{"id":89515,"date":"2026-08-03T07:32:36","date_gmt":"2026-08-02T23:32:36","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/89515.html"},"modified":"2026-08-03T07:32:36","modified_gmt":"2026-08-02T23:32:36","slug":"kimi-leetcode-3797-%e7%bb%9f%e8%ae%a1%e5%9c%a8%e7%9f%a9%e5%bd%a2%e6%a0%bc%e5%ad%90%e9%87%8c%e7%a7%bb%e5%8a%a8%e7%9a%84%e8%b7%af%e5%be%84%e6%95%b0%e7%9b%ae-java%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/89515.html","title":{"rendered":"Kimi    LeetCode 3797. \u7edf\u8ba1\u5728\u77e9\u5f62\u683c\u5b50\u91cc\u79fb\u52a8\u7684\u8def\u5f84\u6570\u76ee Java\u5b9e\u73b0"},"content":{"rendered":"<p>LeetCode 3797. \u7edf\u8ba1\u5728\u77e9\u5f62\u683c\u5b50\u91cc\u79fb\u52a8\u7684\u8def\u5f84\u6570\u76ee<\/p>\n<p>\u601d\u8def<\/p>\n<p>\u8fd9\u9898\u662f\u524d\u7f00\u548c\u4f18\u5316\u7684\u52a8\u6001\u89c4\u5212\u3002<\/p>\n<p>\u72b6\u6001\u5b9a\u4e49&#xff08;\u4ece\u4e0b\u5f80\u4e0a\u9012\u63a8&#xff09;&#xff1a;<\/p>\n<p>&#8211; &#096;f[i][j]&#096;&#xff1a;\u4ece\u6700\u540e\u4e00\u884c\u51fa\u53d1\u5230\u8fbe &#096;(i,j)&#096;&#xff0c;\u4e14\u6700\u540e\u4e00\u6b65\u662f\u4ece\u4e0b\u4e00\u884c\u4e0a\u6765\u7684\u8def\u5f84\u6570<br \/>\n&#8211; &#096;g[i][j]&#096;&#xff1a;\u4ece\u6700\u540e\u4e00\u884c\u51fa\u53d1\u5230\u8fbe &#096;(i,j)&#096;&#xff0c;\u4e14\u6700\u540e\u4e00\u6b65\u662f\u540c\u4e00\u884c\u6a2a\u5411\u79fb\u52a8\u6765\u7684\u8def\u5f84\u6570<\/p>\n<p>\u8f6c\u79fb&#xff1a;<\/p>\n<p>1. \u4ece\u4e0b\u4e00\u884c\u4e0a\u6765&#xff1a;\u4ece &#096;(i&#043;1, j&#039;)&#096; \u5230 &#096;(i, j)&#096;&#xff0c;\u7eb5\u5411\u8ddd\u79bb\u4e3a 1&#xff0c;\u6a2a\u5411\u8ddd\u79bb\u9700\u6ee1\u8db3<\/p>\n<p>\u00a0 \u00a0&#096;1 &#043; (j-j&#039;)\u00b2 \u2264 d\u00b2&#096; \u2192 &#096;|j-j&#039;| \u2264 \u230a\u221a(d\u00b2-1)\u230b&#096;\u3002\u8bb0 &#096;k &#061; \u230a\u221a(d\u00b2-1)\u230b&#096;\u3002<\/p>\n<p>\u00a0 \u00a0&#096;f[i][j] &#061; \u03a3(f[i&#043;1][j&#039;] &#043; g[i&#043;1][j&#039;])&#096;&#xff0c;\u5176\u4e2d &#096;j&#039; \u2208 [j-k, j&#043;k]&#096;<\/p>\n<p>2. \u540c\u4e00\u884c\u6a2a\u5411\u79fb\u52a8&#xff1a;\u4ece &#096;(i, j&#039;)&#096; \u5230 &#096;(i, j)&#096;&#xff0c;\u9700\u6ee1\u8db3 &#096;|j-j&#039;| \u2264 d&#096;&#xff0c;\u4e14\u4e0a\u4e00\u6b65\u5fc5\u987b\u662f\u4ece\u4e0b\u4e00\u884c\u4e0a\u6765\u7684&#xff08;\u4e0d\u80fd\u8fde\u7eed\u4e24\u6b21\u6a2a\u5411&#xff09;\u3002<\/p>\n<p>\u00a0 \u00a0&#096;g[i][j] &#061; \u03a3(f[i][j&#039;])&#096;&#xff0c;\u5176\u4e2d &#096;j&#039; \u2208 [j-d, j&#043;d]&#096; \u4e14 &#096;j&#039; \u2260 j&#096;<\/p>\n<p>3. \u521d\u59cb\u5316&#xff1a;\u6700\u540e\u4e00\u884c\u6bcf\u4e2a\u53ef\u7528\u683c\u5b50\u4f5c\u4e3a\u8d77\u70b9&#xff0c;&#096;f[n-1][j] &#061; 1&#096;<\/p>\n<p>\u4e24\u4e2a\u8f6c\u79fb\u90fd\u662f\u533a\u95f4\u6c42\u548c&#xff0c;\u7528\u524d\u7f00\u548c\u4f18\u5316\u5230 &#096;O(1)&#096;&#xff0c;\u603b\u590d\u6742\u5ea6 &#096;O(n\u00b7m)&#096;\u3002<\/p>\n<p>&#8212;<\/p>\n<p>\u5b8c\u6574 Java \u4ee3\u7801<\/p>\n<p>&#096;&#096;&#096;java<br \/>\nclass Solution {<br \/>\n\u00a0 \u00a0 static final int MOD &#061; 1_000_000_007;<\/p>\n<p>\u00a0 \u00a0 public int numberOfRoutes(String[] grid, int d) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 int n &#061; grid.length;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 int m &#061; grid[0].length();<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u5411\u4e0a\u79fb\u52a8\u65f6&#xff0c;\u6a2a\u5411\u6700\u5927\u504f\u79fb&#xff1a;sqrt(d^2 &#8211; 1)<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 int k &#061; (int) Math.sqrt((long) d * d &#8211; 1);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/ prefix[i][j][0\/1]&#xff1a;\u7b2c i \u884c\u524d j \u4e2a\u4f4d\u7f6e&#xff08;0~j-1&#xff09;\u7684 f\/g \u524d\u7f00\u548c<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u540c\u65f6 prefix[i][j&#043;1][*] &#061; prefix[i][j][*] &#043; dpValue&#xff0c;\u4e00\u7269\u4e24\u7528<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 int[][][] prefix &#061; new int[n][m &#043; 1][2];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for (int i &#061; n &#8211; 1; i &gt;&#061; 0; i&#8211;) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ 1. \u8ba1\u7b97 f[i][j]&#xff1a;\u4ece\u4e0b\u4e00\u884c\u4e0a\u6765<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 for (int j &#061; 0; j &lt; m; j&#043;&#043;) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if (grid[i].charAt(j) &#061;&#061; &#039;.&#039;) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if (i &#061;&#061; n &#8211; 1) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u6700\u540e\u4e00\u884c\u4f5c\u4e3a\u8d77\u70b9<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 prefix[i][j &#043; 1][0] &#061; (prefix[i][j][0] &#043; 1) % MOD;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 } else {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int l &#061; Math.max(j &#8211; k, 0);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int r &#061; Math.min(j &#043; k, m &#8211; 1);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int curr &#061; (rangeSum(prefix, i &#043; 1, l, r, 0)<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#043; rangeSum(prefix, i &#043; 1, l, r, 1)) % MOD;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 prefix[i][j &#043; 1][0] &#061; (prefix[i][j][0] &#043; curr) % MOD;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 } else {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u963b\u585e\u683c\u5b50&#xff0c;\u524d\u7f00\u548c\u4e0d\u53d8<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 prefix[i][j &#043; 1][0] &#061; prefix[i][j][0];<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ 2. \u8ba1\u7b97 g[i][j]&#xff1a;\u540c\u4e00\u884c\u6a2a\u5411\u79fb\u52a8&#xff0c;\u53ea\u80fd\u4ece\u4e0a\u4e00\u6b65\u662f&#034;\u4ece\u4e0b\u4e00\u884c\u4e0a\u6765&#034;\u7684\u72b6\u6001\u8f6c\u79fb<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 for (int j &#061; 0; j &lt; m; j&#043;&#043;) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if (grid[i].charAt(j) &#061;&#061; &#039;.&#039;) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int l &#061; Math.max(j &#8211; d, 0);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int r &#061; Math.min(j &#043; d, m &#8211; 1);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u6392\u9664 j \u672c\u8eab&#xff08;j&#039; !&#061; j&#xff09;&#xff0c;\u62c6\u6210 [l, j-1] \u548c [j&#043;1, r] \u4e24\u6bb5<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int left \u00a0&#061; rangeSum(prefix, i, l, j &#8211; 1, 0);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int right &#061; rangeSum(prefix, i, j &#043; 1, r, 0);<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 int curr &#061; (left &#043; right) % MOD;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 prefix[i][j &#043; 1][1] &#061; (prefix[i][j][1] &#043; curr) % MOD;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 } else {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 prefix[i][j &#043; 1][1] &#061; prefix[i][j][1];<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u7b2c 0 \u884c\u6240\u6709\u53ef\u7528\u683c\u5b50\u7684 f &#043; g \u4e4b\u548c<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 return (prefix[0][m][0] &#043; prefix[0][m][1]) % MOD;<br \/>\n\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \/\/ \u7528\u524d\u7f00\u548c\u6570\u7ec4\u6c42\u7b2c row \u884c [l, r] \u533a\u95f4\u5185\u67d0\u72b6\u6001\u7684\u548c<br \/>\n\u00a0 \u00a0 private int rangeSum(int[][][] prefix, int row, int l, int r, int state) {<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 if (l &gt; r) return 0;<br \/>\n\u00a0 \u00a0 \u00a0 \u00a0 return (prefix[row][r &#043; 1][state] &#8211; prefix[row][l][state] &#043; MOD) % MOD;<br \/>\n\u00a0 \u00a0 }<br \/>\n}<br \/>\n&#096;&#096;&#096;<\/p>\n<p>&#8212;<\/p>\n<p>\u590d\u6742\u5ea6<\/p>\n<p>\u9879\u76ee\u00a0\u00a0 \u00a0\u590d\u6742\u5ea6\u00a0\u00a0 \u00a0<br \/>\n\u65f6\u95f4\u00a0\u00a0 \u00a0&#096;O(n \u00d7 m)&#096;\u00a0\u00a0 \u00a0<br \/>\n\u7a7a\u95f4\u00a0\u00a0 \u00a0&#096;O(n \u00d7 m)&#096;&#xff08;\u53ef\u4f18\u5316\u5230 &#096;O(m)&#096;&#xff0c;\u53ea\u9700\u4fdd\u7559\u76f8\u90bb\u4e24\u884c&#xff09;<\/p>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>LeetCode 3797. \u7edf\u8ba1\u5728\u77e9\u5f62\u683c\u5b50\u91cc\u79fb\u52a8\u7684\u8def\u5f84\u6570\u76ee\u601d\u8def\u8fd9\u9898\u662f\u524d\u7f00\u548c\u4f18\u5316\u7684\u52a8\u6001\u89c4\u5212\u3002\u72b6\u6001\u5b9a\u4e49&#xff08;\u4ece\u4e0b\u5f80\u4e0a\u9012\u63a8&#xff09;&#xff1a;- f[i][j]&#xff1a;\u4ece\u6700\u540e\u4e00\u884c\u51fa\u53d1\u5230\u8fbe (i,j)&#xff0c;\u4e14\u6700\u540e\u4e00\u6b65\u662f\u4ece\u4e0b\u4e00\u884c\u4e0a\u6765\u7684\u8def\u5f84\u6570<br \/>\n&#8211; g[i][j]&#xff1a;\u4ece\u6700\u540e\u4e00\u884c\u51fa\u53d1\u5230\u8fbe (i,j)&#xff0c;\u4e14\u6700\u540e\u4e00\u6b65\u662f\u540c\u4e00\u884c\u6a2a\u5411\u79fb\u52a8\u6765\u7684\u8def\u5f84\u6570\u8f6c\u79fb&#xff1a;1. \u4ece\u4e0b\u4e00\u884c\u4e0a\u6765&#xff1a;\u4ece (i1, j) \u5230 (i, j)<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[99,2692,292,1813,427],"topic":[],"class_list":["post-89515","post","type-post","status-publish","format-standard","hentry","category-server","tag-java","tag-leetcode","tag-292","tag-1813","tag-427"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Kimi  LeetCode 3797. \u7edf\u8ba1\u5728\u77e9\u5f62\u683c\u5b50\u91cc\u79fb\u52a8\u7684\u8def\u5f84\u6570\u76ee Java\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/89515.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta 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