interleaving string

Interleaving String

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.

定义状态f(i,j)为s1[0,i],s2[0,j] 匹配s3[0,i+j]

当s1[0,i]的最后一个字符等于s3[0,i+j]的最后一个字符时，f(i,j)=f(i-1,j)
当s2[0,j]的最后一个字符等于s3[0,i+j]的最后一个字符时，f(i,j)=f(i,j-1)

可以将f(i,j)表示成二维动态组（bool类型）

//二维动态数组 class Solution {public:    bool isInterleave(string s1, string s2, string s3) {        if(s3.length()!=s1.length()+s2.length())        return false;                vector<vector<bool>>f(s1.length()+1,vector<bool>(s2.length()+1,true));                for(size_t i=1;i<=s1.length();i++)        {            f[i][0]=(s1[i-1]==s3[i-1])&&(f[i-1][0]);        }        for(size_t i=1;i<=s2.length();i++)        {            f[0][i]=(s2[i-1]==s3[i-1])&&(f[0][i-1]);        }                for(size_t i=1;i<=s1.length();i++)        {            for(size_t j=1;j<=s2.length();j++)            {                f[i][j]=((s1[i-1]==s3[i+j-1])&&(f[i-1][j]))||((s2[j-1]==s3[i+j-1])&&(f[i][j-1]));            }        }                return f[s1.length()][s2.length()];            }};