97. Interleaving String

• categories: Code, Interview Question, leetcode, Medium
• source: https://leetcode.com/problems/interleaving-string
• topics: Dynamic Programming

Description

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

An interleaving of two strings s and t is a configuration where s and t are divided into n and m 

substrings

 respectively, such that:

• s = s1 + s2 + ... + sn
• t = t1 + t2 + ... + tm
• |n - m| <= 1
• The interleaving is s1 + t1 + s2 + t2 + s3 + t3 + ... or t1 + s1 + t2 + s2 + t3 + s3 + ...

Note: a + b is the concatenation of strings a and b.

Idea

• Top-Down Recursion with memorization using 2 indices

Code

class Solution:
    def isInterleave(self, s1: str, s2: str, s3: str) -> bool:
        @cache
        def dp(t, i, j):
            if t == 1:
                return i == 1 and s1[0] == s3[0] or j == 1 and s2[0] == s3[0]
            return (
                    i > 0 and s3[t-1] == s1[i-1] and dp(t-1, i-1, j) or 
                    j > 0 and s3[t-1] == s2[j-1] and dp(t-1, i, j-1)
                   )  
 
        if len(s1) + len(s2) != len(s3):
            return False
 
        if len(s1) == len(s2) == len(s3) == 0:
            return True 
 
        return dp(len(s3), len(s1), len(s2))