[LeetCode]Scramble String
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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.
Analysis:首先想到的是递归,简单明了,对两个string进行partition,然后比较四个字符串段。但是递归的话,这个时间复杂度比较高。然后想到能否DP,但是即使用DP的话,也要O(n^3)。想想算了,还是在递归里做些剪枝,这样就可以避免冗余计算:
对于每两个要比较的partition,统计他们字符出现次数,如果不相等返回。
网上也有动态规划的解法, 稍后研究一下
Java
public boolean isScramble(String s1, String s2) { if(s1.length()!=s2.length()) return false;int[] frequence = new int[26];for(int i=0;i<s1.length();i++){int temp = s1.charAt(i)-'a';frequence[temp]++;}for(int i=0;i<s2.length();i++){int temp = s2.charAt(i)-'a';frequence[temp]--;}for(int i=0;i<frequence.length;i++){if(frequence[i]!=0) return false;}if(s1.length()==1 && s2.length()==1) return true;for(int i=1;i<s1.length();i++){boolean result = isScramble(s1.substring(0,i), s2.substring(0,i)) && isScramble(s1.substring(i), s2.substring(i));if(result) return true;result = (isScramble(s1.substring(0, i), s2.substring(s2.length()-i))&& isScramble(s1.substring(i), s2.substring(0, s2.length()-i)));if(result) return true;}return false; }c++
bool isScramble(string s1, string s2) { if(s1.size() != s2.size()) return false; int A[26]; memset(A,0,26*sizeof(A[0])); for(int i=0; i<s1.size(); i++){ A[s1[i]-'a']++; } for(int i=0; i<s2.size(); i++){ A[s2[i]-'a']--; } for(int i=0; i<26; i++){ if(A[i] !=0) return false; } if(s1.size() ==1 && s2.size()==1) return true; for(int i=1; i<s1.size(); i++){ bool result = isScramble(s1.substr(0,i), s2.substr(0,i)) && isScramble(s1.substr(i,s1.size()-i),s2.substr(i,s1.size()-i)); result = result || (isScramble(s1.substr(0,i),s2.substr(s2.size()-i,i))&& isScramble(s1.substr(i,s1.size()-i),s2.substr(0,s1.size()-i))); if(result) return true; } return false; }
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