{"id":151,"date":"2025-08-25T11:20:05","date_gmt":"2025-08-25T03:20:05","guid":{"rendered":"https:\/\/heyingnian.com\/?p=151"},"modified":"2025-08-26T15:45:22","modified_gmt":"2025-08-26T07:45:22","slug":"leetcode-560","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/08\/25\/leetcode-560\/","title":{"rendered":"\u548c\u4e3a K \u7684\u5b50\u6570\u7ec4"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u548c\u4e3a K \u7684\u5b50\u6570\u7ec4<\/h1>\n\n\n\n<p>\u9898\u76ee\u6765\u6e90\uff1a<a target=\"_blank\" rel=\"noreferrer noopener\"><\/a><a href=\"https:\/\/leetcode.cn\/problems\/subarray-sum-equals-k\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">560. \u548c\u4e3a K \u7684\u5b50\u6570\u7ec4 &#8211; \u529b\u6263\uff08LeetCode\uff09<\/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> \u548c\u4e00\u4e2a\u6574\u6570 <code>k<\/code>\uff0c\u8bf7\u4f60\u7edf\u8ba1\u5e76\u8fd4\u56de\u8be5\u6570\u7ec4\u4e2d<strong>\u548c\u4e3a <code>k<\/code> \u7684\u5b50\u6570\u7ec4\u7684\u4e2a\u6570<\/strong>\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5b50\u6570\u7ec4<\/strong>&nbsp;\u662f\u6570\u7ec4\u4e2d\u5143\u7d20\u7684\u8fde\u7eed\u975e\u7a7a\u5e8f\u5217\u3002<\/li>\n\n\n\n<li>\u5b50\u6570\u7ec4\u7684\u548c\u7b49\u4e8e&nbsp;<code>k<\/code>&nbsp;\u5373\u4e3a\u6ee1\u8db3\u6761\u4ef6\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 = [1,1,1]<\/code>,&nbsp;<code>k = 2<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>2<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u548c\u4e3a&nbsp;<code>2<\/code>&nbsp;\u7684\u5b50\u6570\u7ec4\u6709\u4e24\u4e2a\uff1a\n<ul class=\"wp-block-list\">\n<li><code>[1,1]<\/code>\uff08\u7d22\u5f15 0 \u5230 1\uff09<\/li>\n\n\n\n<li><code>[1,1]<\/code>\uff08\u7d22\u5f15 1 \u5230 2\uff09<\/li>\n<\/ul>\n<\/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 = [1,2,3]<\/code>,&nbsp;<code>k = 3<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>2<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u548c\u4e3a&nbsp;<code>3<\/code>&nbsp;\u7684\u5b50\u6570\u7ec4\u6709\uff1a\n<ul class=\"wp-block-list\">\n<li><code>[1,2]<\/code>\uff08\u7d22\u5f15 0 \u5230 1\uff09<\/li>\n\n\n\n<li><code>[3]<\/code>\uff08\u7d22\u5f15 2 \u5230 2\uff09<\/li>\n<\/ul>\n<\/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 = [1,-1,0]<\/code>,&nbsp;<code>k = 0<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>3<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u548c\u4e3a&nbsp;<code>0<\/code>&nbsp;\u7684\u5b50\u6570\u7ec4\u6709&nbsp;<code>[1,-1]<\/code>\u3001<code>[0]<\/code>\u3001<code>[1,-1,0]<\/code>\uff0c\u5171 3 \u4e2a\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;= 2 \u00d7 10\u2074<\/code><\/li>\n\n\n\n<li><code>-1000 &lt;= nums[i] &lt;= 1000<\/code><\/li>\n\n\n\n<li><code>-10\u2077 &lt;= k &lt;= 10\u2077<\/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\u524d\u7f00\u548c + \u54c8\u5e0c\u8868\uff08\u4f18\u5316\u66b4\u529b\uff09\u2014\u2014 O(n) \u65f6\u95f4<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>class<\/strong> <strong>Solution<\/strong> {\n    <strong>public<\/strong> <strong>int<\/strong> <strong>subarraySum<\/strong>(<strong>int<\/strong>&#91;] nums, <strong>int<\/strong> k) {\n        <strong>int<\/strong> sum = 0, ans = 0;\n        Map&lt;, Integer> map = <strong>new<\/strong> HashMap&lt;>();\n        map.put(0, 1);\n        <strong>for<\/strong> (<strong>int<\/strong> i = 0; i &lt; nums.length; i++) {\n            sum += nums&#91;i];\n            <strong>if<\/strong> (map.containsKey(sum - k)) {\n                ans += map.get(sum - k);\n            }\n            map.put(sum, map.getOrDefault(sum, 0) + 1);\n        }\n        <strong>return<\/strong> ans;\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\u54c8\u5e0c\u8868\u7684\u63d2\u5165\u4e0e\u67e5\u8be2\u64cd\u4f5c\u5e73\u5747\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(n)<\/strong><br>\u54c8\u5e0c\u8868\u6700\u591a\u5b58\u50a8 <code>n+1<\/code> \u4e2a\u4e0d\u540c\u7684\u524d\u7f00\u548c\uff0c\u56e0\u6b64\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a O(n)\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>\u524d\u7f00\u548c\u5b9a\u4e49<\/strong>\uff1a<br>\u8bbe <code>prefix[i] = nums[0] + nums[1] + ... + nums[i]<\/code>\u3002<br>\u90a3\u4e48\u5b50\u6570\u7ec4 <code>nums[i..j]<\/code> \u7684\u548c\u4e3a\uff1a<br><code>prefix[j] - prefix[i-1]<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u76ee\u6807\u8f6c\u6362<\/strong>\uff1a<br>\u8981\u6c42 <code>sum(i, j) = k<\/code>\uff0c\u5373\uff1a<br><code>prefix[j] - prefix[i-1] = k<\/code><br>\u21d2 <code>prefix[i-1] = prefix[j] - k<\/code>&nbsp;\u56e0\u6b64\uff0c\u5bf9\u4e8e\u5f53\u524d\u524d\u7f00\u548c <code>prefix[j]<\/code>\uff0c\u53ea\u9700\u67e5\u627e\u4e4b\u524d\u6709\u591a\u5c11\u4e2a\u524d\u7f00\u548c\u7b49\u4e8e <code>prefix[j] - k<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u54c8\u5e0c\u8868\u4f18\u5316<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f7f\u7528&nbsp;<code>Map&lt;Integer, Integer&gt;<\/code>&nbsp;\u8bb0\u5f55\u6bcf\u4e2a\u524d\u7f00\u548c\u51fa\u73b0\u7684\u6b21\u6570\u3002<\/li>\n\n\n\n<li>\u904d\u5386\u8fc7\u7a0b\u4e2d\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u5f53\u524d\u524d\u7f00\u548c&nbsp;<code>sum<\/code><\/li>\n\n\n\n<li>\u67e5\u8be2&nbsp;<code>sum - k<\/code>&nbsp;\u662f\u5426\u5b58\u5728\uff0c\u82e5\u5b58\u5728\u5219\u7d2f\u52a0\u5176\u51fa\u73b0\u6b21\u6570<\/li>\n\n\n\n<li>\u5c06\u5f53\u524d&nbsp;<code>sum<\/code>&nbsp;\u52a0\u5165\u54c8\u5e0c\u8868<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u521d\u59cb\u5316\u6280\u5de7<\/strong>\uff1a<br><code>map.put(0, 1)<\/code> \u8868\u793a\u524d\u7f00\u548c\u4e3a <code>0<\/code> \u7684\u60c5\u51b5\u51fa\u73b0\u4e86\u4e00\u6b21\uff08\u7a7a\u533a\u95f4\uff09\uff0c\u7528\u4e8e\u5904\u7406\u4ece\u7d22\u5f15 <code>0<\/code> \u5f00\u59cb\u7684\u5b50\u6570\u7ec4\u3002<\/li>\n\n\n\n<li><strong>\u4e3e\u4f8b\u8bf4\u660e<\/strong>\uff1a<br>\u5bf9\u4e8e <code>nums = [1,1,1], k = 2<\/code>\uff1a\n<ul class=\"wp-block-list\">\n<li>i=0: sum=1, \u67e5\u627e&nbsp;<code>1-2=-1<\/code>&nbsp;\u2192 \u65e0\uff0cmap={0:1, 1:1}<\/li>\n\n\n\n<li>i=1: sum=2, \u67e5\u627e&nbsp;<code>2-2=0<\/code>&nbsp;\u2192 \u5b58\u5728\uff0cans += 1\uff0cmap={0:1,1:1,2:1}<\/li>\n\n\n\n<li>i=2: sum=3, \u67e5\u627e&nbsp;<code>3-2=1<\/code>&nbsp;\u2192 \u5b58\u5728\uff0cans += 1\uff0c\u6700\u7ec8 ans=2<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u548c\u4e3a K \u7684\u5b50\u6570\u7ec4 \u9898\u76ee\u6765\u6e90\uff1a560. \u548c\u4e3a K \u7684\u5b50\u6570\u7ec4 &#8211; \u529b\u6263\uff08LeetCode\uff09 \ud83d\udccc  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,12],"tags":[26,15,14],"class_list":["post-151","post","type-post","status-publish","format-standard","hentry","category-substrings","category-algorithm","tag-prefix_sum","tag-hash","tag-algorithm"],"_links":{"self":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/151","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=151"}],"version-history":[{"count":2,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/151\/revisions"}],"predecessor-version":[{"id":179,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/151\/revisions\/179"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}