Submission #1249701

#	Time	Username	Problem	Language	Result	Execution time	Memory
1249701		jerry	Triple Peaks (IOI25_triples)	C++20	11 / 100	205 ms	82084 KiB

triples

#include "triples.h"

#include <unordered_map>
#include <unordered_set>

long long count_easy_triples(const std::vector<int>& h) {
    const int n = static_cast<int>(h.size());
    std::vector<std::tuple<int, int, int>> triples;

    for (int i = 0; i < n; i++) {
        for (int j : {i - h[i], i + h[i]}) {
            if (j < 0 || j >= n)
                continue;
            for (int k : {j - h[j], j + h[j]}) {
                if (k < 0 || k >= n)
                    continue;
                if (h[k] == abs(k - i)) {
                    triples.emplace_back(i, j, k);
                }
            }
            for (int k : {i - h[j], i + h[j]}) {
                if (k < 0 || k >= n)
                    continue;
                if (h[k] == abs(k - j)) {
                    triples.emplace_back(i, j, k);
                }
            }
        }
    }

    std::unordered_set<long long> deduped;
    for (const auto& [i, j, k] : triples)
        if (i != j && i != k && j != k) {
            std::vector<int> vals{i, j, k};
            std::sort(vals.begin(), vals.end());
            deduped.insert(1ll * n * n * vals[0] + 1ll * n * vals[1] + vals[2]);
        }
    return deduped.size();
}

long long count_hard_triples(const std::vector<int>& h) {
    const int n = static_cast<int>(h.size());
    std::unordered_map<int, std::unordered_map<int, int>> plus_groups;
    std::unordered_map<int, std::unordered_map<int, int>> minus_groups;
    for (int i = 0; i < n; i++) {
        plus_groups[i + h[i]].emplace(h[i], i);
        minus_groups[i - h[i]].emplace(h[i], i);
    }

    long long ans = 0;
    for (int j = 0; j < n; j++) {
        const auto& i_cands = minus_groups[j - h[j]];
        const auto& k_cands = plus_groups[j + h[j]];
        const auto& small = i_cands.size() < k_cands.size() ? i_cands : k_cands;
        for (const auto& [ival, i] : small)
            for (const auto& k : {j - h[i], j + h[i]})
                if (k >= 0 && k < n && h[k] == std::abs(j - i)
                        && h[i] != std::abs(j - i) && h[i] != std::abs(k - i)
                        && h[j] != std::abs(j - i) && h[j] != std::abs(k - j)
                        && h[k] != std::abs(k - i) && h[k] != std::abs(k - j)
                        && ((i < j && j < k) || (i > j && j > k)))
                    ans++;
    }
    return ans;
}

long long count_triples(std::vector<int> h) {
    return count_easy_triples(h) + count_hard_triples(h);
}

std::vector<int> construct_range(int M, int K) {
    return {0};
}

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