Submission #172397

#	Time	Username	Problem	Language	Result	Execution time	Memory
172397		rama_pang	Boat (APIO16_boat)	C++14	9 / 100	466 ms	4472 KiB

boat

#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;

int power(int n, int x) {
    if (x == 0) {
        return 1;
    }
    int res = power(n, x / 2);
    res = (1ll * res * res) % MOD;
    if (x & 1) {
        res = (1ll * res * n) % MOD;
    }
    return res;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);

    int N;
    cin >> N;

    vector<int> A(N + 1);
    vector<int> B(N + 1);
    vector<int> X;
    vector<int> L;
    vector<int> inv(N + 1); // inc[i] = inverse of integer i
    
    for (int i = 1; i <= N; i++) {
        cin >> A[i] >> B[i];
        X.emplace_back(A[i]);
        X.emplace_back(B[i] + 1);
        inv[i] = power(i, MOD - 2); // Fermatt's Little Theorem
    }

    sort(begin(X), end(X));
    X.resize(unique(begin(X), end(X)) - begin(X));

    for (int i = 1; i <= N; i++) {
        A[i] = upper_bound(begin(X), end(X), A[i]) - begin(X);
        B[i] = upper_bound(begin(X), end(X), B[i]) - begin(X);
    }

    L.resize(X.size());
    for (int i = 1; i < X.size(); i++) {
        L[i] = X[i] - X[i - 1];
    }

    vector<vector<int>> DP(N + 1, vector<int>(X.size() + 1, 0));
    vector<vector<int>> Choose(X.size() + 1, vector<int>(N + 1, 0));

    for (int i = 1; i < X.size(); i++) {
        Choose[i][0] = 1;
        for (int j = 1; j <= N; j++) {
            Choose[i][j] = (1ll * Choose[i][j - 1] * (L[i] - j + 1) % MOD) * inv[j] % MOD; // Choose j items from a total of L[i] items
        }
    }

    for (int i = 0; i < X.size(); i++) {
        DP[0][i] = 1;
    }

    for (int i = 1; i <= N; i++) {
        DP[i][0] = 1;
        for (int j = 1; j < X.size(); j++) {
            DP[i][j] = DP[i][j - 1];
            for (int k = i, cnt = 0, choose = 0; k > 0; k--) {
                if (A[k] <= j && j <= B[k]) {
                    cnt++;
                    choose = (1ll * choose + Choose[j][cnt]) % MOD; // Equal to: if we fix the current item, how many ways of using already proccesed items in which all of them is in interval j
                    DP[i][j] = (1ll * DP[i][j] + (1ll * choose * DP[k - 1][j - 1]) % MOD) % MOD;
                }
            }
        }
    }

    cout << (DP[N][X.size() - 1] - 1 + MOD) % MOD << "\n";
    return 0;
}

Compilation message (stderr)

boat.cpp: In function 'int main()':
boat.cpp:46:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 1; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:53:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 1; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:60:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < X.size(); i++) {
                     ~~^~~~~~~~~~
boat.cpp:66:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int j = 1; j < X.size(); j++) {
                         ~~^~~~~~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 0 / 22
• Subtask 3: 0 / 27
• Subtask 4: 0 / 42