{"id":50303,"date":"2025-07-30T22:51:40","date_gmt":"2025-07-30T14:51:40","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/50303.html"},"modified":"2025-07-30T22:51:40","modified_gmt":"2025-07-30T14:51:40","slug":"%e4%bb%a3%e7%a0%81%e9%9a%8f%e6%83%b3%e5%bd%95%e7%ae%97%e6%b3%95%e8%ae%ad%e7%bb%83%e8%90%a5%e7%ac%ac%e4%b8%89%e5%8d%81%e5%85%ad%e5%a4%a9","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/50303.html","title":{"rendered":"\u4ee3\u7801\u968f\u60f3\u5f55\u7b97\u6cd5\u8bad\u7ec3\u8425\u7b2c\u4e09\u5341\u516d\u5929"},"content":{"rendered":"

LeetCode.1049\u00a0\u6700\u540e\u4e00\u5757\u77f3\u5934\u7684\u91cd\u91cf II <\/span><\/h3>\n

\u9898\u76ee\u94fe\u63a5\u00a0\u6700\u540e\u4e00\u5757\u77f3\u5934\u7684\u91cd\u91cfII<\/h4>\n

\u9898\u89e3<\/h4>\n

class Solution {
\n public int lastStoneWeightII(int[] stones) {
\n int len = stones.length;
\n int sum = 0;
\n for(int i = 0;i<len;i++) sum += stones[i];
\n int target = sum \/ 2;
\n int[] dp = new int[target + 1];
\n for(int i = 0;i<len;i++){
\n for(int j = target;j>=stones[i];j–){
\n dp[j] = Math.max(dp[j],dp[j-stones[i]] + stones[i]);
\n }
\n }
\n int max_value = dp[target];
\n return sum – max_value * 2;
\n }
\n} <\/p>\n

\u89e3\u9898\u601d\u8def<\/h4>\n

\u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u6700\u540e\u4e00\u5757\u77f3\u5934\u7684\u91cd\u91cf II" \u95ee\u9898，\u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684\u52a8\u6001\u89c4\u5212\u95ee\u9898，\u672c\u8d28\u4e0a\u53ef\u4ee5\u8f6c\u5316\u4e3a 0-1 \u80cc\u5305\u95ee\u9898\u3002<\/p>\n

\u7b97\u6cd5\u601d\u8def\u89e3\u6790：<\/p>\n

  • \u95ee\u9898\u8f6c\u5316：\u5c06\u77f3\u5934\u5206\u6210\u4e24\u5806，\u4f7f\u4e24\u5806\u7684\u91cd\u91cf\u5c3d\u53ef\u80fd\u63a5\u8fd1\u603b\u548c\u7684\u4e00\u534a\u3002\u8fd9\u6837\u4e24\u5806\u77f3\u5934\u78b0\u649e\u540e\u5269\u4e0b\u7684\u91cd\u91cf\u5c31\u662f\u6700\u5c0f\u53ef\u80fd\u503c\u3002<\/li>\n
  • \u52a8\u6001\u89c4\u5212\u601d\u8def：\n
      \n
    • \u8ba1\u7b97\u6240\u6709\u77f3\u5934\u7684\u603b\u91cd\u91cf sum<\/li>\n
    • \u76ee\u6807\u662f\u627e\u5230\u603b\u548c\u4e0d\u8d85\u8fc7 sum\/2 \u7684\u6700\u5927\u5b50\u96c6\u548c<\/li>\n
    • \u4f7f\u7528 0-1 \u80cc\u5305\u7684\u52a8\u6001\u89c4\u5212\u65b9\u6cd5\u6c42\u89e3\u8fd9\u4e2a\u6700\u5927\u5b50\u96c6\u548c<\/li>\n<\/ul>\n<\/li>\n

      \u4ee3\u7801\u89e3\u91ca：<\/p>\n

        \n
      • sum：\u8ba1\u7b97\u6240\u6709\u77f3\u5934\u7684\u603b\u91cd\u91cf<\/li>\n
      • target：\u603b\u91cd\u91cf\u7684\u4e00\u534a，\u4f5c\u4e3a\u80cc\u5305\u7684\u6700\u5927\u5bb9\u91cf<\/li>\n
      • dp[j]：\u8868\u793a\u5bb9\u91cf\u4e3a j \u7684\u80cc\u5305\u80fd\u88c5\u4e0b\u7684\u6700\u5927\u77f3\u5934\u91cd\u91cf<\/li>\n
      • \u5185\u5c42\u5faa\u73af\u91c7\u7528\u5012\u5e8f\u904d\u5386j，\u662f\u4e3a\u4e86\u907f\u514d\u540c\u4e00\u77f3\u5934\u88ab\u591a\u6b21\u4f7f\u7528（0-1 \u80cc\u5305\u7279\u6027）<\/li>\n
      • \u6700\u7ec8\u7ed3\u679csum – max_value * 2\u8868\u793a\u4e24\u5806\u77f3\u5934\u78b0\u649e\u540e\u5269\u4f59\u7684\u6700\u5c0f\u91cd\u91cf<\/li>\n<\/ul>\n

        LeetCode.494 \u76ee\u6807\u548c<\/h3>\n

        \u9898\u76ee\u94fe\u63a5\u00a0\u76ee\u6807\u548c<\/h4>\n

        \u9898\u89e3<\/h4>\n

        class Solution {
        \n public int findTargetSumWays(int[] nums, int target) {
        \n int sum = 0;
        \n int len = nums.length;
        \n for(int i = 0;i<len;i++) sum += nums[i];
        \n if ((target + sum) % 2 == 1) return 0;
        \n if (Math.abs(target) > sum) return 0;
        \n int n = (sum + target) \/ 2;
        \n \/\/ \u80fd\u51d1\u6210i\u5bb9\u91cf\u7684dp[i]\u79cd\u65b9\u6cd5
        \n int[] dp = new int[n+1];
        \n dp[0] = 1;
        \n for(int i = 0;i<len;i++){
        \n for(int j = n;j>=nums[i];j–){
        \n dp[j] += dp[j – nums[i]];
        \n }
        \n }
        \n return dp[n];
        \n }
        \n} <\/p>\n

        \u89e3\u9898\u601d\u8def<\/h4>\n

        \u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u76ee\u6807\u548c" \u95ee\u9898，\u5373\u901a\u8fc7\u7ed9\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u6570\u5b57\u6dfb\u52a0 "+" \u6216 "-"，\u4f7f\u5f97\u5b83\u4eec\u7684\u548c\u7b49\u4e8e\u76ee\u6807\u503c target，\u8ba1\u7b97\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u3002<\/p>\n

        \u7b97\u6cd5\u601d\u8def\u89e3\u6790：<\/p>\n

      • \n

        \u95ee\u9898\u8f6c\u5316：\u5047\u8bbe\u6570\u7ec4\u4e2d\u6dfb\u52a0 "+" \u7684\u5143\u7d20\u548c\u4e3asumA，\u6dfb\u52a0 "-" \u7684\u5143\u7d20\u548c\u4e3asumB，\u5219\u6709：<\/p>\n

          \n
        • sumA – sumB = target<\/li>\n
        • sumA + sumB = sum（\u6570\u7ec4\u603b\u548c） \u4e24\u5f0f\u76f8\u52a0\u53ef\u5f97\u00a02*sumA = target + sum，\u5373\u00a0sumA = (target + sum) \/ 2<\/li>\n<\/ul>\n<\/li>\n
        • \n

          \u5173\u952e\u5224\u65ad：<\/p>\n

            \n
          • \u5982\u679c(target + sum)\u662f\u5947\u6570，\u65e0\u6cd5\u6574\u9664，\u76f4\u63a5\u8fd4\u56de 0<\/li>\n
          • \u5982\u679ctarget\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u603b\u548csum，\u4e5f\u8fd4\u56de 0<\/li>\n<\/ul>\n<\/li>\n
          • \n

            \u52a8\u6001\u89c4\u5212\u601d\u8def：<\/p>\n

              \n
            • \u95ee\u9898\u8f6c\u5316\u4e3a：\u4ece\u6570\u7ec4\u4e2d\u9009\u53d6\u82e5\u5e72\u5143\u7d20，\u4f7f\u5176\u548c\u7b49\u4e8esumA，\u8ba1\u7b97\u6709\u591a\u5c11\u79cd\u9009\u6cd5<\/li>\n
            • \u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684 "\u5b50\u96c6\u548c\u8ba1\u6570" \u95ee\u9898，\u53ef\u7528 0-1 \u80cc\u5305\u7684\u52a8\u6001\u89c4\u5212\u65b9\u6cd5\u89e3\u51b3<\/li>\n<\/ul>\n<\/li>\n

              \u4ee3\u7801\u89e3\u91ca：<\/p>\n

                \n
              • sum：\u8ba1\u7b97\u6570\u7ec4\u6240\u6709\u5143\u7d20\u7684\u603b\u548c<\/li>\n
              • n：\u5373\u4e0a\u8ff0\u7684sumA，\u8868\u793a\u9700\u8981\u51d1\u51fa\u7684\u76ee\u6807\u548c<\/li>\n
              • dp[i]：\u8868\u793a\u80fd\u51d1\u6210\u548c\u4e3a i \u7684\u65b9\u6cd5\u603b\u6570<\/li>\n
              • \u521d\u59cb\u5316dp[0] = 1：\u8868\u793a\u51d1\u6210\u548c\u4e3a 0 \u7684\u65b9\u6cd5\u6709 1 \u79cd（\u4ec0\u4e48\u90fd\u4e0d\u9009）<\/li>\n
              • \u5185\u5c42\u5faa\u73af\u5012\u5e8f\u904d\u5386，\u907f\u514d\u540c\u4e00\u5143\u7d20\u88ab\u91cd\u590d\u4f7f\u7528<\/li>\n
              • \u6700\u7ec8\u7ed3\u679cdp[n]\u5c31\u662f\u80fd\u51d1\u6210\u76ee\u6807\u548c\u7684\u65b9\u6cd5\u603b\u6570<\/li>\n<\/ul>\n

                LeetCode.474 \u4e00\u548c\u96f6<\/h3>\n

                \u9898\u76ee\u94fe\u63a5\u00a0\u4e00\u548c\u96f6<\/h4>\n

                \u9898\u89e3<\/h4>\n

                class Solution {
                \n public int findMaxForm(String[] strs, int m, int n) {
                \n int[][][] dpArr = new int[strs.length][m + 1][n + 1];<\/p>\n

                int zeroNum = 0;
                \n int oneNum = 0;
                \n for (char c : strs[0].toCharArray()) {
                \n if (c == '0') {
                \n zeroNum++;
                \n } else {
                \n oneNum++;
                \n }
                \n }
                \n for (int j = zeroNum; j <= m; j++) {
                \n for (int k = oneNum; k <= n; k++) {
                \n dpArr[0][j][k] = 1;
                \n }
                \n }
                \n for (int i = 1; i < strs.length; i++) {
                \n zeroNum = 0;
                \n oneNum = 0;
                \n for (char c : strs[i].toCharArray()) {
                \n if (c == '0') {
                \n zeroNum++;
                \n } else {
                \n oneNum++;
                \n }
                \n }
                \n for (int j = 0; j <= m; j++) {
                \n for (int k = 0; k <= n; k++) {
                \n if (j >= zeroNum && k >= oneNum) {
                \n dpArr[i][j][k] = Math.max(dpArr[i – 1][j][k], dpArr[i – 1][j – zeroNum][k – oneNum] + 1);
                \n } else {
                \n dpArr[i][j][k] = dpArr[i – 1][j][k];
                \n }
                \n }
                \n }
                \n }
                \n return dpArr[dpArr.length – 1][m][n];
                \n }
                \n} <\/p>\n

                \u89e3\u9898\u601d\u8def<\/h4>\n

                \u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u4e00\u548c\u96f6" \u95ee\u9898，\u5373\u5728\u7ed9\u5b9a 0 \u548c 1 \u7684\u6700\u5927\u6570\u91cf\u9650\u5236 (m \u548c n) \u7684\u60c5\u51b5\u4e0b，\u4ece\u5b57\u7b26\u4e32\u6570\u7ec4\u4e2d\u9009\u51fa\u6700\u591a\u6570\u91cf\u7684\u5b57\u7b26\u4e32，\u4f7f\u8fd9\u4e9b\u5b57\u7b26\u4e32\u4e2d\u5305\u542b\u7684 0 \u603b\u6570\u4e0d\u8d85\u8fc7 m，1 \u603b\u6570\u4e0d\u8d85\u8fc7 n\u3002<\/p>\n

                \u7b97\u6cd5\u601d\u8def\u89e3\u6790：<\/p>\n

                \u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684\u4e8c\u7ef4 0-1 \u80cc\u5305\u95ee\u9898：<\/p>\n

                  \n
                • \u6bcf\u4e2a\u5b57\u7b26\u4e32\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u7269\u54c1<\/li>\n
                • \u6bcf\u4e2a\u7269\u54c1\u6709\u4e24\u4e2a "\u91cd\u91cf" \u5c5e\u6027：0 \u7684\u6570\u91cf\u548c 1 \u7684\u6570\u91cf<\/li>\n
                • \u80cc\u5305\u7684\u4e24\u4e2a\u5bb9\u91cf\u9650\u5236\u5206\u522b\u662f m (0 \u7684\u6700\u5927\u6570\u91cf) \u548c n (1 \u7684\u6700\u5927\u6570\u91cf)<\/li>\n
                • \u76ee\u6807\u662f\u9009\u62e9\u6700\u591a\u6570\u91cf\u7684\u7269\u54c1 (\u5b57\u7b26\u4e32) \u800c\u4e0d\u8d85\u8fc7\u80cc\u5305\u5bb9\u91cf<\/li>\n<\/ul>\n

                  \u4ee3\u7801\u89e3\u91ca：<\/p>\n

                • \n

                  \u4e09\u7ef4 DP \u6570\u7ec4\u5b9a\u4e49：dpArr[i][j][k]\u8868\u793a\u5728\u524d i \u4e2a\u5b57\u7b26\u4e32\u4e2d，\u4f7f\u7528\u4e0d\u8d85\u8fc7 j \u4e2a 0 \u548c k \u4e2a 1 \u65f6\u80fd\u9009\u53d6\u7684\u6700\u5927\u5b57\u7b26\u4e32\u6570\u91cf<\/p>\n<\/li>\n

                • \n

                  \u521d\u59cb\u5316\u5904\u7406：<\/p>\n

                    \n
                  • \u8ba1\u7b97\u7b2c\u4e00\u4e2a\u5b57\u7b26\u4e32\u4e2d 0 \u548c 1 \u7684\u6570\u91cf<\/li>\n
                  • \u5bf9\u4e8e\u80fd\u5bb9\u7eb3\u7b2c\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684\u6240\u6709 (j,k) \u7ec4\u5408，\u521d\u59cb\u5316\u4e3a 1 (\u8868\u793a\u9009\u62e9\u7b2c\u4e00\u4e2a\u5b57\u7b26\u4e32)<\/li>\n<\/ul>\n<\/li>\n
                  • \n

                    \u72b6\u6001\u8f6c\u79fb：<\/p>\n

                      \n
                    • \u5bf9\u6bcf\u4e2a\u5b57\u7b26\u4e32，\u5148\u8ba1\u7b97\u5176\u5305\u542b\u7684 0 \u548c 1 \u7684\u6570\u91cf<\/li>\n
                    • \u5bf9\u6bcf\u79cd\u53ef\u80fd\u7684 0 \u548c 1 \u7684\u6570\u91cf\u9650\u5236 (j,k)：\n
                        \n
                      • \u5982\u679c\u5f53\u524d\u5b57\u7b26\u4e32\u53ef\u4ee5\u88ab\u5bb9\u7eb3 (j>= 0 \u7684\u6570\u91cf\u4e14 k >= 1 \u7684\u6570\u91cf)，\u5219\u53d6 "\u4e0d\u9009\u5f53\u524d\u5b57\u7b26\u4e32" \u548c "\u9009\u5f53\u524d\u5b57\u7b26\u4e32" \u4e24\u79cd\u60c5\u51b5\u7684\u6700\u5927\u503c<\/li>\n
                      • \u5426\u5219，\u53ea\u80fd\u7ee7\u627f\u4e0d\u9009\u5f53\u524d\u5b57\u7b26\u4e32\u7684\u7ed3\u679c<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                      • \n

                        \u6700\u7ec8\u7ed3\u679c：dpArr[strs.length – 1][m][n]\u8868\u793a\u8003\u8651\u6240\u6709\u5b57\u7b26\u4e32\u540e，\u5728 m \u548c n \u9650\u5236\u4e0b\u80fd\u9009\u53d6\u7684\u6700\u5927\u5b57\u7b26\u4e32\u6570\u91cf<\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"

                        \u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb220\u6b21\u3002\u89e3\u9898\u601d\u8def\u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u6700\u540e\u4e00\u5757\u77f3\u5934\u7684\u91cd\u91cf II" \u95ee\u9898\uff0c\u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684\u52a8\u6001\u89c4\u5212\u95ee\u9898\uff0c\u672c\u8d28\u4e0a\u53ef\u4ee5\u8f6c\u5316\u4e3a 0-1 \u80cc\u5305\u95ee\u9898\u3002\u7b97\u6cd5\u601d\u8def\u89e3\u6790\uff1a\u4ee3\u7801\u89e3\u91ca\uff1a\u89e3\u9898\u601d\u8def\u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u76ee\u6807\u548c" \u95ee\u9898\uff0c\u5373\u901a\u8fc7\u7ed9\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u6570\u5b57\u6dfb\u52a0 "+" \u6216 "-"\uff0c\u4f7f\u5f97\u5b83\u4eec\u7684\u548c\u7b49\u4e8e\u76ee\u6807\u503c target\uff0c\u8ba1\u7b97\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u3002\u7b97\u6cd5\u601d\u8def\u89e3\u6790\uff1a\u95ee\u9898\u8f6c\u5316\uff1a\u5047\u8bbe\u6570\u7ec4\u4e2d\u6dfb\u52a0 "+" \u7684\u5143\u7d20\u548c\u4e3a\uff0c\u6dfb\u52a0 "-" \u7684\u5143\u7d20\u548c\u4e3a\uff0c\u5219\u6709\uff1a\u5173\u952e\u5224\u65ad\uff1a\u52a8\u6001\u89c4\u5212\u601d\u8def\uff1a\u4ee3\u7801\u89e3\u91ca\uff1a\u89e3\u9898\u601d\u8def\u8fd9\u6bb5\u4ee3\u7801\u89e3\u51b3\u7684\u662f "\u4e00\u548c\u96f6" \u95ee\u9898\uff0c\u5373\u5728\u7ed9\u5b9a 0<\/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":[427],"topic":[],"class_list":["post-50303","post","type-post","status-publish","format-standard","hentry","category-server","tag-427"],"yoast_head":"\n\u4ee3\u7801\u968f\u60f3\u5f55\u7b97\u6cd5\u8bad\u7ec3\u8425\u7b2c\u4e09\u5341\u516d\u5929 - 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