Submission #1227070

#	Time	Username	Problem	Language	Result	Execution time	Memory
1227070		cpdreamer	Boat (APIO16_boat)	C++20	100 / 100	1912 ms	36944 KiB

boat

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

const long long INF = 1e17;
using ll = long long;
const ll MOD = 1e9 + 7;

inline ll add(ll a, ll b) {
    a += b;
    if (a >= MOD) a -= MOD;
    return a;
}

inline ll mul(ll a, ll b) {
    return (a * b) % MOD;
}

inline ll dif(ll a, ll b) {
    a -= b;
    if (a < 0) a += MOD;
    return a;
}

ll binpow(ll a, ll b) {
    ll res = 1;
    a %= MOD;
    while (b > 0) {
        if (b & 1) res = mul(res, a);
        a = mul(a, a);
        b >>= 1;
    }
    return res;
}

inline ll mod_inv(ll a) {
    return binpow(a, MOD - 2);
}

ll v[2000][2000];
ll fact[2000], invfact[2000];
ll ncr[2000][2000];
ll ncr_i[2000][2000];
ll dp[2000][2000];

inline ll perm_range(ll a, ll b) {
    ll x = 1;
    for (ll i = a + 1; i <= b; ++i) x = mul(x, i);
    return x;
}

void precompute_factorials(int n) {
    fact[0] = invfact[0] = 1;
    for (int i = 1; i <= n; ++i) {
        fact[i] = mul(fact[i - 1], i);
        invfact[i] = mod_inv(fact[i]);
    }
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= i; ++j) {
            ncr[i][j] = mul(fact[i], mul(invfact[j], invfact[i - j]));
        }
    }
}

ll f(int n, ll A[], ll B[]) {
    precompute_factorials(n);
    vector<ll> vp;
    for (int i = 0; i < n; ++i) {
        vp.push_back(A[i]);
        vp.push_back(B[i]);
    }
    sort(vp.begin(), vp.end());
    vp.erase(unique(vp.begin(), vp.end()), vp.end());

    vector<ll> l, r;
    for (size_t i = 0; i + 1 < vp.size(); ++i) {
        l.push_back(vp[i]); r.push_back(vp[i]);
        if (vp[i] + 1 <= vp[i + 1] - 1) {
            l.push_back(vp[i] + 1);
            r.push_back(vp[i + 1] - 1);
        }
    }
    l.push_back(vp.back());
    r.push_back(vp.back());

    int m = l.size();

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            v[i][j] = (A[i] <= l[j] && r[j] <= B[i]);
        }
    }

    for (int j = 0; j <= n; ++j) {
        for (int i = 0; i < m; ++i) {
            if (j > r[i] - l[i] + 1) {
                ncr_i[i][j] = 0;
            } else {
                ll len = r[i] - l[i] + 1;
                ll x = perm_range(len - j, len);
                ncr_i[i][j] = mul(x, invfact[j]);
            }
        }
    }

    static ll x[501][501];
    for (int j = 0; j < m; ++j) {
        for (int i = 0; i <= n; ++i) {
            x[i][0] = r[j] - l[j] + 1;
            for (int g = 1; g <= n; ++g) {
                x[i][g] = add(x[i][g - 1], mul(ncr[i][g], ncr_i[j][g + 1]));
            }
        }
        dp[0][j] = v[0][j] ? r[j] - l[j] + 1 : 0;
        if (j > 0) dp[0][j] = add(dp[0][j], dp[0][j - 1]);

        for (int i = 1; i < n; ++i) {
            int c = 0;
            dp[i][j] = 0;
            if (v[i][j]) {
                for (int g = i - 1; g >= 0; --g) {
                    if (j > 0) {
                        dp[i][j] = add(dp[i][j], mul(dp[g][j - 1], x[c][c]));
                    }
                    if (v[g][j]) ++c;
                }
                dp[i][j] = add(dp[i][j], x[c][c]);
            }
            if (j > 0) dp[i][j] = add(dp[i][j], dp[i][j - 1]);
        }
    }

    ll ans = 0;
    for (int i = 0; i < n; ++i) ans = add(ans, dp[i][m - 1]);
    return ans;
}

void solve() {
    int n;
    cin >> n;
    ll A[501], B[501];
    for (int i = 0; i < n; ++i) cin >> A[i] >> B[i];
    cout << f(n, A, B) << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    solve();
    return 0;
}

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