时间轴

2026-03-21

init

题目：

P1143 最长公共子序列

https://leetcode.cn/problems/longest-common-subsequence/description/?envType=study-plan-v2&envId=top-100-liked

经典问题了，dp[i][j] 表示 text1[0..=i] 和 text2[0..=j] 的最长公共子序列长度，状态转移方程为

  • $ text1[i] == text2[j] $ 时：
    • $ dp[i][j] = dp[i-1][j-1] + 1 $
  • otherwise:
    • $ dp[i][j] = max(dp[i-1][j], dp[i][j-1]) $
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#include <string>
#include <vector>

using std::string;
using std::vector;

class Solution {
    public:
        int longestCommonSubsequence(string text1, string text2)
        {
                int i, j, n1 = text1.size(), n2 = text2.size();
                vector<vector<int> > dp(n1, vector<int>(n2, 0));

                for (i = 0; i < n1; i++) {
                        if (text1[i] == text2[0]) {
                                while (i < n1)
                                        dp[i++][0] = 1;
                                break;
                        }
                }

                for (j = 0; j < n2; j++) {
                        if (text2[j] == text1[0]) {
                                while (j < n2)
                                        dp[0][j++] = 1;
                                break;
                        }
                }

                // dp[i][j] 表示 text1[0..=i] 和 text2[0..=j] 的最长公共子序列长度

                // dp[i][j] = dp[i-1][j-1] + 1 (text1[i] == text2[j])
                // dp[i][j] = max(dp[i-1][j], dp[i][j-1])
                for (i = 1; i < n1; i++) {
                        for (j = 1; j < n2; j++) {
                                if (text1[i] == text2[j])
                                        dp[i][j] = dp[i - 1][j - 1] + 1;
                                else
                                        dp[i][j] = std::max(dp[i - 1][j], dp[i][j - 1]);
                        }
                }

                return dp[n1 - 1][n2 - 1];
        }
};