77. Longest Common Subsequence

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参考 https://algorithm.yuanbin.me/zh-hans/dynamic_programming/longest_common_subsequence.html
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状态转移方程：

c[i][j] =
(1) 0 if i == 0 && j == 0
(2) c[i - 1][j - 1] + 1, if A[i] == B[j]
(3) max(c[i][j - 1], c[i - 1][j]) if A[i] != B[j]

class Solution {
public:
    /**
     * @param A: A string
     * @param B: A string
     * @return: The length of longest common subsequence of A and B
     */
    int longestCommonSubsequence(string &A, string &B) {
        // write your code here
        if(A.empty()) return 0;
        if(B.empty()) return 0;
        int lenA = A.size();
        int lenB = B.size();
        vector<vector<int>> dp(lenA + 1);
        for(int i = 0; i < lenA + 1; i++){
            dp[i].resize(lenB + 1, 0);
        }
        for(int i = 1; i < lenA + 1; i++){
            for(int j = 1; j < lenB + 1; j++){
                if(A[i - 1] == B[j - 1]) dp[i][j] = dp[i - 1][j - 1] + 1;
                else{
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        return dp[lenA][lenB];
    }
};