97. Interleaving String LeetCode Solution | Easy Approach

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Given strings s1s2, 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 they are divided into non-empty substrings 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.

Example 1:

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

Example 2:

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

Example 3:

Input: s1 = "", s2 = "", s3 = ""
Output: true

Constraints:

  • 0 <= s1.length, s2.length <= 100
  • 0 <= s3.length <= 200
  • s1s2, and s3 consist of lowercase English letters.

Follow up: Could you solve it using only O(s2.length) additional memory space?

Interleaving StringSolutions

Time: $O(mn)$
Space:$O(mn)$

C++

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];
  }
};

Java

 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];
  }
}

Python

 
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[i][j] := true if s3[0..i + j) is formed by the interleaving of
    #             s1[0..i) and s2[0..j)
    dp = [[False] * (n + 1) for _ in range(m + 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]

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