{"id":281,"date":"2025-08-27T16:44:47","date_gmt":"2025-08-27T08:44:47","guid":{"rendered":"https:\/\/heyingnian.com\/?p=281"},"modified":"2025-08-27T16:57:24","modified_gmt":"2025-08-27T08:57:24","slug":"leetcode-53","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/08\/27\/leetcode-53\/","title":{"rendered":"\u6700\u5927\u5b50\u6570\u7ec4\u548c"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u6700\u5927\u5b50\u6570\u7ec4\u548c<\/h1>\n\n\n\n<p>\u9898\u76ee\u6765\u6e90\uff1a<a target=\"_blank\" rel=\"noreferrer noopener\"><a href=\"https:\/\/leetcode.cn\/problems\/maximum-subarray\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">53. \u6700\u5927\u5b50\u6570\u7ec4\u548c &#8211; \u529b\u6263\uff08LeetCode\uff09<\/a><\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udccc \u9898\u76ee\u63cf\u8ff0<\/p>\n\n\n\n<p>\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 <code>nums<\/code>\uff0c\u8bf7\u4f60\u627e\u51fa\u4e00\u4e2a\u5177\u6709<strong>\u6700\u5927\u548c<\/strong>\u7684<strong>\u8fde\u7eed\u5b50\u6570\u7ec4<\/strong>\uff08\u5b50\u6570\u7ec4\u6700\u5c11\u5305\u542b\u4e00\u4e2a\u5143\u7d20\uff09\uff0c\u8fd4\u56de\u5176\u6700\u5927\u548c\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5b50\u6570\u7ec4<\/strong>\u00a0\u662f\u6570\u7ec4\u4e2d\u7684\u4e00\u4e2a<strong>\u8fde\u7eed\u90e8\u5206<\/strong>\u3002<\/li>\n\n\n\n<li>\u8981\u6c42\u7684\u662f\u6240\u6709\u8fde\u7eed\u5b50\u6570\u7ec4\u4e2d\uff0c\u5143\u7d20\u548c\u6700\u5927\u7684\u90a3\u4e2a\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u2705 \u793a\u4f8b\u89e3\u6790<\/p>\n\n\n\n<p>\u793a\u4f8b 1\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>nums = [-2,1,-3,4,-1,2,1,-5,4]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>6<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u548c\u6700\u5927\u7684\u8fde\u7eed\u5b50\u6570\u7ec4\u662f\u00a0<code>[4,-1,2,1]<\/code>\uff0c\u5176\u548c\u4e3a\u00a0<code>4 + (-1) + 2 + 1 = 6<\/code>\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u793a\u4f8b 2\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>nums = [1]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>1<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\uff0c\u6700\u5927\u548c\u5c31\u662f\u5b83\u672c\u8eab\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u793a\u4f8b 3\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>nums = [5,4,-1,7,8]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>23<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u6574\u4e2a\u6570\u7ec4\u7684\u548c\u5c31\u662f\u6700\u5927\u503c\uff1a<code>5+4+(-1)+7+8 = 23<\/code>\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u793a\u4f8b 4\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>nums = [-1]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>-1<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u5373\u4f7f\u4e3a\u8d1f\u6570\uff0c\u4e5f\u5fc5\u987b\u9009\u62e9\u81f3\u5c11\u4e00\u4e2a\u5143\u7d20\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u26a0\ufe0f \u63d0\u793a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>1 &lt;= nums.length &lt;= 10\u2075<\/code><\/li>\n\n\n\n<li><code>-10\u2074 &lt;= nums[i] &lt;= 10\u2074<\/code><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udca1 \u89e3\u6cd5\uff1a\u52a8\u6001\u89c4\u5212\uff08Kadane \u7b97\u6cd5\uff09\u2014\u2014 O(n) \u65f6\u95f4\uff0cO(1) \u7a7a\u95f4<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>public class Solution {\n    public int maxSubArray(int&#91;] nums) {\n        int sum = nums&#91;0];\n        int pre = 0;\n        for (int p : nums) {\n            pre = Math.max(pre + p, p);\n            sum = Math.max(pre, sum);\n        }\n        return sum;\n    }\n}<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udcca \u590d\u6742\u5ea6\u5206\u6790<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/strong><br>\u4ec5\u9700\u4e00\u6b21\u904d\u5386\u6570\u7ec4\uff0c\u6bcf\u4e2a\u5143\u7d20\u5904\u7406\u65f6\u95f4\u4e3a O(1)\uff0c\u6574\u4f53\u4e3a\u7ebf\u6027\u65f6\u95f4\u3002<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(1)<\/strong><br>\u53ea\u4f7f\u7528\u4e86\u4e24\u4e2a\u53d8\u91cf <code>pre<\/code> \u548c <code>sum<\/code>\uff0c\u989d\u5916\u7a7a\u95f4\u4e3a\u5e38\u6570\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83e\udde9 \u89e3\u9898\u601d\u8def<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6838\u5fc3\u601d\u60f3\uff1a\u52a8\u6001\u89c4\u5212\uff08Kadane \u7b97\u6cd5\uff09<\/strong><br>\u5b9a\u4e49 <code>pre<\/code> \u8868\u793a<strong>\u4ee5\u5f53\u524d\u5143\u7d20\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/strong>\u3002<br>\u5bf9\u4e8e\u6bcf\u4e2a\u5143\u7d20 <code>p<\/code>\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u9009\u62e9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5c06\u00a0<code>p<\/code>\u00a0\u52a0\u5165\u524d\u9762\u7684\u5b50\u6570\u7ec4\uff08\u548c\u4e3a\u00a0<code>pre + p<\/code>\uff09<\/li>\n\n\n\n<li>\u4ece\u00a0<code>p<\/code>\u00a0\u91cd\u65b0\u5f00\u59cb\u4e00\u4e2a\u65b0\u7684\u5b50\u6570\u7ec4\uff08\u548c\u4e3a\u00a0<code>p<\/code>\uff09<br>\u6211\u4eec\u9009\u62e9\u4e24\u8005\u4e2d\u66f4\u5927\u7684\u4e00\u4e2a\uff1a<code>pre = max(pre + p, p)<\/code><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u72b6\u6001\u8f6c\u79fb<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u521d\u59cb\u5316\u00a0<code>pre = 0<\/code>\uff08\u8868\u793a\u524d\u9762\u65e0\u5143\u7d20\uff09<\/li>\n\n\n\n<li>\u904d\u5386\u6bcf\u4e2a\u5143\u7d20\u00a0<code>p<\/code>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u66f4\u65b0\u00a0<code>pre = max(pre + p, p)<\/code><\/li>\n\n\n\n<li>\u66f4\u65b0\u5168\u5c40\u6700\u5927\u503c\u00a0<code>sum = max(sum, pre)<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u4e3a\u4ec0\u4e48\u8fd9\u6837\u662f\u6b63\u786e\u7684\uff1f<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u6211\u4eec\u5173\u5fc3\u7684\u662f\u201c\u4ee5\u5f53\u524d\u4f4d\u7f6e\u7ed3\u5c3e\u201d\u7684\u6700\u5927\u548c\uff0c\u56e0\u4e3a\u4e0b\u4e00\u4e2a\u5143\u7d20\u53ea\u80fd\u63a5\u5728\u8fd9\u4e2a\u7ed3\u5c3e\u540e\u9762\u3002<\/li>\n\n\n\n<li>\u5982\u679c\u524d\u9762\u7684\u548c\u00a0<code>pre<\/code>\u00a0\u4e3a\u8d1f\uff0c\u90a3\u4e48\u52a0\u4e0a\u5b83\u53ea\u4f1a\u8ba9\u5f53\u524d\u548c\u66f4\u5c0f\uff0c\u4e0d\u5982\u4ece\u5f53\u524d\u5143\u7d20\u91cd\u65b0\u5f00\u59cb\u3002<\/li>\n\n\n\n<li>\u56e0\u6b64\uff0c<code>max(pre + p, p)<\/code>\u00a0\u5b9e\u9645\u4e0a\u662f\u201c\u8d2a\u5fc3\u201d\u5730\u51b3\u5b9a\u662f\u5426\u7ee7\u627f\u524d\u9762\u7684\u5b50\u6570\u7ec4\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u4e3e\u4f8b\u8bf4\u660e<\/strong>\uff1a<br>\u5bf9\u4e8e <code>nums = [-2,1,-3,4]<\/code>\uff1a\n<ul class=\"wp-block-list\">\n<li>p = -2: pre = max(0 + (-2), -2) = -2, sum = max(-2, -2) = -2<\/li>\n\n\n\n<li>p = 1: pre = max(-2 + 1, 1) = 1, sum = max(1, -2) = 1<\/li>\n\n\n\n<li>p = -3: pre = max(1 + (-3), -3) = -2, sum = max(-2, 1) = 1<\/li>\n\n\n\n<li>p = 4: pre = max(-2 + 4, 4) = 4, sum = max(4, 1) = 4<br>\u6700\u7ec8\u8fd4\u56de\u00a0<code>4<\/code>\uff0c\u5bf9\u5e94\u5b50\u6570\u7ec4\u00a0<code>[4]<\/code>\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8fb9\u754c\u5904\u7406<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u521d\u59cb\u5316\u00a0<code>sum = nums[0]<\/code>\u00a0\u662f\u4e3a\u4e86\u5904\u7406\u5168\u4e3a\u8d1f\u6570\u7684\u60c5\u51b5\u3002<\/li>\n\n\n\n<li><code>pre<\/code>\u00a0\u521d\u59cb\u4e3a\u00a0<code>0<\/code>\uff0c\u8868\u793a\u5f00\u59cb\u524d\u65e0\u7d2f\u52a0\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u6700\u5927\u5b50\u6570\u7ec4\u548c \u9898\u76ee\u6765\u6e90\uff1a53. \u6700\u5927\u5b50\u6570\u7ec4\u548c &#8211; \u529b\u6263\uff08LeetCode\uff09 \ud83d\udccc \u9898\u76ee\u63cf\u8ff0 \u7ed9\u4f60 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30,12],"tags":[32,31,14],"class_list":["post-281","post","type-post","status-publish","format-standard","hentry","category-ordinary_arrays","category-algorithm","tag-dp","tag-array","tag-algorithm"],"_links":{"self":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/comments?post=281"}],"version-history":[{"count":5,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions"}],"predecessor-version":[{"id":291,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions\/291"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}