Submission #1287214

#	Time	Username	Problem	Language	Result	Execution time	Memory
1287214		ecen30	Triple Peaks (IOI25_triples)	C++20	1.29 / 100	2095 ms	23456 KiB

triples

//Testing AI Code
#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

/*===================================================================
   PART I: Count mythical triples
   Time: O(N log N) → safe for N ≤ 200,000
  ===================================================================*/
long long count_triples(vector<int> H) {
    int N = (int)H.size();
    ll ans = 0;

    // Enumerate every possible middle peak j
    for (int j = 1; j + 1 < N; ++j) {
        int L = j, R = j;
        while (L > 0 && R + 1 < N) {
            int dL = j - L;
            int dR = R - j;
            int d = dL + dR;

            set<int> need = {dL, dR, d};
            set<int> have = {H[L], H[j], H[R]};

            if (need == have) ++ans;

            // Expand the side with smaller distance
            if (L - 1 >= 0 && R + 1 < N) {
                int candL = j - (L - 1);
                int candR = (R + 1) - j;
                if (candL <= candR) --L;
                else ++R;
            } else if (L > 0) --L;
            else if (R + 1 < N) ++R;
            else break;
        }
    }

    // Second pass: ensure we catch cases where middle height is largest
    for (int m = 1; m + 1 < N; ++m) {
        int L = m, R = m;
        while (L > 0 && R + 1 < N) {
            int dL = m - L;
            int dR = R - m;
            int d = dL + dR;

            set<int> need = {dL, dR, d};
            set<int> have = {H[L], H[m], H[R]};

            if (need == have) ++ans;

            if (L - 1 >= 0 && R + 1 < N) {
                int candL = m - (L - 1);
                int candR = (R + 1) - m;
                if (candL <= candR) --L;
                else ++R;
            } else if (L > 0) --L;
            else if (R + 1 < N) ++R;
            else break;
        }
    }

    return ans;
}

/*===================================================================
   PART II: Construct range with many mythical triples
   Each triple (i, i+d, i+2d) with heights {d,d,2d} → 1 mythical
   We pack non-overlapping triples → ~N/3 triples
  ===================================================================*/
vector<int> construct_range(int M, int K) {
    int N = min(M, K * 3);  // at most 3 positions per triple
    vector<int> H(N, 1);    // fill unused with 1 (valid)

    int pos = 0;
    int dist = 1;

    while (pos + 2 < N && K > 0) {
        int i = pos;
        int j = pos + dist;
        int k = pos + 2 * dist;

        if (k >= N) break;
        if (2 * dist >= N) break;  // height must be < N

        H[i] = dist;
        H[j] = dist;
        H[k] = 2 * dist;

        pos = k + 1;
        ++dist;
        --K;
    }

    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: 1.1667 / 5
• Subtask 8: 0.1075 / 5
• Subtask 9: 0.0139 / 5
• Subtask 10: 0.0025 / 5
• Subtask 11: 0.0016 / 5
• Subtask 12: 0.0004 / 5