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Constrained Palindromic Split

Thinking Mode

Summary

  • •Phase 4 / palindromes/dp/partition
  • •Reasoning-first competitive programming drill

Problem Description

Given a string S of length N, partition it into the minimum number of contiguous substrings such that each substring is a palindrome and no substring is longer than K. Output the minimum number of cuts needed. How to read this problem in plain language: - This is a Phase 4 reasoning drill focused on palindromes/dp/partition. - Typical lenses to test first: dynamic programming, palindrome, partition. - Constraints reminder: 1 ≤ N≤3,000; 1 ≤ K≤N Mini examples for mental simulation: 1) Boundary example: Describe why this case is tricky. Explain expected behavior and why naive logic may fail. 2) Adversarial example: Adversarial case where naive greedy/local decision looks correct but fails globally. Lite-mode writing target: - Write 1~2 observations that shrink the search space. - Name one final algorithm and state target complexity explicitly. - Validate with at least 2 edge cases and one hand simulation.

Constraints

  • •
    1 ≤ N≤3,000; 1 ≤ K≤N

Analysis

Key Insight

Use this hint to refine your reasoning. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.

dynamic programmingpalindromepartition
dynamic programmingpalindromepartition