[leetcode] Scramble String

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.

https://oj.leetcode.com/problems/scramble-string/

思路1：枚举DFS，比如要比较s1和s2，s1分成a1和b1，s2分成a2和b2，需要分别比较((a1~a2) && (b1~b2)）或者 （(a1~b2) && (a1~b2))。

思路2：DP。dp[i][j][k]表示s1从i开始k长度的字符串与s2从从j开始k长度的字符串是否是scrambled string。

当k=1时，只需比较s1.charAt(i)是否等于s2.charAt(j)即可。

当k>1是，需要枚举分割点，令左半边长度为l，则右边长度为k-l，（1<l<k）。对于每个l，比较((a1~a2) && (b1~b2)）或者 （(a1~b2) && (a1~b2))。

public class Solution {
    public boolean isScramble(String s1, String s2) {
        if (s1.length() != s2.length())
            return false;
        int len = s1.length();
        boolean dp[][][] = new boolean[len][len][len + 1];

        for (int k = 1; k <= len; k++) {
            for (int i = 0; i <= len - k; i++) {
                for (int j = 0; j <= len - k; j++) {
                    if (k == 1)
                        dp[i][j][k] = (s1.charAt(i) == s2.charAt(j));
                    else {
                        for (int l = 1; l < k; l++) {
                            if (dp[i][j][l] && dp[i + l][j + l][k - l] || dp[i][j + k - l][l] && dp[i + l][j][k - l]) {
                                dp[i][j][k] = true;
                                break;
                            }
                        }

                    }

                }
            }
        }
        return dp[0][0][len];

    }

    public static void main(String[] args) {
        System.out.println(new Solution().isScramble("great", "rgeat"));
        System.out.println(new Solution().isScramble("great", "rgtae"));
        System.out.println(new Solution().isScramble("great", "rgtta"));

    }

}

第二遍参考：暴力法，注意长度为1时的判断，不要忘记了。

public class Solution {
    public boolean isScramble(String s1, String s2) {
        int len1 = s1.length();
        int len2 = s2.length();
        if (len1 != len2)
            return false;
        if (len1 == 0)
            return true;
        if (len1 == 1)
            return s1.equals(s2);

        char[] c1 = s1.toCharArray();
        char[] c2 = s2.toCharArray();

        Arrays.sort(c1);
        Arrays.sort(c2);
        for (int i = 0; i < len1; i++) {
            if (c1[i] != c2[i])
                return false;
        }

        for (int i = 1; i < len1; i++) {
            String s11 = s1.substring(0, i);
            String s12 = s1.substring(i);
            String s21 = s2.substring(0, i);
            String s22 = s2.substring(i);
            if (isScramble(s11, s21) && isScramble(s12, s22))
                return true;
            else {
                String s31 = s2.substring(0, len1 - i);
                String s32 = s2.substring(len1 - i);
                if (isScramble(s11, s32) && isScramble(s12, s31))
                    return true;
            }
        }
        return false;

    }


}

DP解法注意递推公式： if (dp[i][j][l] && dp[i + l][j + l][k - l] || dp[i][j + k - l][l] && dp[i + l][j][k - l])

第三遍记录：

dfs法重新写了下超时， 排序优化后就可以过了。

import java.util.Arrays;

public class Solution {

    public boolean isScramble(String s1, String s2) {
        //terminal condition
        int len1 = s1.length();
        int len2 = s2.length();
        if (len1 != len2)
            return false;
        if (s1.equals(s2))
            return true;
        
        //optimization
        char[] c1 = s1.toCharArray();
        char[] c2 = s2.toCharArray();
        Arrays.sort(c1);
        Arrays.sort(c2);
        for (int i = 0; i < len1; i++) {
            if (c1[i] != c2[i])
                return false;
        }
        
        //recursion
        for (int i = 1; i < len1; i++) {
            String s11 = s1.substring(0, i);
            String s12 = s1.substring(i, len1);
            String s21 = s2.substring(0, i);
            String s22 = s2.substring(i, len2);
            if (isScramble(s11, s21) && isScramble(s12, s22))
                return true;
            String s31 = s2.substring(0, len2 - i);
            String s32 = s2.substring(len2 - i, len2);

            if (isScramble(s11, s32) && isScramble(s12, s31))
                return true;

        }

        return false;

    }

    public static void main(String[] args) {
        System.out.println(new Solution().isScramble("great", "rgeat"));
        System.out.println(new Solution().isScramble("great", "rgtae"));
        System.out.println(new Solution().isScramble("abcdefghijklmnopq", "efghijklmnopqcadb"));

    }

}

参考：

http://blog.csdn.net/pickless/article/details/11501443

http://www.blogjava.net/sandy/archive/2013/05/22/399605.html