LeetCode - Interleaving String

4 minute read

Problem description

description

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.

Example 1:

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Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
Output: true

Example 2:

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Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
Output: false

Analysis

The first thought is to use backtrack to get all possible interleaving strings and check if s3 is in it. However, this method will get a TLE.

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class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        HashSet<String> set = new HashSet<>();
        
        int len = s1.length() + s2.length();
        
        if (s3.length() != len){
            return false;
        }
        
        backtrack(set, s1, s2, new StringBuilder(), 0, 0);
        
        return set.contains(s3);
    }
    
    void backtrack(HashSet<String> set, String s1, String s2, StringBuilder sb, int i, int j){
        if (i == s1.length() & j == s2.length()){
            set.add(sb.toString());
            return;
        }
        else if (i == s1.length()){
            set.add(sb.toString() + s2.substring(j));
        }
        else if (j == s2.length()){
            set.add(sb.toString() + s1.substring(i));
        }
        else{
            sb.append(s1.charAt(i));
            backtrack(set, s1, s2, sb, i+1, j);
            sb.deleteCharAt(sb.length() - 1);
            
            
            sb.append(s2.charAt(j));
            backtrack(set, s1, s2, sb, i, j+1);
            sb.deleteCharAt(sb.length() - 1);
        }
    }
}

And then I come up with a solution using two pointers.

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class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        int len = s1.length() + s2.length();
        
        if (s3.length() != len){
            return false;
        }
        
        
        return test(s1, s2, s3, 0 , 0 , 0);
    }
    
    boolean test(String s1, String s2, String s3, int i, int j, int index){
        if (i == s1.length() && j == s2.length()){
            return true;
        }
        else if (i == s1.length()){
            return s3.substring(index).equals(s2.substring(j));
        }
        else if (j == s2.length()){
            return s3.substring(index).equals(s1.substring(i));
        }
        else{
            boolean isS1Match = s1.charAt(i) == s3.charAt(index);
            boolean isS2Match = s2.charAt(j) == s3.charAt(index);
            
            return (isS1Match && test(s1, s2, s3, i+1, j, index+1)) || (isS2Match && test(s1, s2, s3, i, j+1, index+1));
        }
    }
}

But this solution runs in low performance with TC O(2 m+n). m is the length of s1 and n is the length of s2.

So we introduce a memo to save all computed result.

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class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        int len = s1.length() + s2.length();
        
        if (s3.length() != len){
            return false;
        }
        
        int[][] memo = new int[s1.length() + 1][s2.length()+1];
        
        return test(s1, s2,s3, 0 , 0 , 0, memo);
    }
    
    boolean test(String s1, String s2, String s3, int i, int j, int index, int[][] memo){
        if (memo[i][j] != 0){
            return memo[i][j]> 0;
        }
        
        if (i == s1.length() && j == s2.length()){
            return true;
        }
        else if (i == s1.length()){
            boolean res = s3.substring(index).equals(s2.substring(j));
            memo[i][j] = res ? 1:-1;
            return res;
        }
        else if (j == s2.length()){
            boolean res = s3.substring(index).equals(s1.substring(i));
            memo[i][j] = res ? 1:-1;
            return res;
        }
        else{
            boolean isS1Match = s1.charAt(i) == s3.charAt(index);
            boolean isS2Match = s2.charAt(j) == s3.charAt(index);
            
            boolean res = (isS1Match && test(s1, s2, s3, i+1, j, index+1, memo)) || (isS2Match && test(s1, s2, s3, i, j+1, index+1, memo));
            
            memo[i][j] = res ? 1:-1;
                
            return res;
        }
    }
}

And if we can use recursion with memorization, we can also use DP.

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public class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        if (s3.length() != s1.length() + s2.length()) {
            return false;
        }
        boolean dp[][] = new boolean[s1.length() + 1][s2.length() + 1];
        for (int i = 0; i <= s1.length(); i++) {
            for (int j = 0; j <= s2.length(); j++) {
                if (i == 0 && j == 0) {
                    dp[i][j] = true;
                } else if (i == 0) {
                    dp[i][j] = dp[i][j - 1] && s2.charAt(j - 1) == s3.charAt(i + j - 1);
                } else if (j == 0) {
                    dp[i][j] = dp[i - 1][j] && s1.charAt(i - 1) == s3.charAt(i + j - 1);
                } else {
                    dp[i][j] = (dp[i - 1][j] && s1.charAt(i - 1) == s3.charAt(i + j - 1)) || (dp[i][j - 1] && s2.charAt(j - 1) == s3.charAt(i + j - 1));
                }
            }
        }
        return dp[s1.length()][s2.length()];
    }
}

What to improve

  • When do recursion, remember to check if we can use memorization to reduce TC.