CustomCC0-1.0#cpq002-8771700

Lowest Absent Number in Ranges

Summary

•Phase 1 / mo-algorithm, sqrt-decomposition
•Reasoning-first competitive programming drill

Problem Description

Given an array A of N positive integers, answer Q queries. Each query provides indices L and R. For each query, find the smallest positive integer not present in the subarray A[L..R]. How to read this problem in plain language: - This is a Phase 1 reasoning drill focused on mo-algorithm, sqrt-decomposition. - Typical lenses to test first: mo-algorithm, range-query, mex. - Constraints reminder: 1 <= N, Q <= 1e5; 1 <=

A_{i}

<= N; 1 <= L <= R <= 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, Q <= 1e5; 1 <= $A_{i}$ <= N; 1 <= L <= R <= 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.

mo-algorithmrange-querymex