{"id":107249,"date":"2026-09-19T07:49:18","date_gmt":"2026-09-18T23:49:18","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/107249.html"},"modified":"2026-09-19T07:49:18","modified_gmt":"2026-09-18T23:49:18","slug":"deepseek-leetcode-120-%e4%b8%89%e8%a7%92%e5%bd%a2%e6%9c%80%e5%b0%8f%e8%b7%af%e5%be%84%e5%92%8c-java%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/107249.html","title":{"rendered":"DeepSeek LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java\u5b9e\u73b0"},"content":{"rendered":"

LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java \u5b9e\u73b0<\/p>\n

\u9898\u76ee\u7406\u89e3<\/p>\n

\u7ed9\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62 triangle，\u8fd4\u56de\u4ece\u9876\u90e8\u5230\u5e95\u90e8\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002\u6bcf\u4e00\u6b65\u53ea\u80fd\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u4e2d\u76f8\u90bb\u7684\u8282\u70b9\u3002<\/p>\n

\u4f8b\u5982：<\/p>\n

2
\n 3 4
\n 6 5 7
\n4 1 8 3<\/p>\n

\u6700\u5c0f\u8def\u5f84\u548c\u4e3a 2 + 3 + 5 + 1 = 11\u3002<\/p>\n

\n

\u89e3\u6cd5\u4e00：\u4e8c\u7ef4 DP（\u81ea\u9876\u5411\u4e0b）<\/p>\n

\u5b9a\u4e49 dp[i][j] \u4e3a\u4ece\u9876\u90e8\u8d70\u5230\u4f4d\u7f6e (i, j) \u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002<\/p>\n

class<\/span> Solution<\/span> {<\/span>
\n public<\/span> int<\/span> minimumTotal<\/span>(<\/span>List<\/span><<\/span>List<\/span><<\/span>Integer<\/span>><\/span>><\/span><\/span> triangle)<\/span> {<\/span>
\n int<\/span> n =<\/span> triangle.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
\n int<\/span>[<\/span>]<\/span>[<\/span>]<\/span> dp =<\/span> new<\/span> int<\/span>[<\/span>n]<\/span>[<\/span>n]<\/span>;<\/span>
\n dp[<\/span>0<\/span>]<\/span>[<\/span>0<\/span>]<\/span> =<\/span> triangle.<\/span>get<\/span>(<\/span>0<\/span>)<\/span>.<\/span>get<\/span>(<\/span>0<\/span>)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\n \/\/ \u6700\u5de6\u5217\u53ea\u80fd\u4ece\u4e0a\u4e00\u884c\u6700\u5de6\u5217\u8fc7\u6765<\/span>
\n dp[<\/span>i]<\/span>[<\/span>0<\/span>]<\/span> =<\/span> dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>0<\/span>]<\/span> +<\/span> triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>get<\/span>(<\/span>0<\/span>)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> j =<\/span> 1<\/span>;<\/span> j <<\/span> i;<\/span> j++<\/span>)<\/span> {<\/span>
\n dp[<\/span>i]<\/span>[<\/span>j]<\/span> =<\/span> Math<\/span>.<\/span>min<\/span>(<\/span>dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>j –<\/span> 1<\/span>]<\/span>,<\/span> dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>j]<\/span>)<\/span>
\n +<\/span> triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>get<\/span>(<\/span>j)<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u6700\u53f3\u5217\u53ea\u80fd\u4ece\u4e0a\u4e00\u884c\u6700\u53f3\u5217\u8fc7\u6765<\/span>
\n dp[<\/span>i]<\/span>[<\/span>i]<\/span> =<\/span> dp[<\/span>i –<\/span> 1<\/span>]<\/span>[<\/span>i –<\/span> 1<\/span>]<\/span> +<\/span> triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>get<\/span>(<\/span>i)<\/span>;<\/span>
\n }<\/span><\/p>\n

int<\/span> ans =<\/span> dp[<\/span>n –<\/span> 1<\/span>]<\/span>[<\/span>0<\/span>]<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 1<\/span>;<\/span> j <<\/span> n;<\/span> j++<\/span>)<\/span> {<\/span>
\n ans =<\/span> Math<\/span>.<\/span>min<\/span>(<\/span>ans,<\/span> dp[<\/span>n –<\/span> 1<\/span>]<\/span>[<\/span>j]<\/span>)<\/span>;<\/span>
\n }<\/span>
\n return<\/span> ans;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u00b7 \u65f6\u95f4\u590d\u6742\u5ea6：O(n\u00b2)
\n\u00b7 \u7a7a\u95f4\u590d\u6742\u5ea6：O(n\u00b2)<\/p>\n

\n

\u89e3\u6cd5\u4e8c：\u4e00\u7ef4 DP（\u81ea\u5e95\u5411\u4e0a，\u63a8\u8350）<\/p>\n

\u4ece\u5012\u6570\u7b2c\u4e8c\u884c\u5f00\u59cb\u5411\u4e0a\u9012\u63a8\u3002
\ndp[j] \u8868\u793a\u4ece\u5f53\u524d\u884c\u7b2c j \u4e2a\u4f4d\u7f6e\u5230\u5e95\u90e8\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002<\/p>\n

\u521d\u59cb\u5316 dp \u4e3a\u6700\u540e\u4e00\u884c\u7684\u503c，\u7136\u540e\u5411\u4e0a\u66f4\u65b0：<\/p>\n

class<\/span> Solution<\/span> {<\/span>
\n public<\/span> int<\/span> minimumTotal<\/span>(<\/span>List<\/span><<\/span>List<\/span><<\/span>Integer<\/span>><\/span>><\/span><\/span> triangle)<\/span> {<\/span>
\n int<\/span> n =<\/span> triangle.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
\n int<\/span>[<\/span>]<\/span> dp =<\/span> new<\/span> int<\/span>[<\/span>n]<\/span>;<\/span><\/p>\n

\/\/ \u521d\u59cb\u5316\u6700\u540e\u4e00\u884c\u7684\u503c<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> n;<\/span> j++<\/span>)<\/span> {<\/span>
\n dp[<\/span>j]<\/span> =<\/span> triangle.<\/span>get<\/span>(<\/span>n –<\/span> 1<\/span>)<\/span>.<\/span>get<\/span>(<\/span>j)<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u4ece\u5012\u6570\u7b2c\u4e8c\u884c\u5f00\u59cb\u5411\u4e0a\u9012\u63a8<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> n –<\/span> 2<\/span>;<\/span> i >=<\/span> 0<\/span>;<\/span> i—<\/span>)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <=<\/span> i;<\/span> j++<\/span>)<\/span> {<\/span>
\n dp[<\/span>j]<\/span> =<\/span> triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>get<\/span>(<\/span>j)<\/span> +<\/span> Math<\/span>.<\/span>min<\/span>(<\/span>dp[<\/span>j]<\/span>,<\/span> dp[<\/span>j +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

return<\/span> dp[<\/span>0<\/span>]<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u00b7 \u65f6\u95f4\u590d\u6742\u5ea6：O(n\u00b2)
\n\u00b7 \u7a7a\u95f4\u590d\u6742\u5ea6：O(n)<\/p>\n

\n

\u89e3\u6cd5\u4e09：\u539f\u5730\u4fee\u6539（\u989d\u5916\u7a7a\u95f4 O(1)）<\/p>\n

\u5982\u679c\u5141\u8bb8\u4fee\u6539\u539f\u4e09\u89d2\u5f62，\u53ef\u4ee5\u76f4\u63a5\u5728 triangle \u4e0a\u4ece\u4e0b\u5f80\u4e0a\u7d2f\u52a0，\u6700\u7ec8 triangle.get(0).get(0) \u5c31\u662f\u7b54\u6848\u3002<\/p>\n

class<\/span> Solution<\/span> {<\/span>
\n public<\/span> int<\/span> minimumTotal<\/span>(<\/span>List<\/span><<\/span>List<\/span><<\/span>Integer<\/span>><\/span>><\/span><\/span> triangle)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> triangle.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> 2<\/span>;<\/span> i >=<\/span> 0<\/span>;<\/span> i—<\/span>)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <=<\/span> i;<\/span> j++<\/span>)<\/span> {<\/span>
\n int<\/span> min =<\/span> Math<\/span>.<\/span>min<\/span>(<\/span>triangle.<\/span>get<\/span>(<\/span>i +<\/span> 1<\/span>)<\/span>.<\/span>get<\/span>(<\/span>j)<\/span>,<\/span>
\n triangle.<\/span>get<\/span>(<\/span>i +<\/span> 1<\/span>)<\/span>.<\/span>get<\/span>(<\/span>j +<\/span> 1<\/span>)<\/span>)<\/span>;<\/span>
\n triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>set<\/span>(<\/span>j,<\/span> triangle.<\/span>get<\/span>(<\/span>i)<\/span>.<\/span>get<\/span>(<\/span>j)<\/span> +<\/span> min)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> triangle.<\/span>get<\/span>(<\/span>0<\/span>)<\/span>.<\/span>get<\/span>(<\/span>0<\/span>)<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u00b7 \u65f6\u95f4\u590d\u6742\u5ea6：O(n\u00b2)
\n\u00b7 \u7a7a\u95f4\u590d\u6742\u5ea6：O(1)（\u4e0d\u8ba1\u8f93\u5165\u672c\u8eab）<\/p>\n

\n

\u603b\u7ed3<\/p>\n

\u89e3\u6cd5 \u65f6\u95f4\u590d\u6742\u5ea6 \u7a7a\u95f4\u590d\u6742\u5ea6 \u7279\u70b9
\n\u4e8c\u7ef4 DP O(n\u00b2) O(n\u00b2) \u601d\u8def\u76f4\u89c2，\u6613\u4e8e\u7406\u89e3
\n\u4e00\u7ef4 DP（\u81ea\u5e95\u5411\u4e0a） O(n\u00b2) O(n) \u63a8\u8350，\u4e0d\u4fee\u6539\u8f93\u5165
\n\u539f\u5730\u4fee\u6539 O(n\u00b2) O(1) \u7a7a\u95f4\u6700\u4f18，\u4f46\u4f1a\u4fee\u6539\u8f93\u5165<\/p>\n

\u9762\u8bd5\u5efa\u8bae：\u4f18\u5148\u5199\u4e00\u7ef4 DP \u81ea\u5e95\u5411\u4e0a\u7684\u89e3\u6cd5，\u4ee3\u7801\u7b80\u6d01\u3001\u7a7a\u95f4\u4f18\u5316\u597d，\u4e14\u4e0d\u7834\u574f\u8f93\u5165\u6570\u636e\u3002
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n","protected":false},"excerpt":{"rendered":"

LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java \u5b9e\u73b0
\n\u9898\u76ee\u7406\u89e3
\n\u7ed9\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62 triangle，\u8fd4\u56de\u4ece\u9876\u90e8\u5230\u5e95\u90e8\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002\u6bcf\u4e00\u6b65\u53ea\u80fd\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u4e2d\u76f8\u90bb\u7684\u8282\u70b9\u3002
\n\u4f8b\u5982：23 46 5 7
\n4 1 8 3\u6700\u5c0f\u8def\u5f84\u548c\u4e3a 2 3 5 1 11\u3002\u89e3\u6cd5\u4e00：\u4e8c\u7ef4 DP（\u81ea\u9876\u5411\u4e0b）
\n\u5b9a\u4e49 dp[i][j] \u4e3a\u4ece\u9876\u90e8\u8d70\u5230\u4f4d\u7f6e (i, j) \u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002
\nclass Solution {public i<\/p>\n","protected":false},"author":2,"featured_media":107248,"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-107249","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-java","tag-leetcode","tag-292","tag-1813","tag-427"],"yoast_head":"\nDeepSeek LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c 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\/107249.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"DeepSeek LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java\u5b9e\u73b0 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java \u5b9e\u73b0 \u9898\u76ee\u7406\u89e3 \u7ed9\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62 triangle，\u8fd4\u56de\u4ece\u9876\u90e8\u5230\u5e95\u90e8\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002\u6bcf\u4e00\u6b65\u53ea\u80fd\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u4e2d\u76f8\u90bb\u7684\u8282\u70b9\u3002 \u4f8b\u5982：23 46 5 7 4 1 8 3\u6700\u5c0f\u8def\u5f84\u548c\u4e3a 2 3 5 1 11\u3002\u89e3\u6cd5\u4e00：\u4e8c\u7ef4 DP（\u81ea\u9876\u5411\u4e0b） \u5b9a\u4e49 dp[i][j] \u4e3a\u4ece\u9876\u90e8\u8d70\u5230\u4f4d\u7f6e (i, j) \u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002 class Solution {public i\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/107249.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-09-18T23:49:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260918234915-6aadcdfbf0b4a.jpg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/107249.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/107249.html\",\"name\":\"DeepSeek LeetCode 120. \u4e09\u89d2\u5f62\u6700\u5c0f\u8def\u5f84\u548c Java\u5b9e\u73b0 - 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