80171\u4efd\u98df\u7269\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u5c0fR\u5728\u8def\u9014\u4e2d\u6bcf\u5929\u90fd\u4f1a\u7ecf\u8fc7\u4e00\u4e2a\u8865\u7ed9\u7ad9\uff0c\u53ef\u4ee5\u5148\u8d2d\u4e70\u5b8c\u98df\u7269\u540e\u518d\u6d88\u8017\u4eca\u5929\u76841\u4efd\u98df\u7269\u3002\u7136\u800c\uff0c\u6bcf\u4e2a\u8865\u7ed9\u7ad9\u7684\u98df\u7269\u6bcf\u4efd\u7684\u4ef7\u683c\u53ef\u80fd\u4e0d\u540c\uff0c\u5e76\u4e14\u5c0fR\u5728\u8d2d\u4e70\u5b8c\u98df\u7269\u540e\u6700\u591a\u53ea\u80fd\u540c\u65f6\u643a\u5e26 K \u4efd\u98df\u7269\u3002 \u73b0\u5728\uff0c\u5c0fR\u5e0c\u671b\u5728\u4fdd\u8bc1\u6bcf\u5929\u98df\u7269\u6d88\u8017\u7684\u524d\u63d0\u4e0b\uff0c\u4ee5\u6700\u5c0f\u7684\u82b1\u8d39\u5b8c\u6210\u8fd9\u6b21\u5f92\u6b65\u65c5\u884c\u3002\u4f60\u80fd\u5e2e\u52a9\u5c0fR\u8ba1\u7b97\u51fa\u6700\u4f4e\u7684\u82b1\u8d39\u662f\u591a\u5c11\u5417\uff1f **\u8f93\u5165 ** n \u603b\u8def\u7a0b\u9700\u8981\u7684\u5929\u6570k \u5c0fR\u6700\u591a\u80fd\u540c\u65f6\u643a\u5e26\u98df\u7269\u7684\u4efd\u6570data[i] \u7b2ci\u5929\u8865\u7ed9\u7ad9\u6bcf\u4efd\u98df\u7269\u7684\u4ef7\u683c**\u8f93\u51fa ** \u8fd4\u56de\u5b8c\u6210\u8fd9\u6b21\u5f92\u6b65\u65c5\u884c\u7684\u6700\u5c0f\u82b1\u8d39**\u7ea6\u675f\u6761\u4ef6 ** 1 &lt; n,k &lt; 10001 &lt; data[i] &lt; 10000\u6d4b\u8bd5\u6837\u4f8b\u6837\u4f8b1\uff1a \u8f93\u5165\uff1an = 5 ,k = 2&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-709","post","type-post","status-publish","format-standard","hentry","category-python"],"_links":{"self":[{"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/posts\/709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=709"}],"version-history":[{"count":1,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/posts\/709\/revisions"}],"predecessor-version":[{"id":711,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=\/wp\/v2\/posts\/709\/revisions\/711"}],"wp:attachment":[{"href":"http:\/\/www.cnitw.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=709"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.cnitw.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}