{"id":817,"date":"2024-12-04T21:15:41","date_gmt":"2024-12-04T13:15:41","guid":{"rendered":"https:\/\/womeifei.cn\/?p=817"},"modified":"2024-12-06T15:00:35","modified_gmt":"2024-12-06T07:00:35","slug":"%e5%ad%97%e8%8a%82%e7%ae%97%e6%b3%95dna%e5%ba%8f%e5%88%97%e7%bc%96%e8%be%91%e8%b7%9d%e7%a6%bb-%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92","status":"publish","type":"post","link":"https:\/\/womeifei.cn\/index.php\/2024\/12\/04\/%e5%ad%97%e8%8a%82%e7%ae%97%e6%b3%95dna%e5%ba%8f%e5%88%97%e7%bc%96%e8%be%91%e8%b7%9d%e7%a6%bb-%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92\/","title":{"rendered":"\u5b57\u8282\u7b97\u6cd5DNA\u5e8f\u5217\u7f16\u8f91\u8ddd\u79bb-\u52a8\u6001\u89c4\u5212"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/womeifei.cn\/wp-content\/uploads\/2024\/12\/image-7.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"487\" height=\"795\" data-original=\"https:\/\/womeifei.cn\/wp-content\/uploads\/2024\/12\/image-7.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-818\" style=\"width:620px;height:auto\"  sizes=\"auto, (max-width: 487px) 100vw, 487px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">       \u8fd9\u4e2a\u7b97\u6cd5\u4e00\u770b\u5c31\u662f\u6bd4\u8f83\u590d\u6742\u7684 \u8981\u662f\u76f4\u63a5\u53bb\u5bf9\u5b57\u7b26\u4e32\u8fdb\u884c\u64cd\u4f5c \u4e00\u5b9a\u5341\u5206\u9ebb\u70e6  \u6211\u4eec\u81ea\u7136\u5c31\u60f3\u5230\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u7684\u601d\u8def \u53bb\u628a\u5927\u95ee\u9898\u5206\u89e3\u4e3a\u4e00\u4e2a\u4e2a\u5b50\u95ee\u9898 \u901a\u8fc7\u524d\u9762\u7684\u72b6\u6001\u6765\u51b3\u5b9a\u540e\u9762\u7684\u72b6\u6001 \u8fdb\u800c\u4e00\u6b65\u6b65\u63a8\u51fa\u6700\u7ec8\u7ed3\u679c<\/p>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\">\u63a5\u4e0b\u6765\u6211\u4eec\u518d\u8bf4\u660e\u4e00\u4e0b<strong>\u52a8\u6001\u89c4\u5212\u7684\u57fa\u672c\u64cd\u4f5c\u6b65\u9aa4<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\">1.&nbsp;<strong>\u5b9a\u4e49\u72b6\u6001\uff08State Definition\uff09<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u786e\u5b9a\u72b6\u6001\u53d8\u91cf<\/strong>\uff1a\u9996\u5148\uff0c\u786e\u5b9a\u95ee\u9898\u7684\u6700\u4f18\u89e3\u53ef\u4ee5\u901a\u8fc7\u54ea\u4e9b\u72b6\u6001\u53d8\u91cf\u6765\u8868\u793a\u3002\u8fd9\u4e9b\u72b6\u6001\u53d8\u91cf\u901a\u5e38\u8868\u793a\u5b50\u95ee\u9898\u7684\u89e3\u3002<\/li>\n\n\n\n<li><strong>\u72b6\u6001\u7684\u542b\u4e49<\/strong>\uff1a\u72b6\u6001\u901a\u5e38\u662f\u4e00\u4e2a\u6570\u7ec4\u6216\u8868\u683c\uff0c\u7528\u6765\u5b58\u50a8\u5b50\u95ee\u9898\u7684\u89e3\u3002\u4f8b\u5982\uff0c\u5728\u80cc\u5305\u95ee\u9898\u4e2d\uff0c<code>dp[i][w]<\/code>&nbsp;\u8868\u793a\u524d&nbsp;<code>i<\/code>&nbsp;\u4e2a\u7269\u54c1\u4e2d\uff0c\u91cd\u91cf\u4e3a&nbsp;<code>w<\/code>&nbsp;\u65f6\u7684\u6700\u5927\u4ef7\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading has-large-font-size\">2.&nbsp;<strong>\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff08State Transition or Recurrence Relation\uff09<\/strong><\/h5>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u786e\u5b9a\u72b6\u6001\u4e4b\u95f4\u7684\u5173\u7cfb<\/strong>\uff1a\u6839\u636e\u95ee\u9898\u7684\u7ed3\u6784\uff0c\u627e\u51fa\u5982\u4f55\u4ece\u5df2\u77e5\u7684\u5b50\u95ee\u9898\u89e3\u6784\u5efa\u66f4\u5927\u95ee\u9898\u7684\u89e3\u3002\u901a\u5e38\uff0c\u8fd9\u662f\u901a\u8fc7<strong>\u9012\u63a8\u516c\u5f0f\uff08\u4e5f\u53eb\u9012\u5f52\u516c\u5f0f\uff09<\/strong>\u6765\u63cf\u8ff0\u7684\u3002<\/li>\n\n\n\n<li>\u4f8b\u5982\uff0c\u5728\u80cc\u5305\u95ee\u9898\u4e2d\uff0c<code>dp[i][w]<\/code>&nbsp;\u7684\u503c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4e24\u79cd\u65b9\u5f0f\u83b7\u5f97\uff1a\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0d\u9009\u7b2c&nbsp;<code>i<\/code>&nbsp;\u4e2a\u7269\u54c1<\/strong>\uff1a<code>dp[i][w] = dp[i-1][w]<\/code><\/li>\n\n\n\n<li><strong>\u9009\u62e9\u7b2c&nbsp;<code>i<\/code>&nbsp;\u4e2a\u7269\u54c1<\/strong>\uff1a<code>dp[i][w] = dp[i-1][w-weight[i]] + value[i]<\/code>\uff08\u5982\u679c\u5bb9\u91cf&nbsp;<code>w<\/code>&nbsp;\u8db3\u591f\uff09<\/li>\n\n\n\n<li>\u7136\u540e\uff0c\u9009\u62e9\u8fd9\u4e24\u8005\u4e2d\u7684\u6700\u5927\u503c\uff1a<code>dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i])<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3.&nbsp;<strong>\u521d\u59cb\u5316\uff08Initialization\uff09<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u521d\u59cb\u5316\u8fb9\u754c\u6761\u4ef6<\/strong>\uff1a\u6839\u636e\u95ee\u9898\u7684\u8981\u6c42\uff0c\u521d\u59cb\u5316\u52a8\u6001\u89c4\u5212\u8868\u683c\u7684\u8fb9\u754c\u3002\u8fb9\u754c\u6761\u4ef6\u901a\u5e38\u5bf9\u5e94\u6700\u7b80\u5355\u7684\u5b50\u95ee\u9898\uff0c\u901a\u5e38\u662f\u72b6\u6001\u53d8\u91cf\u7684\u521d\u59cb\u503c\u3002<\/li>\n\n\n\n<li>\u4f8b\u5982\uff0c\u80cc\u5305\u95ee\u9898\u7684\u521d\u59cb\u5316\u8fb9\u754c\u4e3a\uff1a\n<ul class=\"wp-block-list\">\n<li><code>dp[0][w] = 0<\/code>\uff1a0\u4e2a\u7269\u54c1\u65f6\uff0c\u4efb\u4f55\u5bb9\u91cf\u4e0b\u7684\u6700\u5927\u4ef7\u503c\u4e3a 0\u3002<\/li>\n\n\n\n<li><code>dp[i][0] = 0<\/code>\uff1a\u4efb\u4f55\u7269\u54c1\u96c6\u5408\uff0c\u5bb9\u91cf\u4e3a 0 \u65f6\u7684\u6700\u5927\u4ef7\u503c\u4e3a 0\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4.&nbsp;<strong>\u586b\u5145 DP \u8868\u683c\uff08Fill DP Table\uff09<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6309\u987a\u5e8f\u586b\u8868<\/strong>\uff1a\u901a\u5e38\uff0c\u52a8\u6001\u89c4\u5212\u8868\u683c\u662f\u4ece\u5c0f\u5230\u5927\u9010\u6b65\u586b\u5145\u7684\u3002\u6839\u636e\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff0c\u586b\u5145\u6bcf\u4e2a\u5b50\u95ee\u9898\u7684\u89e3\uff0c\u5e76\u5c06\u5176\u4fdd\u5b58\u5230\u8868\u683c\u4e2d\u3002<strong>\u586b\u5145\u65f6\u8981\u786e\u4fdd\u6bcf\u4e2a\u72b6\u6001\u7684\u503c\u662f\u57fa\u4e8e\u5df2\u7ecf\u8ba1\u7b97\u51fa\u7684\u5b50\u95ee\u9898\u89e3<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5.&nbsp;<strong>\u83b7\u53d6\u7b54\u6848\uff08Extract Result\uff09<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982\uff0c\u5728\u80cc\u5305\u95ee\u9898\u4e2d\uff0c<code>dp[n][W]<\/code>&nbsp;\u4ee3\u8868\u4f7f\u7528\u524d&nbsp;<code>n<\/code>&nbsp;\u4e2a\u7269\u54c1\uff0c\u80cc\u5305\u5bb9\u91cf\u4e3a&nbsp;<code>W<\/code>&nbsp;\u65f6\u7684\u6700\u5927\u4ef7\u503c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4ece\u8868\u683c\u4e2d\u8bfb\u53d6\u6700\u7ec8\u7ed3\u679c<\/strong>\uff1a\u6700\u7ec8\u7ed3\u679c\u901a\u5e38\u4fdd\u5b58\u5728\u52a8\u6001\u89c4\u5212\u8868\u683c\u7684\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u53ef\u80fd\u662f\u8868\u683c\u7684\u53f3\u4e0b\u89d2\u6216\u8005\u67d0\u4e2a\u7279\u5b9a\u7684\u5355\u5143\u683c\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u95ee\u9898\u7684\u5b9a\u4e49\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-x-large-font-size wp-block-paragraph\"><strong>\u672c\u9898\u89e3\u51b3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b80\u5355\u4ecb\u7ecd\u4e86\u52a8\u6001\u89c4\u5212\u7684\u57fa\u672c\u6b65\u9aa4 \u73b0\u5728\u6211\u4eec\u6765\u89e3\u51b3\u8fd9\u4e2a\u7b97\u6cd5\u95ee\u9898<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9898\u76ee\u8ba9\u6211\u4eec\u8ba1\u7b97\u64cd\u4f5c\u7684\u6700\u5c11\u6b21\u6570\u4f7f\u5f97DNA1\u53d8\u4e3aDNA2  \u6211\u4eec\u53ef\u4ee5\u4ece\u7b2c\u4e00\u4e2a\u5b57\u7b26\u5f00\u59cb\u8ba1\u7b97 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1.\u5b9a\u4e49\u72b6\u6001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u521b\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4&nbsp;<code>dp<\/code>\uff0c\u5176\u4e2d&nbsp;<code>dp[i][j]<\/code>&nbsp;\u8868\u793a\u5c06&nbsp;<strong><code>DNA1<\/code>&nbsp;\u7684\u524d&nbsp;<code>i<\/code>&nbsp;\u4e2a\u5b57\u7b26\u8f6c\u6362\u4e3a&nbsp;<code>DNA2<\/code>&nbsp;\u7684\u524d&nbsp;<code>j<\/code>&nbsp;\u4e2a\u5b57\u7b26\u6240\u9700\u7684\u6700\u5c0f\u64cd\u4f5c\u6b21\u6570<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2.\u521d\u59cb\u5316<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>dp[i][0] = i<\/code>\uff1a\u5c06&nbsp;<code>dna1<\/code>&nbsp;\u7684\u524d&nbsp;<code>i<\/code>&nbsp;\u4e2a\u5b57\u7b26\u8f6c\u6362\u4e3a\u7a7a\u5b57\u7b26\u4e32\uff0c\u9700\u8981&nbsp;<code>i<\/code>&nbsp;\u6b21\u5220\u9664\u64cd\u4f5c\u3002<\/li>\n\n\n\n<li><code>dp[0][j] = j<\/code>\uff1a\u5c06\u7a7a\u5b57\u7b26\u4e32\u8f6c\u6362\u6210&nbsp;<code>dna2<\/code>&nbsp;\u7684\u524d&nbsp;<code>j<\/code>&nbsp;\u4e2a\u5b57\u7b26\uff0c\u9700\u8981&nbsp;<code>j<\/code>&nbsp;\u6b21\u63d2\u5165\u64cd\u4f5c\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u786e\u5b9a\u4e86\u52a8\u6001\u89c4\u5212\u7684\u8fb9\u754c \u4ee5\u8fd9\u4e2a\u8fb9\u754c\u4e3a\u57fa\u7840\u8fdb\u884c\u540e\u7eed\u7684\u9012\u63a8\u8ba1\u7b97 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3.<strong>\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(1) <strong>\u5982\u679c <code>dna1[i-1] == dna2[j-1]<\/code><\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u610f\u5473\u7740\u5f53\u524d\u7684\u5b57\u7b26\u662f\u76f8\u540c\u7684\uff0c\u4e0d\u9700\u8981\u8fdb\u884c\u4efb\u4f55\u64cd\u4f5c\uff0c\u76f4\u63a5\u7ee7\u627f\u4e0a\u4e00\u6b65\u7684\u6700\u4f18\u89e3\u3002<\/li>\n\n\n\n<li>\u4e5f\u5c31\u662f\u8bf4\uff0c<code>dp[i][j] = dp[i-1][j-1]<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u4f8b\u5b50<\/strong>\uff1a\u5047\u8bbe&nbsp;<code>dna1 = \"AGCT\"<\/code>&nbsp;\u548c&nbsp;<code>dna2 = \"AGCT\"<\/code>\uff0c\u6bd4\u8f83\u5230&nbsp;<code>A<\/code>&nbsp;\u548c&nbsp;<code>A<\/code>&nbsp;\u65f6\uff0c\u5b83\u4eec\u76f8\u540c\uff0c\u5c31\u4e0d\u9700\u8981\u4efb\u4f55\u64cd\u4f5c\uff0c\u6240\u4ee5&nbsp;<code>dp[i][j]<\/code>&nbsp;\u4fdd\u6301\u4e3a&nbsp;<code>dp[i-1][j-1]<\/code>&nbsp;\u7684\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">(2) <strong>\u5982\u679c <code>dna1[i-1] != dna2[j-1]<\/code><\/strong>\uff1a<ul><li>\u8fd9\u610f\u5473\u7740\u5f53\u524d\u5b57\u7b26\u4e0d\u540c\uff0c\u6211\u4eec\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u64cd\u4f5c\uff08\u5220\u9664\u3001\u63d2\u5165\u6216\u66ff\u6362\uff09\u6765\u4f7f\u4e24\u4e2a\u5b57\u7b26\u4e32\u5339\u914d\u3002\u7136\u540e\u6211\u4eec\u9009\u62e9\u8fd9\u4e09\u79cd\u64cd\u4f5c\u4e2d\u7684\u6700\u5c0f\u64cd\u4f5c\u6b21\u6570\u3002<\/li><\/ul>\u5bf9\u4e8e <code>dp[i][j]<\/code> \u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u6709\u4e09\u79cd\u9009\u62e9\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5220\u9664<\/strong>\uff08<code>dna1[i-1]<\/code>\uff09\uff1a\u5982\u679c\u6211\u4eec\u9009\u62e9\u5220\u9664&nbsp;<code>dna1[i-1]<\/code>\uff0c\u5219&nbsp;<code>dp[i][j] = dp[i-1][j] + 1<\/code>\uff0c\u8868\u793a<strong>\u6211\u4eec\u5c06&nbsp;<code>dna1<\/code>&nbsp;\u7684\u524d&nbsp;<code>i-1<\/code>&nbsp;\u4e2a\u5b57\u7b26\u8f6c\u6362\u4e3a&nbsp;<code>dna2<\/code>&nbsp;\u7684\u524d&nbsp;<code>j<\/code>&nbsp;\u4e2a\u5b57\u7b26\u540e\uff0c\u518d\u8fdb\u884c\u4e00\u6b21\u5220\u9664\u64cd\u4f5c\uff08\u5373\u5220\u9664&nbsp;<code>dna1[i-1]<\/code>\uff09<\/strong><\/li>\n\n\n\n<li><strong>\u63d2\u5165<\/strong>\uff08<code>dna2[j-1]<\/code>\uff09\uff1a\u5982\u679c\u6211\u4eec\u9009\u62e9\u5728&nbsp;<code>dna1[i-1]<\/code>&nbsp;\u540e\u63d2\u5165&nbsp;<code>dna2[j-1]<\/code>\uff0c\u5219&nbsp;<code>dp[i][j] = dp[i][j-1] + 1<\/code>\uff0c\u8868\u793a<strong>\u6211\u4eec\u5c06&nbsp;<code>dna1<\/code>&nbsp;\u7684\u524d&nbsp;<code>i<\/code>&nbsp;\u4e2a\u5b57\u7b26\u8f6c\u6362\u4e3a&nbsp;<code>dna2<\/code>&nbsp;\u7684\u524d&nbsp;<code>j-1<\/code>&nbsp;\u4e2a\u5b57\u7b26\u540e\uff0c\u518d\u8fdb\u884c\u4e00\u6b21\u63d2\u5165\u64cd\u4f5c\uff08\u5373\u63d2\u5165&nbsp;<code>dna2[j-1]<\/code>\uff09<\/strong><\/li>\n\n\n\n<li><strong>\u66ff\u6362<\/strong>\uff08<code>dna1[i-1]<\/code>&nbsp;\u548c&nbsp;<code>dna2[j-1]<\/code>\uff09\uff1a\u5982\u679c\u6211\u4eec\u9009\u62e9\u5c06&nbsp;<code>dna1[i-1]<\/code>&nbsp;\u66ff\u6362\u6210&nbsp;<code>dna2[j-1]<\/code>\uff0c\u5219&nbsp;<code>dp[i][j] = dp[i-1][j-1] + 1<\/code>\uff0c\u8868\u793a<strong>\u6211\u4eec\u5c06&nbsp;<code>dna1<\/code>&nbsp;\u7684\u524d&nbsp;<code>i-1<\/code>&nbsp;\u4e2a\u5b57\u7b26\u8f6c\u6362\u4e3a&nbsp;<code>dna2<\/code>&nbsp;\u7684\u524d&nbsp;<code>j-1<\/code>&nbsp;\u4e2a\u5b57\u7b26\u540e\uff0c\u518d\u8fdb\u884c\u4e00\u6b21\u66ff\u6362\u64cd\u4f5c\uff08\u5373\u5c06&nbsp;<code>dna1[i-1]<\/code>&nbsp;\u66ff\u6362\u4e3a&nbsp;<code>dna2[j-1]<\/code>\uff09<\/strong><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u603b\u7ed3\u9012\u63a8\u516c\u5f0f\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c&nbsp;<code>dna1[i-1] == dna2[j-1]<\/code>\uff0c\u5219&nbsp;<code>dp[i][j] = dp[i-1][j-1]<\/code>\u3002<\/li>\n\n\n\n<li>\u5982\u679c&nbsp;<code>dna1[i-1] != dna2[j-1]<\/code>\uff0c\u5219&nbsp;<code>dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1])<\/code>\uff0c\u5176\u4e2d\uff1a\n<ul class=\"wp-block-list\">\n<li><code>dp[i-1][j]<\/code>&nbsp;\u8868\u793a\u5220\u9664\u64cd\u4f5c\u7684\u7ed3\u679c\uff0c<\/li>\n\n\n\n<li><code>dp[i][j-1]<\/code>&nbsp;\u8868\u793a\u63d2\u5165\u64cd\u4f5c\u7684\u7ed3\u679c\uff0c<\/li>\n\n\n\n<li><code>dp[i-1][j-1]<\/code>&nbsp;\u8868\u793a\u66ff\u6362\u64cd\u4f5c\u7684\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">4.<strong>\u6700\u7ec8\u7ed3\u679c<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6700\u540e\uff0c<code>dp[m][n]<\/code>&nbsp;\u5c31\u662f\u5c06&nbsp;<code>dna1<\/code>&nbsp;\u8f6c\u6362\u4e3a&nbsp;<code>dna2<\/code>&nbsp;\u6240\u9700\u7684\u6700\u5c0f\u64cd\u4f5c\u6b21\u6570\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u4ee5\u5b57\u7b26\u4e32&#8221;kitten&#8221;(dna1)\u548c\u5b57\u7b26\u4e32&#8221;sitting&#8221;(dna2)\u4e3a\u4f8b \u5bf9\u8fd9\u4e2a\u72b6\u6001\u65b9\u7a0b\u8fdb\u884c\u8bf4\u660e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u8be6\u7ec6\u5730\u753b\u51fa\u4e86dp\u72b6\u6001\u8868 \u5e76\u4e3e\u4f8b\u5206\u6790\u4e86\u6bcf\u79cd\u64cd\u4f5c\u7684\u610f\u4e49( \u5e94\u8be5\u8db3\u591f\u8be6\u7ec6\u4e86\u5427 )<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/womeifei.cn\/wp-content\/uploads\/2024\/12\/image-8-1024x698.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"698\" data-original=\"https:\/\/womeifei.cn\/wp-content\/uploads\/2024\/12\/image-8-1024x698.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-819\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f88\u660e\u663e \u6700\u5c11\u64cd\u4f5c\u6b21\u6570\u5c31\u662f3\u5566~<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u662f\u4e00\u4e2a\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u7684\u5e94\u7528 \u539f\u5b9e\u73b0\u51fd\u6570\u7684\u4ee3\u7801\u8d34\u5728\u4e0b\u9762<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">int solution(std::string dna1, std::string dna2) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; int m = dna1.size();<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; int n = dna2.size();<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; \/\/ \u521b\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4 dp\uff0c\u5927\u5c0f\u4e3a (m+1) x (n+1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; std::vector&lt;std::vector&lt;int&gt;&gt; dp(m + 1, std::vector&lt;int&gt;(n + 1, 0));<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; \/\/ \u521d\u59cb\u5316 dp \u6570\u7ec4\u7684\u7b2c\u4e00\u884c\u548c\u7b2c\u4e00\u5217<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; for (int i = 0; i &lt;= m; ++i) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; dp[i][0] = i; &nbsp;\/\/ \u5c06 dna1 \u7684\u524d i \u4e2a\u5b57\u7b26\u8f6c\u6362\u6210\u7a7a\u5b57\u7b26\u4e32\uff0c\u9700\u8981 i \u6b21\u5220\u9664\u64cd\u4f5c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; }<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; for (int j = 0; j &lt;= n; ++j) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; dp[0][j] = j; &nbsp;\/\/ \u5c06\u7a7a\u5b57\u7b26\u4e32\u8f6c\u6362\u6210 dna2 \u7684\u524d j \u4e2a\u5b57\u7b26\uff0c\u9700\u8981 j \u6b21\u63d2\u5165\u64cd\u4f5c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; }<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; \/\/ \u586b\u5145 dp \u6570\u7ec4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; for (int i = 1; i &lt;= m; ++i) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; for (int j = 1; j &lt;= n; ++j) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; if (dna1[i &#8211; 1] == dna2[j &#8211; 1]) {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; dp[i][j] = dp[i &#8211; 1][j &#8211; 1]; &nbsp;\/\/ \u4e0d\u9700\u8981\u4efb\u4f55\u7f16\u8f91\u64cd\u4f5c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; } else {<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; dp[i][j] = 1 + std::min({dp[i &#8211; 1][j], &nbsp; &nbsp;\/\/ \u5220\u9664<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;dp[i][j &#8211; 1], &nbsp; &nbsp;\/\/ \u63d2\u5165<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;dp[i &#8211; 1][j &#8211; 1] \/\/ \u66ff\u6362<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; });<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; }<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; }<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; }<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; \/\/ \u8fd4\u56de\u6700\u7ec8\u7ed3\u679c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; &nbsp; return dp[m][n];<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u4e2a\u7b97\u6cd5\u4e00\u770b\u5c31\u662f\u6bd4\u8f83\u590d\u6742\u7684 \u8981\u662f\u76f4\u63a5\u53bb\u5bf9\u5b57\u7b26\u4e32\u8fdb\u884c\u64cd\u4f5c \u4e00\u5b9a\u5341\u5206\u9ebb\u70e6 \u6211\u4eec\u81ea\u7136\u5c31\u60f3\u5230\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u7684\u601d\u8def \u53bb\u628a\u5927 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,4,7],"tags":[],"class_list":["post-817","post","type-post","status-publish","format-standard","hentry","category-18","category-4","category-7"],"_links":{"self":[{"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/posts\/817","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/comments?post=817"}],"version-history":[{"count":2,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/posts\/817\/revisions"}],"predecessor-version":[{"id":824,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/posts\/817\/revisions\/824"}],"wp:attachment":[{"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=817"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=817"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/womeifei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=817"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}