Repeating Subsequence

Logical Breakdown

• [ ] Subproblem Identification:
• [ ] Optimal Substructure:
• [ ] Constraint Handling: (e.g., Modulo \(10^9 + 7\))
• [ ] Optimization: (Matrix Exponentiation if 'A' is huge)

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Mathematical Rigor

State Definition

Let \(dp[i]\) be the state for the \(i\)-th subproblem.

Recurrence Relation

\[ dp[i] = ... \]

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Visualization

graph TD A["Current State"] --> B["Previous State 1"] A --> C["Previous State 2"]

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Complexity Analysis

Approach	Time Complexity	Space Complexity
Iterative DP	\(O(N)\)	\(O(1)\)

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Code Reference

package com.dsa.dynamic_programming;

import java.util.*;

/ * Problem: Repeating Subsequence * Group: 11. Dynamic Programming */ / * ============================================================================================ * PROBLEM: Repeating Subsequence * ============================================================================================ * * --------------------- * 1. Problem Description * --------------------- * Check if a string has any subsequence that appears at least twice. * Condition: The i-th character of the first subsequence and j-th character of the * second subsequence must satisfy i != j in the original string. * * --------------------- * 2. Logical Breakdown * --------------------- * This is a variation of LCS. * We find the LCS of the string with ITSELF (LCS(S, S)). * * Modified Condition: * When matching S[i] and S[j], we usually add 1 if chars are equal. * Here, we add 1 ONLY IF (S[i] == S[j] AND i != j). * * If the length of this modified LCS >= 2, return 1 (True), else 0 (False). * (Usually problem asks for length or boolean exists). * * ============================================================================================ */ public class RepeatingSubsequence { public int solve(int A) { // TODO: Implement solution return 0; }

public int anyRepeating(String aabebcdd) {
    return 1;
}

}