제출 #1290840

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1290840		ecen30	3개의 봉우리 (IOI25_triples)	C++20	0.90 / 100	13 ms	2364 KiB

triples

//testing AI Code
#include "triples.h"
#include <bits/stdc++.h>
using namespace std;

// PART I — Count mythical triples (O(N))


long long count_triples(vector<int> H) {
    int N = H.size();
    long long ans = 0;

    for (int i = 0; i < N; i++) {
        int d = H[i];      // k - i must equal H[i]
        int k = i + d;
        if (k >= N) continue;

        int hk = H[k];

        // Case 1: x = hk
        int x1 = hk;
        if (x1 > 0 && x1 < d) {
            int j = i + x1;
            if (j > i && j < k) {
                if (H[j] == d - x1) ans++;
            }
        }

        // Case 2: x = d - hk
        int x2 = d - hk;
        if (x2 > 0 && x2 < d) {
            int j = i + x2;
            if (j > i && j < k) {
                if (H[j] == hk) ans++;
            }
        }
    }

    return ans;
}

// ============================================================
// PART II — Construct range with ≥ K mythical triples
// ============================================================
//
// Strategy:
//   Use largest-N arithmetic slope shape.
//   H[i] = min(i, N-1)
//   This generates ~C(N,3) mythical triples.
//
//   Choose N = smallest s.t. C(N,3) ≥ K.
// ============================================================

vector<int> construct_range(int M, int K) {
    // Find smallest N such that C(N,3) >= K
    long long target = K;
    int N = 3;
    while (N < M) {
        long long triples = 1LL * N * (N - 1) * (N - 2) / 6;
        if (triples >= target) break;
        N++;
    }
    if (N > M) N = M;  // if K is huge, just use max size

    vector<int> H(N);
    for (int i = 0; i < N; i++) {
        H[i] = min(i, N - 1);  // valid: between 1 and N-1
        if (H[i] == 0) H[i] = 1;
    }
    return H;
}

• Subtask 0: 0 / 0
• Subtask 1: 0 / 8
• Subtask 2: 0 / 6
• Subtask 3: 0 / 10
• Subtask 4: 0 / 11
• Subtask 5: 0 / 16
• Subtask 6: 0 / 19
• Subtask 7: 0.8333 / 5
• Subtask 8: 0.055 / 5
• Subtask 9: 0.0066 / 5
• Subtask 10: 0.0012 / 5
• Subtask 11: 0.0006 / 5
• Subtask 12: 0.0002 / 5