Leetcode 115. Distinct Subsequences 计算子串 解题报告

1 解题思想

给了S作为一个全串，然后试问，有多少种按顺序删除S中的某些元素而得到T的方案？

其实这道题是个动态规划

由此动态规划，最后输出最终位置的就可以了

2 原题

Given a string S and a string T, count the number of distinct subsequences of T in S. 
A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not). 
Here is an example:
S = "rabbbit", T = "rabbit" 
Return 3. 

3 AC解

public class Solution {
    /**
     * 
     * */
    public int numDistinct(String s, String t) {
        int n = s.length(), m = t.length();
        char sc[] = s.toCharArray(),tc[] = t.toCharArray();
        int dp[][] = new int[n+1][m+1];
        for(int i=0;i<=n;i++) dp[i][0]=1;
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                dp[i][j] = dp[i-1][j];
                if(sc[i-1] == tc[j-1]) dp[i][j] += dp[i-1][j-1];
            }
        }
        return dp[n][m];
    }
}