Problem: Interleaving String

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`.


Python solution:
import math
import itertools
import bisect
import collections
import string
import heapq
import functools
import sortedcontainers
from typing import List, Dict, Tuple, Iterator

class Solution:
  def isInterleave(self, s1: str, s2: str, s3: str) -> bool:
    m = len(s1)
    n = len(s2)
    if m + n != len(s3):
      return False

    dp=[]
    for _ in range(m + 1):
      dp.append([False] * (n + 1))
    dp[0][0] = True

    for i in range(1, m + 1):
      dp[i][0] = dp[i - 1][0] and s1[i - 1] == s3[i - 1]

    for j in range(1, n + 1):
      dp[0][j] = dp[0][j - 1] and s2[j - 1] == s3[j - 1]

    for i in range(1, m + 1):
      for j in range(1, n + 1):
        dp[i][j] = (dp[i - 1][j] and s1[i - 1] == s3[i + j - 1]) or (dp[i][j - 1] and s2[j - 1] == s3[i + j - 1])

    return dp[m][n]


Java solution:
class Solution {
  public boolean isInterleave(String s1, String s2, String s3) {
    final int m = s1.length();
    final int n = s2.length();
    if (m + n != s3.length())
      return false;

    // dp[i][j] := true if s3[0..i + j) is formed by the interleaving of
    // s1[0..i) and s2[0..j)
    boolean[][] dp = new boolean[m + 1][n + 1];
    dp[0][0] = true;

    for (int i = 1; i <= m; ++i)
      dp[i][0] = dp[i - 1][0] && s1.charAt(i - 1) == s3.charAt(i - 1);

    for (int j = 1; j <= n; ++j)
      dp[0][j] = dp[0][j - 1] && s2.charAt(j - 1) == s3.charAt(j - 1);

    for (int i = 1; i <= m; ++i)
      for (int j = 1; j <= n; ++j)
        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[m][n];
  }
}


C++ solution:
class Solution {
 public:
  bool isInterleave(string s1, string s2, string s3) {
    const int m = s1.length();
    const int n = s2.length();
    if (m + n != s3.length())
      return false;

    // dp[i][j] := true if s3[0..i + j) is formed by the interleaving of
    // s1[0..i) and s2[0..j)
    vector<vector<bool>> dp(m + 1, vector<bool>(n + 1));
    dp[0][0] = true;

    for (int i = 1; i <= m; ++i)
      dp[i][0] = dp[i - 1][0] && s1[i - 1] == s3[i - 1];

    for (int j = 1; j <= n; ++j)
      dp[0][j] = dp[0][j - 1] && s2[j - 1] == s3[j - 1];

    for (int i = 1; i <= m; ++i)
      for (int j = 1; j <= n; ++j)
        dp[i][j] = dp[i - 1][j] && s1[i - 1] == s3[i + j - 1] ||
                   dp[i][j - 1] && s2[j - 1] == s3[i + j - 1];

    return dp[m][n];
  }
};