Submission #839859

#	Time	Username	Problem	Language	Result	Execution time	Memory
839859		popovicirobert	Boat (APIO16_boat)	C++14	100 / 100	1603 ms	12404 KiB

boat

#include <bits/stdc++.h>
 
using namespace std;

constexpr int MOD = (int) 1e9 + 7;

inline int logpow(int a, int b) {
    int answer = 1;
    while (b > 0) {
        if (b & 1) answer = (1LL * answer * a) % MOD;
        b >>= 1;
        a = (1LL * a * a) % MOD;
    }
    return answer;
}

inline void add(int& x, int y) {
    x += y;
    if (x >= MOD)
        x -= MOD;
}

constexpr int MAXN = 505;

int dp[2][4 * MAXN + 1][MAXN + 1];
int sp[2][4 * MAXN + 1];
 
int main() {
#ifdef HOME
    ifstream cin("input.in");
    ofstream cout("output.out");
#endif
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int n;
    cin >> n;
    
    vector<int> a(n + 1), b(n + 1);
    vector<int> x;

    for (int i = 1; i <= n; i++) {
        cin >> a[i] >> b[i];
        x.push_back(a[i]);
        x.push_back(b[i]);
    }

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

    vector<pair<int, int>> segs;
    segs.push_back({0, 0});

    for (int i = 0; i < (int)x.size(); i++) {
        segs.push_back({x[i], x[i]});
        if (i + 1 < (int)x.size() && x[i] + 1 <= x[i + 1] - 1) {    
            segs.push_back({x[i] + 1, x[i + 1] - 1});
        }
    }

    vector<vector<int>> comb(segs.size(), vector<int>(n + 1));
    for (int i = 0; i < (int)segs.size(); i++) {
        auto s = segs[i];
        int size = s.second - s.first + 1;

        int fact = 1, prod = 1;

        comb[i][0] = 1;
        for (int j = 1; j <= n; j++) {
            if (j > size) {
                comb[i][j] = 0;
                continue;
            }
            prod = (1LL * prod * (size - j + 1)) % MOD;
            fact = (1LL * fact * j) % MOD;
            comb[i][j] = (1LL * logpow(fact, MOD - 2) * prod) % MOD;
        }
    }

    // for (auto itr : segs) {
    //     cerr << itr.first << " " << itr.second << "    "; 
    // }
    // cerr << "\n";

    auto Comb = [&segs, &comb](int j, int k) {
        return segs[j].second - segs[j].first + 1 < k ? 0 : comb[j][k];
    };

    auto Calc = [&segs, &Comb](int i) {
        for (int j = 0; j < (int)segs.size(); j++) {
            for (int k = 1; k <= i + 1; k++) {
                int curr = dp[i & 1][j][k];
                if (curr == 0) continue;

                sp[i & 1][j] = (sp[i & 1][j] + 1LL * Comb(j, k) * curr) % MOD;
            }
        }

        for (int j = 1; j < (int)segs.size(); j++) {
            add(sp[i & 1][j], sp[i & 1][j - 1]);
        }
    };

    dp[0][0][1] = 1;
    Calc(0);

    for (int i = 1; i <= n; i++) {
        memset(sp[i & 1], 0, sizeof(sp[i & 1]));
        memset(dp[i & 1], 0, sizeof(dp[i & 1]));

        for (int j = 0; j < (int)segs.size(); j++) {
            for (int k = 1; k <= i; k++) {
                dp[i & 1][j][k] = dp[1 - i & 1][j][k];
            }
            if (a[i] <= segs[j].first && segs[j].second <= b[i]) {
                add(dp[i & 1][j][1], sp[1 - i & 1][j - 1]);
                for (int k = 1; k <= i; k++) {    
                    add(dp[i & 1][j][k], dp[1 - i & 1][j][k - 1]);
                }
            }
        }

        // for (int j = 0; j < (int)segs.size(); j++) {
        //     cerr << sp[1 - i & 1][j] << " "; 
        // }
        // cerr << "\n";

        // for (int j = 0; j < (int)segs.size(); j++) {
        //     for (int k = 1; k <= i; k++) {
        //         cerr << dp[i & 1][j][k] << " ";
        //     }
        //     cerr << "\n";
        // }
        // cerr << "\n";

        Calc(i);
    }

    cout << (sp[n & 1][(int)segs.size() - 1] + MOD - 1) % MOD;
 
    return 0;
}

Compilation message (stderr)

boat.cpp: In function 'int main()':
boat.cpp:113:40: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  113 |                 dp[i & 1][j][k] = dp[1 - i & 1][j][k];
      |                                      ~~^~~
boat.cpp:116:43: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  116 |                 add(dp[i & 1][j][1], sp[1 - i & 1][j - 1]);
      |                                         ~~^~~
boat.cpp:118:47: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  118 |                     add(dp[i & 1][j][k], dp[1 - i & 1][j][k - 1]);
      |                                             ~~^~~

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