【leetcode】 Scramble String (hard)★

Given a string s1, we may represent it as a binary tree by partitioning it to two non-empty substrings recursively.

Below is one possible representation of s1 = "great":

    great
   /    
  gr    eat
 /     /  
g   r  e   at
           / 
          a   t

To scramble the string, we may choose any non-leaf node and swap its two children.

For example, if we choose the node "gr" and swap its two children, it produces a scrambled string "rgeat".

    rgeat
   /    
  rg    eat
 /     /  
r   g  e   at
           / 
          a   t

We say that "rgeat" is a scrambled string of "great".

Similarly, if we continue to swap the children of nodes "eat" and "at", it produces a scrambled string "rgtae".

    rgtae
   /    
  rg    tae
 /     /  
r   g  ta  e
       / 
      t   a

We say that "rgtae" is a scrambled string of "great".

Given two strings s1 and s2 of the same length, determine if s2 is a scrambled string of s1.

判断两个字符串s1和s2是否可以通过旋转实现。

思路：开始傻眼了，反应不过来。第二天恍然大悟，用递归，分左右部分，变成子问题。但是最开始我以为划分树只有一种方式，后来发现树可以随意的划分，左子树可以有任意个字符，右子树也是。所以需要循环遍历所有条件。再然后是可能s1的左半部分在s2中位于左半部分 或者是右半部分，所以对这两种情况也要都考虑到。

　　循环的时候用了截枝，如果两边的字符有不一致的直接跳过该次循环。

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <stack>
#include <string>
using namespace std;

class Solution {
public:
    bool isScramble(string s1, string s2) {
        if(s1.length() != s2.length())
            return false;
        if(s1 == s2)
            return true;

        if(!isEqual(s1 , s2))
        {
            return false;
        }

        for(int i = 1; i < s1.length(); i++)
        {
            int leftlength = i;
            int rightlength = s1.length() - leftlength;
            string s1left1 = s1.substr(0, leftlength);
            string s2left1 = s2.substr(0, leftlength);
            string s1right1 = s1.substr(leftlength, rightlength);
            string s2right1 = s2.substr(leftlength, rightlength);

            string s1left2 = s1.substr(rightlength, leftlength);
            string s1right2 = s1.substr(0, rightlength);

            if(!isEqual(s1left1,s2left1) && !isEqual(s1left2,s2left1))
            {
                continue;
            }
            if((isScramble(s1left1, s2left1) && isScramble(s1right1, s2right1)) || (isScramble(s1left2, s2left1) && isScramble(s1right2, s2right1)))
            {
                return true;
            }
        }
        return false;
    }

    //判断两个字符串的字母组成是否一致
    bool isEqual(string s1, string s2)
    {
        if(s1.length() != s2.length())
            return false;
        for(int i = 0; i < s1.length(); i++)
        {
            int locate = s2.find(s1[i]);
            if(locate == string::npos)
            {
                return false;
            }
            else
            {
                s2.erase(s2.begin() + locate);
            }
        }
        return true;
    }
};

int main()
{
    Solution s;
    string s1 = "oatzzffqpnwcxhejzjsnpmkmzngneo";
    string s2 = "acegneonzmkmpnsjzjhxwnpqffzzto";
    //string s1 = "gneo";
    //string s2 = "gneo";
    bool ans = s.isScramble(s1, s2);

    return 0;
}

有大神给出了正宗动态规划的解法，非常精简，要好好学习。 不过这个方法算了所有的情况所以时间比我的要长，差不多150ms, 我的是50ms左右。

dp[i][j][l] means whether s2.substr(j,l) is a scrambled string of s1.substr(i,l) or not.

class Solution {
public:
    bool isScramble(string s1, string s2) {
        int len=s1.size();
        bool dp[100][100][100]={false};
        for (int i=len-1;i>=0;i--)
            for (int j=len-1;j>=0;j--) {
                dp[i][j][1]=(s1[i]==s2[j]);
                for (int l=2;i+l<=len && j+l<=len;l++) {
                    for (int n=1;n<l;n++) { //所有划分左右区间的情况
                        dp[i][j][l]|=dp[i][j][n]&&dp[i+n][j+n][l-n]; //s1的左边对s2的左边
                        dp[i][j][l]|=dp[i][j+l-n][n]&&dp[i+n][j][l-n];//s1的左边对s2的右边
                    }
                }
            }
        return dp[0][0][len];
    }
};