{"id":282,"date":"2026-04-14T00:09:11","date_gmt":"2026-04-13T16:09:11","guid":{"rendered":"https:\/\/edryan.top\/index.php\/2026\/04\/14\/%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92%e5%85%a5%e9%97%a8%ef%bc%9a%e4%bb%8e0-1%e8%83%8c%e5%8c%85%e5%88%b0%e6%9c%80%e9%95%bf%e5%85%ac%e5%85%b1%e5%ad%90%e5%ba%8f%e5%88%97\/"},"modified":"2026-04-14T00:09:11","modified_gmt":"2026-04-13T16:09:11","slug":"%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92%e5%85%a5%e9%97%a8%ef%bc%9a%e4%bb%8e0-1%e8%83%8c%e5%8c%85%e5%88%b0%e6%9c%80%e9%95%bf%e5%85%ac%e5%85%b1%e5%ad%90%e5%ba%8f%e5%88%97","status":"publish","type":"post","link":"https:\/\/edryan.top\/index.php\/2026\/04\/14\/%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92%e5%85%a5%e9%97%a8%ef%bc%9a%e4%bb%8e0-1%e8%83%8c%e5%8c%85%e5%88%b0%e6%9c%80%e9%95%bf%e5%85%ac%e5%85%b1%e5%ad%90%e5%ba%8f%e5%88%97\/","title":{"rendered":"\u52a8\u6001\u89c4\u5212\u5165\u95e8\uff1a\u4ece0-1\u80cc\u5305\u5230\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217"},"content":{"rendered":"<p>\u52a8\u6001\u89c4\u5212\uff08Dynamic Programming\uff0c\u7b80\u79f0DP\uff09\u662f\u7b97\u6cd5\u5b66\u4e60\u4e2d\u6700\u91cd\u8981\u4e5f\u6700\u5177\u6311\u6218\u6027\u7684\u601d\u60f3\u4e4b\u4e00\u3002\u5b83\u901a\u8fc7\u5c06\u590d\u6742\u95ee\u9898\u5206\u89e3\u4e3a\u76f8\u4e92\u91cd\u53e0\u7684\u5b50\u95ee\u9898\uff0c\u5e76\u5b58\u50a8\u5b50\u95ee\u9898\u7684\u89e3\u6765\u907f\u514d\u91cd\u590d\u8ba1\u7b97\uff0c\u4ece\u800c\u5927\u5e45\u63d0\u5347\u6548\u7387\u3002\u672c\u6587\u5c06\u901a\u8fc7\u4e24\u4e2a\u7ecf\u5178\u4f8b\u9898\uff0c\u5e26\u4f60\u638c\u63e1\u52a8\u6001\u89c4\u5212\u7684\u6838\u5fc3\u601d\u8def\u3002<\/p>\n<h2>\u4e00\u3001\u52a8\u6001\u89c4\u5212\u7684\u672c\u8d28<\/h2>\n<p>\u52a8\u6001\u89c4\u5212\u7684\u6838\u5fc3\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u6982\u62ec\uff1a<strong>&#8220;\u8bb0\u4f4f\u4f60\u4e4b\u524d\u7b97\u8fc7\u7684\u7ed3\u679c\uff0c\u907f\u514d\u91cd\u590d\u52b3\u52a8\u3002&#8221;<\/strong><\/p>\n<p>\u4e00\u4e2a\u95ee\u9898\u80fd\u7528\u52a8\u6001\u89c4\u5212\u89e3\u51b3\uff0c\u901a\u5e38\u9700\u8981\u6ee1\u8db3\u4e24\u4e2a\u6761\u4ef6\uff1a<\/p>\n<ul>\n<li><strong>\u6700\u4f18\u5b50\u7ed3\u6784<\/strong>\uff1a\u95ee\u9898\u7684\u6700\u4f18\u89e3\u5305\u542b\u5b50\u95ee\u9898\u7684\u6700\u4f18\u89e3<\/li>\n<li><strong>\u91cd\u53e0\u5b50\u95ee\u9898<\/strong>\uff1a\u4e0d\u540c\u7684\u51b3\u7b56\u8def\u5f84\u4f1a\u91cd\u590d\u9047\u5230\u76f8\u540c\u7684\u5b50\u95ee\u9898<\/li>\n<\/ul>\n<h2>\u4e8c\u3001\u7ecf\u5178\u4f8b\u9898\u4e00\uff1a0-1\u80cc\u5305\u95ee\u9898<\/h2>\n<h3>\u95ee\u9898\u63cf\u8ff0<\/h3>\n<p>\u7ed9\u5b9an\u4e2a\u7269\u54c1\uff0c\u6bcf\u4e2a\u7269\u54c1\u6709\u91cd\u91cfweight[i]\u548c\u4ef7\u503cvalue[i]\u3002\u80cc\u5305\u5bb9\u91cf\u4e3aW\uff0c\u6bcf\u4e2a\u7269\u54c1\u53ea\u80fd\u9009\u4e00\u6b21\u3002\u6c42\u80fd\u88c5\u5165\u80cc\u5305\u7684\u6700\u5927\u4ef7\u503c\u3002<\/p>\n<h3>\u72b6\u6001\u5b9a\u4e49<\/h3>\n<p>\u8bbe<code>dp[i][j]<\/code>\u8868\u793a\u524d<code>i<\/code>\u4e2a\u7269\u54c1\uff0c\u5728\u80cc\u5305\u5bb9\u91cf\u4e3a<code>j<\/code>\u65f6\u80fd\u83b7\u5f97\u7684\u6700\u5927\u4ef7\u503c\u3002<\/p>\n<h3>\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h3>\n<pre><code>if j &gt;= weight[i]:\n    dp[i][j] = max(dp[i-1][j], dp[i-1][j-weight[i]] + value[i])\nelse:\n    dp[i][j] = dp[i-1][j]\n<\/code><\/pre>\n<h3>\u7a7a\u95f4\u4f18\u5316<\/h3>\n<p>\u89c2\u5bdf\u5230<code>dp[i][j]<\/code>\u53ea\u4f9d\u8d56\u4e8e\u4e0a\u4e00\u884c\u7684\u6570\u636e\uff0c\u53ef\u4ee5\u5c06\u4e8c\u7ef4\u6570\u7ec4\u4f18\u5316\u4e3a\u4e00\u7ef4\uff0c\u5e76\u91c7\u7528<strong>\u5012\u5e8f\u904d\u5386<\/strong>\uff1a<\/p>\n<pre><code># \u4e00\u7ef4DP\u7248\u672c\nfor i in range(n):\n    for j in range(W, weight[i]-1, -1):\n        dp[j] = max(dp[j], dp[j-weight[i]] + value[i])\n<\/code><\/pre>\n<h2>\u4e09\u3001\u7ecf\u5178\u4f8b\u9898\u4e8c\uff1a\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\uff08LCS\uff09<\/h2>\n<h3>\u95ee\u9898\u63cf\u8ff0<\/h3>\n<p>\u7ed9\u5b9a\u4e24\u4e2a\u5b57\u7b26\u4e32text1\u548ctext2\uff0c\u8fd4\u56de\u5b83\u4eec\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002\u5b50\u5e8f\u5217\u4e0d\u8981\u6c42\u8fde\u7eed\uff0c\u4f46\u8981\u6c42\u76f8\u5bf9\u987a\u5e8f\u4e00\u81f4\u3002<\/p>\n<h3>\u72b6\u6001\u5b9a\u4e49<\/h3>\n<p>\u8bbe<code>dp[i][j]<\/code>\u8868\u793atext1[0:i]\u548ctext2[0:j]\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u957f\u5ea6\u3002<\/p>\n<h3>\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h3>\n<pre><code>if text1[i-1] == text2[j-1]:\n    dp[i][j] = dp[i-1][j-1] + 1\nelse:\n    dp[i][j] = max(dp[i-1][j], dp[i][j-1])\n<\/code><\/pre>\n<h3>Python\u5b9e\u73b0<\/h3>\n<pre><code>def longestCommonSubsequence(text1, text2):\n    m, n = len(text1), len(text2)\n    dp = [[0] * (n + 1) for _ in range(m + 1)]\n    \n    for i in range(1, m + 1):\n        for j in range(1, n + 1):\n            if text1[i-1] == text2[j-1]:\n                dp[i][j] = dp[i-1][j-1] + 1\n            else:\n                dp[i][j] = max(dp[i-1][j], dp[i][j-1])\n    \n    return dp[m][n]\n<\/code><\/pre>\n<h2>\u56db\u3001\u52a8\u6001\u89c4\u5212\u7684\u89e3\u9898\u6846\u67b6<\/h2>\n<p>\u9762\u5bf9\u4e00\u9053\u52a8\u6001\u89c4\u5212\u9898\u76ee\uff0c\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u601d\u8003\uff1a<\/p>\n<ol>\n<li><strong>\u660e\u786e\u72b6\u6001<\/strong>\uff1a\u7528\u4ec0\u4e48\u53d8\u91cf\u63cf\u8ff0\u5b50\u95ee\u9898\u7684\u89e3\uff1f<\/li>\n<li><strong>\u5b9a\u4e49dp\u6570\u7ec4<\/strong>\uff1adp[i]\u6216dp[i][j]\u4ee3\u8868\u4ec0\u4e48\u542b\u4e49\uff1f<\/li>\n<li><strong>\u5bfb\u627e\u8f6c\u79fb\u65b9\u7a0b<\/strong>\uff1a\u5f53\u524d\u72b6\u6001\u5982\u4f55\u4ece\u4e4b\u524d\u7684\u72b6\u6001\u63a8\u5bfc\u800c\u6765\uff1f<\/li>\n<li><strong>\u786e\u5b9a\u521d\u59cb\u6761\u4ef6\u548c\u8fb9\u754c<\/strong>\uff1a\u54ea\u4e9b\u72b6\u6001\u662f\u5df2\u77e5\u7684\uff1f<\/li>\n<li><strong>\u8003\u8651\u4f18\u5316<\/strong>\uff1a\u80fd\u5426\u964d\u4f4e\u65f6\u95f4\u6216\u7a7a\u95f4\u590d\u6742\u5ea6\uff1f<\/li>\n<\/ol>\n<h2>\u4e94\u3001\u590d\u6742\u5ea6\u5bf9\u6bd4<\/h2>\n<table>\n<tr>\n<th>\u95ee\u9898<\/th>\n<th>\u65f6\u95f4\u590d\u6742\u5ea6<\/th>\n<th>\u7a7a\u95f4\u590d\u6742\u5ea6<\/th>\n<th>\u4f18\u5316\u540e\u7a7a\u95f4<\/th>\n<\/tr>\n<tr>\n<td>0-1\u80cc\u5305<\/td>\n<td>O(n\u00d7W)<\/td>\n<td>O(n\u00d7W)<\/td>\n<td>O(W)<\/td>\n<\/tr>\n<tr>\n<td>\u5b8c\u5168\u80cc\u5305<\/td>\n<td>O(n\u00d7W)<\/td>\n<td>O(n\u00d7W)<\/td>\n<td>O(W)<\/td>\n<\/tr>\n<tr>\n<td>\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217<\/td>\n<td>O(m\u00d7n)<\/td>\n<td>O(m\u00d7n)<\/td>\n<td>O(min(m,n))<\/td>\n<\/tr>\n<\/table>\n<h2>\u7ed3\u8bed<\/h2>\n<p>\u52a8\u6001\u89c4\u5212\u662f\u7b97\u6cd5\u9762\u8bd5\u4e2d\u7684\u9ad8\u9891\u8003\u70b9\uff0c\u4e5f\u662f\u89e3\u51b3\u5b9e\u9645\u4f18\u5316\u95ee\u9898\u7684\u5229\u5668\u3002\u638c\u63e10-1\u80cc\u5305\u548c\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u8fd9\u4e24\u4e2a\u7ecf\u5178\u6a21\u578b\uff0c\u4f60\u5c31\u5df2\u7ecf\u8fc8\u5165\u4e86\u52a8\u6001\u89c4\u5212\u7684\u5927\u95e8\u3002\u540e\u7eed\u53ef\u4ee5\u7ee7\u7eed\u6311\u6218\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\u3001\u7f16\u8f91\u8ddd\u79bb\u3001\u80a1\u7968\u4e70\u5356\u95ee\u9898\u7b49\u8fdb\u9636\u9898\u76ee\uff0c\u9010\u6b65\u5efa\u7acb\u8d77\u5bf9DP\u7684\u76f4\u89c9\u548c\u4fe1\u5fc3\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u52a8\u6001\u89c4\u5212\uff08Dynamic Programming\uff0c\u7b80\u79f0DP\uff09\u662f\u7b97\u6cd5\u5b66\u4e60\u4e2d\u6700\u91cd\u8981\u4e5f\u6700\u5177\u6311\u6218\u6027\u7684\u601d\u60f3\u4e4b\u4e00\u3002\u5b83\u901a\u8fc7\u5c06 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[14,15],"tags":[],"class_list":["post-282","post","type-post","status-publish","format-standard","hentry","category-14","category-15"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/posts\/282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/comments?post=282"}],"version-history":[{"count":0,"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/posts\/282\/revisions"}],"wp:attachment":[{"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/media?parent=282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/categories?post=282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/edryan.top\/index.php\/wp-json\/wp\/v2\/tags?post=282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}