leetcode-1/src/scrambleString/scrambleString.cpp at master · daction/leetcode-1 · GitHub

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

// Author : Hao Chen

// Date : 2014-10-09

/**********************************************************************************

* 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.

**********************************************************************************/

#include <stdlib.h>

#include <time.h>

#include <iostream>

#include <vector>

#include <string>

#include <algorithm>

using namespace std;

// The recursive way is quite simple.

// 1) break the string to two parts:

// s1[0..j] s1[j+1..n]

// s2[0..j] s2[j+1..n]

// 2) then

// isScramble(s1[0..j], s2[0..j]) && isScramble(s1[j+1..n], s2[j+1..n])

// OR

// isScramble(s1[0..j], s2[j+1, n]) && isScramble(s1[j+1..n], s2[0..j])

bool isScramble_recursion(string s1, string s2) {

if (s1.size()!= s2.size() || s1.size()==0 || s2.size()==0) {

return false;

}

if (s1 == s2){

return true;

}

string ss1 = s1;

string ss2 = s2;

sort(ss1.begin(), ss1.end());

sort(ss2.begin(), ss2.end());

if (ss1 != ss2 ) {

return false;

}

for (int i=1; i<s1.size(); i++) {

if ( isScramble_recursion(s1.substr(0,i), s2.substr(0,i)) &&

isScramble_recursion(s1.substr(i, s1.size()-i), s2.substr(i, s2.size()-i)) ) {

return true;

}

if ( isScramble_recursion(s1.substr(0,i), s2.substr(s2.size()-i, i)) &&

isScramble_recursion(s1.substr(i, s1.size()-i), s2.substr(0, s2.size()-i)) ) {

return true;

}

return false;

}

* Definition

* dp[k][i][j] means:

* a) s1[i] start from 'i'

* b) s2[j] start from 'j'

* c) 'k' is the length of substring

* Initialization

* dp[1][i][j] = (s1[i] == s2[j] ? true : false)

* Formula

* same as the above recursive method idea

* dp[k][i][j] =

* dp[divk][i][j] && dp[k-divk][i+divk][j+divk] ||

* dp[divk][i][j+k-divk] && dp[k-divk][i+divk][j]

* `divk` mean split the k to two parts, so 0 <= divk <= k;

bool isScramble_dp(string s1, string s2) {

if (s1.size()!= s2.size() || s1.size()==0 || s2.size()==0) {

return false;

}

if (s1 == s2){

return true;

}

const int len = s1.size();

// dp[len+1][len][len]

vector< vector< vector<bool> > > dp(len+1, vector< vector<bool> >(len, vector<bool>(len) ) );

// ignor the k=0, just for readable code.

// initialization k=1

for (int i=0; i<len; i++){

for (int j=0; j<len; j++) {

dp[1][i][j] = (s1[i] == s2[j]);

}

// start from k=2 to len, O(n^4) loop.

for (int k=2; k<=len; k++){

for (int i=0; i<len-k+1; i++){

for (int j=0; j<len-k+1; j++){

dp[k][i][j] = false;

for (int divk = 1; divk < k && dp[k][i][j]==false; divk++){

dp[k][i][j] = ( dp[divk][i][j] && dp[k-divk][i+divk][j+divk] ) ||

( dp[divk][i][j+k-divk] && dp[k-divk][i+divk][j] );

}

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

}

bool isScramble(string s1, string s2) {

srand(time(0));

if (random()%2) {

cout << "---- recursion ---" << endl;

return isScramble_recursion(s1, s2);

}

cout << "---- dynamic programming ---" << endl;

return isScramble_dp(s1, s2);

}

int main(int argc, char** argv)

{

string s1="great", s2="rgtae";

if (argc>2){

s1 = argv[1];

s2 = argv[2];

}

cout << s1 << ", " << s2 << endl;

cout << isScramble(s1, s2) << endl;

return 0;

}

leetcode-1/src/scrambleString/scrambleString.cpp at master · daction/leetcode-1 · GitHub

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