QOJ.ac

QOJ

ID题目提交者结果用时内存语言文件大小提交时间测评时间
#496983#6137. Sub-cycle Graphucup-team1198#AC ✓80ms6768kbC++142.0kb2024-07-28 17:41:062024-07-28 17:41:10

Judging History

你现在查看的是最新测评结果

  • [2024-07-28 17:41:10]
  • 评测
  • 测评结果:AC
  • 用时:80ms
  • 内存:6768kb
  • [2024-07-28 17:41:06]
  • 提交

answer

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

const int MOD = 1e9 + 7;

int add(int a, int b) {
    return a + b >= MOD ? a + b - MOD : a + b;
}

int sub(int a, int b) {
    return a >= b ? a - b : a + MOD - b;
}

int mul(int a, int b) {
    return (1ll * a * b) % MOD;
}

int pw(int x, int n) {
    int res = 1;
    while (n) {
        if (n % 2 == 0) {
            x = mul(x, x);
            n /= 2;
        } else {
            res = mul(res, x);
            --n;
        }
    }
    return res;
}

const int MAXF = 2e5 + 100;
int fact[MAXF], invf[MAXF];
const int HALF = (MOD + 1) / 2;
int pw2[MAXF], invpw2[MAXF];

int C(int n, int k) {
    if (k < 0 || k > n) return 0;
    return mul(fact[n], mul(invf[k], invf[n - k]));
}

void solve_() {
    int n;
    int64_t m;
    cin >> n >> m;
    if (m > n) {
        cout << "0\n";
        return;
    }
    if (m == n) {
        cout << mul(fact[n - 1], HALF) << "\n";
        return;
    }
    int l = n - m;
    int ans = 0;
    for (int i = 0; i <= m; ++i) {
        if (m - i > n - m) continue;
        int cur = C(i + l - 1, l - 1);
        cur = mul(cur, C(l, m - i));
        cur = mul(cur, pw2[n - 2 * m + i]);
        if ((m - i) % 2 == 0) {
            ans = add(ans, cur);
        } else {
            ans = sub(ans, cur);
        }
    }
    ans = mul(ans, fact[n]);
    ans = mul(ans, invf[l]);
    ans = mul(ans, invpw2[n - m]);
    cout << ans << "\n";
}

#define MULTITEST

main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    fact[0] = 1;
    pw2[0] = invpw2[0] = 1;
    for (int i = 1; i < MAXF; ++i) {
        fact[i] = mul(fact[i - 1], i);
        pw2[i] = mul(pw2[i - 1], 2);
        invpw2[i] = mul(invpw2[i - 1], HALF);
    }
    invf[MAXF - 1] = pw(fact[MAXF - 1], MOD - 2);
    for (int i = MAXF - 1; i > 0; --i) {
        invf[i - 1] = mul(invf[i], i);
    }


    int tst = 1;
#ifdef MULTITEST
    cin >> tst;
#endif // MULTITEST
    while (tst--) {
        solve_();
    }
    return 0;
}

详细

Test #1:

score: 100
Accepted
time: 4ms
memory: 6768kb

input:

3
4 2
4 3
5 3

output:

15
12
90

result:

ok 3 number(s): "15 12 90"

Test #2:

score: 0
Accepted
time: 80ms
memory: 6756kb

input:

17446
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4
5 5
6 0
6 1
6 2
6 3
6 4
6 5
6 6
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 7
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 8
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 9
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11...

output:

1
3
3
1
1
6
15
12
3
1
10
45
90
60
12
1
15
105
375
630
360
60
1
21
210
1155
3465
5040
2520
360
1
28
378
2940
13545
35280
45360
20160
2520
1
36
630
6552
42525
170100
393120
453600
181440
20160
1
45
990
13230
114345
643545
2286900
4762800
4989600
1814400
181440
1
55
1485
24750
273735
2047815
10239075
3...

result:

ok 17446 numbers