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Submission #1102401

# Submission time Handle Problem Language Result Execution time Memory
1102401 2024-10-18T04:04:53 Z shidou26 Zapina (COCI20_zapina) C++14
110 / 110
 386 ms 3708 KB 
#include <bits/stdc++.h>
using namespace std;

#define endl '\n'

typedef long long ll;

const int MOD = 1e9 + 7;
ll add(ll x, ll y) {return ((x % MOD) + (y % MOD)) % MOD;}
ll prod(ll x, ll y) {return ((x % MOD) * (y % MOD)) % MOD;}
ll sub(ll x, ll y) {return ((x - y) % MOD + MOD) % MOD;}
ll pwer(ll x, ll y) {
    if(y == 0) return 1;
    ll half = pwer(x, y / 2);
    half = prod(half, half);
    if(y & 1) return prod(half, x);
    else return half;
}

const int N = 1e3 + 3;

int n;

ll fact[N + 1], inv[N + 1];

void preprocess() {
    fact[0] = 1;
    for(int i = 1; i <= N; i++) fact[i] = prod(fact[i - 1], i);
    inv[N] = pwer(fact[N], MOD - 2);
    for(int i = N - 1; i >= 0; i--) inv[i] = prod(inv[i + 1], i + 1);
}

ll C(ll k, ll n) {
    if(k > n) return 0;
    return prod(fact[n], prod(inv[k], inv[n - k]));
}

void input() {
    cin >> n;
}

namespace subtask_two {
    ll compute(int mask) {
        ll candies = n, remains = 0, ways = 1;
        for(int i = 0; i < n; i++) {
            if(mask & (1 << i)) {
                ways = prod(ways, C(i + 1, candies));
                candies -= i + 1;
            }else remains++;
        }
        ways = prod(ways, pwer(remains, candies));
        if(candies < 0) return 0;
        else return ways;
    }

    void solve() {
        ll total = pwer(n, n), answer = 0;
        for(int mask = 0; mask < (1 << n); mask++) {
            if(__builtin_popcount(mask) % 2 == 0) answer = add(answer, compute(mask));
            else answer = sub(answer, compute(mask));
        }
        cout << sub(total, answer) << endl;
    }

    bool check() {
        return n <= 20;
    }
}

namespace subtask_three {
    ll dp[N][N][2];

    void solve() {
        dp[0][0][0] = 1;
        for(int i = 1; i <= n; i++) {
            for(int j = 0; j <= n; j++) {
                for(int c = 0; c <= j; c++) {
                    if(c == i)
                        dp[i][j][1] = add(dp[i][j][1], add(prod(dp[i - 1][j - c][0], C(c, j)), prod(dp[i - 1][j - c][1], C(c, j))));
                    else {
                        dp[i][j][0] = add(dp[i][j][0], prod(dp[i - 1][j - c][0], C(c, j)));
                        dp[i][j][1] = add(dp[i][j][1], prod(dp[i - 1][j - c][1], C(c, j)));
                    }
                }
            }
        }
        cout << dp[n][n][1] << endl;
    }

    bool check() {
        return n <= 350;
    }
}

void process() {
    if(subtask_two::check()) return subtask_two::solve(), void();
    if(subtask_three::check()) return subtask_three::solve(), void();
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    preprocess();
    input();
    process();

    return 0;
}

Subtask #1
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 1 ms 336 KB Output is correct
5 Correct 1 ms 336 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 1 ms 336 KB Output is correct
5 Correct 1 ms 336 KB Output is correct
6 Correct 1 ms 336 KB Output is correct
7 Correct 1 ms 336 KB Output is correct
8 Correct 1 ms 336 KB Output is correct
9 Correct 2 ms 336 KB Output is correct
10 Correct 3 ms 336 KB Output is correct
11 Correct 4 ms 336 KB Output is correct
12 Correct 7 ms 480 KB Output is correct
13 Correct 14 ms 476 KB Output is correct
14 Correct 29 ms 476 KB Output is correct
15 Correct 57 ms 336 KB Output is correct
16 Correct 125 ms 336 KB Output is correct

Subtask #3
55.0 / 55.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 1 ms 336 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 1 ms 336 KB Output is correct
5 Correct 1 ms 336 KB Output is correct
6 Correct 1 ms 336 KB Output is correct
7 Correct 1 ms 336 KB Output is correct
8 Correct 1 ms 336 KB Output is correct
9 Correct 2 ms 336 KB Output is correct
10 Correct 3 ms 336 KB Output is correct
11 Correct 4 ms 336 KB Output is correct
12 Correct 7 ms 480 KB Output is correct
13 Correct 14 ms 476 KB Output is correct
14 Correct 29 ms 476 KB Output is correct
15 Correct 57 ms 336 KB Output is correct
16 Correct 125 ms 336 KB Output is correct
17 Correct 184 ms 2748 KB Output is correct
18 Correct 2 ms 760 KB Output is correct
19 Correct 42 ms 1408 KB Output is correct
20 Correct 1 ms 760 KB Output is correct
21 Correct 257 ms 2944 KB Output is correct
22 Correct 29 ms 1364 KB Output is correct
23 Correct 3 ms 592 KB Output is correct
24 Correct 53 ms 1612 KB Output is correct
25 Correct 37 ms 1352 KB Output is correct
26 Correct 71 ms 1864 KB Output is correct
27 Correct 352 ms 3400 KB Output is correct
28 Correct 352 ms 3544 KB Output is correct
29 Correct 368 ms 3656 KB Output is correct
30 Correct 358 ms 3656 KB Output is correct
31 Correct 373 ms 3656 KB Output is correct
32 Correct 368 ms 3536 KB Output is correct
33 Correct 385 ms 3636 KB Output is correct
34 Correct 367 ms 3664 KB Output is correct
35 Correct 383 ms 3596 KB Output is correct
36 Correct 381 ms 3656 KB Output is correct
37 Correct 386 ms 3708 KB Output is correct