97. Interleaving String Add to List

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.

For example,
Given:
s1 = "aabcc",
s2 = "dbbca",

When s3 = "aadbbcbcac", return true.
When s3 = "aadbbbaccc", return false.

解题思路：很经典的一道DP题。table[i][j]表示字符串s1的位置位i，s2的位置位j时能否用s1[0..i-1],s2[0...j-1]拼成s3[0...i+j-1]。初始化时table[0][0]=1表示全都为空时，可以完成。

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        if(s1.length()+s2.length()!=s3.length())return false;
        vector<vector<int> >table(s1.length()+1,vector<int>(s2.length()+1,0));
        for(int i=0;i<s1.length()+1;i++)
            for(int j=0;j<s2.length()+1;j++)
                if(i==0&&j==0)table[i][j]=1;
                else if(i==0)table[i][j]=(table[i][j-1]&&s2[j-1]==s3[j-1]);
                else if(j==0)table[i][j]=(table[i-1][j]&&s1[i-1]==s3[i-1]);
                else table[i][j]=table[i-1][j]&&s1[i-1]==s3[i+j-1]||table[i][j-1]&&s2[j-1]==s3[i+j-1];
        return table[s1.length()][s2.length()];
    }
};