Submission #1249897

#	Time	Username	Problem	Language	Result	Execution time	Memory
1249897		kduckp	Triple Peaks (IOI25_triples)	C++20	15.33 / 100	2096 ms	20336 KiB

triples

#include "triples.h"
#include <vector>
#include <algorithm>
#include <unordered_map>
#include <map>
using namespace std;

long long count_triples(vector<int> H) {
    int n = H.size();
    long long res = 0;
    
    if (n <= 100) {
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                for (int k = j + 1; k < n; ++k) {
                    vector<int> h = {H[i], H[j], H[k]};
                    vector<int> d = {j - i, k - i, k - j};
                    sort(h.begin(), h.end());
                    sort(d.begin(), d.end());
                    if (h == d) res++;
                }
            }
        }
        return res;
    }
    
    bool small_values = true;
    for (int height : H) {
        if (height > 10) {
            small_values = false;
            break;
        }
    }
    
    if (small_values) {
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n && j <= i + 10; ++j) {
                for (int k = j + 1; k < n && k <= i + 20; ++k) {
                    vector<int> h = {H[i], H[j], H[k]};
                    vector<int> d = {j - i, k - i, k - j};
                    sort(h.begin(), h.end());
                    sort(d.begin(), d.end());
                    if (h == d) res++;
                }
            }
        }
        return res;
    }
    
    if (n <= 2000) {
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                for (int k = j + 1; k < n; ++k) {
                    vector<int> h = {H[i], H[j], H[k]};
                    vector<int> d = {j - i, k - i, k - j};
                    sort(h.begin(), h.end());
                    sort(d.begin(), d.end());
                    if (h == d) res++;
                }
            }
        }
        return res;
    }
    
    bool is_non_decreasing = true;
    for (int i = 1; i < n; i++) {
        if (H[i] < H[i-1]) {
            is_non_decreasing = false;
            break;
        }
    }
    
    if (is_non_decreasing) {
        unordered_map<int, vector<int>> pos;
        for (int i = 0; i < n; i++) {
            pos[H[i]].push_back(i);
        }
        
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int d_ij = j - i;
                
                for (auto& [height, positions] : pos) {
                    auto it = upper_bound(positions.begin(), positions.end(), j);
                    for (; it != positions.end(); ++it) {
                        int k = *it;
                        vector<int> h = {H[i], H[j], height};
                        vector<int> d = {d_ij, k - i, k - j};
                        sort(h.begin(), h.end());
                        sort(d.begin(), d.end());
                        if (h == d) res++;
                    }
                }
            }
        }
        return res;
    }
    
    if (n <= 50000) {
        unordered_map<int, vector<int>> pos;
        for (int i = 0; i < n; i++) {
            pos[H[i]].push_back(i);
        }
        
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int d_ij = j - i;
                
                for (auto& [height, positions] : pos) {
                    auto it = upper_bound(positions.begin(), positions.end(), j);
                    for (; it != positions.end(); ++it) {
                        int k = *it;
                        vector<int> h = {H[i], H[j], height};
                        vector<int> d = {d_ij, k - i, k - j};
                        sort(h.begin(), h.end());
                        sort(d.begin(), d.end());
                        if (h == d) res++;
                    }
                }
            }
        }
        return res;
    }
    
    unordered_map<int, vector<int>> pos;
    for (int i = 0; i < n; i++) {
        pos[H[i]].push_back(i);
    }
    
    int limit = 10000;
    for (int i = 0; i < min(n, limit); i++) {
        for (int j = i + 1; j < min(n, i + limit/10); j++) {
            int d_ij = j - i;
            
            for (auto& [height, positions] : pos) {
                if (height > 2 * d_ij) continue;
                
                auto it = upper_bound(positions.begin(), positions.end(), j);
                int count = 0;
                for (; it != positions.end() && count < 100; ++it, ++count) {
                    int k = *it;
                    if (k >= i + limit/5) break;
                    
                    vector<int> h = {H[i], H[j], height};
                    vector<int> d = {d_ij, k - i, k - j};
                    sort(h.begin(), h.end());
                    sort(d.begin(), d.end());
                    if (h == d) res++;
                }
            }
        }
    }
    
    return res;
}

vector<int> construct_range(int M, int K) {
    vector<int> result;
    
    if (M == 20 && K == 30) {
        result = {1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2};
    }
    else if (M == 500 && K == 2000) {
        for (int cycle = 0; cycle < 100; cycle++) {
            for (int h = 1; h <= 5 && result.size() < M; h++) {
                result.push_back(h);
            }
        }
    }
    else if (M == 5000 && K == 50000) {
        for (int cycle = 0; cycle < 200; cycle++) {
            for (int h = 1; h <= 25 && result.size() < M; h++) {
                result.push_back(h);
            }
        }
    }
    else if (M == 30000 && K == 700000) {
        for (int cycle = 0; cycle < 1000; cycle++) {
            for (int h = 1; h <= 30 && result.size() < M; h++) {
                result.push_back(h);
            }
        }
    }
    else if (M == 100000 && K == 2000000) {
        for (int cycle = 0; cycle < 2500; cycle++) {
            for (int h = 1; h <= 40 && result.size() < M; h++) {
                result.push_back(h);
            }
        }
    }
    else if (M == 200000 && K == 12000000) {
        for (int cycle = 0; cycle < 4000; cycle++) {
            for (int h = 1; h <= 50 && result.size() < M; h++) {
                result.push_back(h);
            }
        }
    }
    else {
        for (int i = 0; i < M && i < 3; i++) {
            result.push_back(i + 1);
        }
        while (result.size() < M) {
            result.push_back(1);
        }
    }
    
    long long actual_count = count_triples(result);
    
    return result;
}

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