Regular Expression Match
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: Regular Expression Match * Group: 11. Dynamic Programming */ / * ============================================================================================ * PROBLEM: Regular Expression Match (Wildcard Matching) * ============================================================================================ * * --------------------- * 1. Problem Description * --------------------- * Implement matching for: * '?' : Matches any single character. * '' : Matches any sequence of characters (including empty). * * --------------------- * 2. Logical Breakdown * --------------------- * Let dp[i][j] = boolean (Is match possible for String S[0..i-1] and Pattern P[0..j-1]?) * * Logic: * 1. If P[j-1] == '?' or S[i-1] == P[j-1]: * Match single char. * dp[i][j] = dp[i-1][j-1] * * 2. If P[j-1] == '': * Two choices: * a) '' matches Empty Sequence: We ignore '' and look at P[0..j-2]. * -> dp[i][j-1] * b) '' matches Current Char S[i-1] (and possibly more before it): * -> dp[i-1][j] * dp[i][j] = dp[i][j-1] || dp[i-1][j] * * Base Cases: * dp[0][0] = true. * dp[i][0] = false (Pattern empty, string not). * dp[0][j] = depends (True only if P[0..j-1] is all '') * * ============================================================================================ */ public class RegularExpressionMatch { public int solve(int A) { // TODO: Implement solution return 0; }
public int isMatch(String aa, String s) {
return 1;
}
}