[20251215] BOJ / P4 / Tourists / 권혁준 #1680
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🧷 문제 링크
https://www.acmicpc.net/problem/13059
🧭 풀이 시간
15분
👀 체감 난이도
✏️ 문제 설명
정점 N개인 트리가 주어진다. x<y이면서 y가 x의 배수인 모든 (x,y) 쌍에 대해, x에서 y를 잇는 경로 상의 모든 정점 수를 합한 값을 구해보자.
🔍 풀이 방법
x = i인 쌍의 개수는 약 N/i개이다.
따라서 전체 쌍의 개수는 N + N/2 + N/3 + ... + N/N이고, 이는 O(NlogN)에 떨어진다. ->
harmonic lemma어떤 쌍에 대한 경로상의 정점 수를
희소 배열로 O(logN)에 구할 수 있으므로 전체 시간복잡도 O(Nlog^2N)에 해결할 수 있다.⏳ 회고
알면 쉬운 문제