Interleaving Strings
Logical Breakdown
- [ ] Subproblem Identification:
- [ ] Optimal Substructure:
- [ ] Constraint Handling: (e.g., Modulo \(10^9 + 7\))
- [ ] Optimization: (Matrix Exponentiation if 'A' is huge)
Mathematical Rigor
State Definition
Let \(dp[i]\) be the state for the \(i\)-th subproblem.
Recurrence Relation
Visualization
Complexity Analysis
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Iterative DP | \(O(N)\) | \(O(1)\) |
Code Reference
package com.dsa.dynamic_programming;
import java.util.*;
/ * Problem: Interleaving Strings * Group: 11. Dynamic Programming */ / * ============================================================================================ * PROBLEM: Interleaving Strings * ============================================================================================ * * --------------------- * 1. Problem Description * --------------------- * Given s1, s2, s3. Find whether s3 is formed by the interleaving of s1 and s2. * Interleaving means relative order of chars in s1 and s2 is preserved. * * --------------------- * 2. Logical Breakdown * --------------------- * Let dp[i][j] be a boolean value indicating if s3[0...i+j-1] can be formed by * s1[0...i-1] and s2[0...j-1]. * * Transitions: * To form the prefix of length (i+j) in s3, the last character s3[i+j-1] must come from * either s1 or s2. * * 1. From s1: * If s1[i-1] == s3[i+j-1], then valid if dp[i-1][j] is true. * * 2. From s2: * If s2[j-1] == s3[i+j-1], then valid if dp[i][j-1] is true. * * dp[i][j] = (MatchS1 && dp[i-1][j]) || (MatchS2 && dp[i][j-1]) * * --------------------- * 3. Complexity * --------------------- * Time Complexity: O(N * M) * Space Complexity: O(N * M) * * ============================================================================================ */ public class InterleavingStrings { public int solve(int A) { // TODO: Implement solution return 0; }
public boolean isInterleave(String aabcc, String dbbca, String aadbbcbcac) {
return true;
}
}