最長公共子字符串（動態規劃）

和經典DP最長公共子串（不要求字符連續）不同，最長公共子字符串要求字符是連續的

class LongestSubstring {
public:
    int findLongest(string A, int n, string B, int m) {
        //f[i][j] represent the longest common substring starting with A[i] and B[j]
        vector<vector<int>> f(n+1, vector<int>(m+1, 0));
        //maxlen is the overall max common substring length, starting anywhere
        int maxlen = 0;
        //dp
        for(int i = n-1; i > -1; --i){
            for(int j = m-1; j > -1; --j){
                if(A[i] != B[j]){
                    //no such common substring ended with A[i] and B[j]
                    //f[i][j] remain 0 as initialized
                }
                else{
                    //common substring starts with A[i] and B[j]
                    f[i][j] = f[i+1][j+1] + 1;
                    maxlen = max(maxlen, f[i][j]);
                }
            }
        }
        return maxlen;
    }
};