762 · longest common subsequence II

describe

Given two sequences P and Q .
You can treat this pair of P This sequence cannot be modified more than k An element to any value , The longest common subsequence of the two modified sequences is required to be the longest .

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Examples

Examples 1:

 Input :
[8,3]
[1,3]
1
 Output :
2

 explain :
 hold 8 become 1, The common subsequence is [1,3]

Examples 2:

 Input :
[1, 2, 3, 4, 5]
[5, 3, 1, 4, 2]
1
 Output :
3

int longestCommonSubsequence2(vector<int> &P, vector<int> &Q, int k)
{
    int lenP = P.size(), lenQ = Q.size();
    vector<vector<vector<int>>> dp(lenP + 1, vector<vector<int>>(lenQ + 1, vector<int>(k + 1, 0)));
    
    for (int i = 1; i <= lenP; i++)
    {
        for (int j = 1; j <= lenQ; j++)
        {
            for (int m = 0; m <= k; m++)
            {
                if (P[i - 1] == Q[j - 1])
                {
                    dp[i][j][m] = dp[i - 1][j - 1][m] + 1;
                }            
                else
                {
                    if (m == 0)
                    {
                        dp[i][j][m] = max(dp[i][j - 1][m], dp[i - 1][j][m]);
                    }
                    else
                    {
                        dp[i][j][m] = max(max(dp[i - 1][j - 1][m - 1] + 1, dp[i][j - 1][m]), dp[i - 1][j][m]);
                    }
                }
            }
        }
    }
    return dp[lenP][lenQ][k];
}