Submission #366711

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
366711	2021-02-15T07:03:55 Z	Kevin_Zhang_TW	Asceticism (JOI18_asceticism)	C++17	100 / 100	30 ms	2796 KB

asceticism

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb emplace_back
#define AI(i) begin(i), end(i)
template<class T> bool chmin(T &a, T b) { return b < a && (a = b, true); }
template<class T> bool chmax(T &a, T b) { return a < b && (a = b, true); }
#ifdef KEV
#define DE(args...) kout("[ " + string(#args) + " ] = ", args)
void kout() { cerr << endl; }
template<class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ', kout(b...); }
template<class T> void debug(T L, T R) { while (L != R) cerr << *L << " \n"[next(L) == R], ++L; }
#else
#define DE(...) 0
#define debug(...) 0
#endif

const int MAX_N = 300010, p = 1e9 + 7;

int n, k;
ll fa[MAX_N], fai[MAX_N], inv[MAX_N];

void init() {
	for (int i : {0, 1})
		fa[i] = fai[i] = inv[i] = 1;
	for (int i = 2;i <= n;++i) {
		fa[i] = fa[i-1] * i % p;
		inv[i] = (p - p / i) * inv[p % i] % p;
		fai[i] = inv[i] * fai[i-1] % p;
	}
}

ll C(int N, int M) { return N < M ? 0 : fa[N] * fai[M] % p * fai[N - M] % p; }

ll bin_pow(ll v, ll t) {
	ll res = 1;
	for (;t;t>>=1, v = v * v % p)
		if (t&1) res = res * v % p;
	return res;
}

// The problem is calculate # permutation P that
// # P_i < P_{i-1} = K
//

ll ginv(ll v) { return bin_pow(v, p - 2); }

// area of N dimension sum(X_i) <= K equals to K^N / N!
// if K <= sum(Y) < K+1
// it means that the number of X_i < X_{i-1} = K

// the area of sum(Y) < a
ll area(ll sum) {
	return bin_pow(sum, n) * fai[n] % p ;
}

ll calsum(int a) {
	ll res = 0;
	for (int i = 0;i <= n;++i) {
		if (i > a) break;
		ll si = i & 1 ? -1 : 1;
		res += si * area(a - i) * C(n, i) % p;
	}
	res %= p;
	if (res < 0) res += p;
	return res;
}

int32_t main() {
	ios_base::sync_with_stdio(0), cin.tie(0);

	cin >> n >> k; 
	
	--k;

	init();

	ll all = calsum(n), ok = calsum(k + 1) - calsum(k) ;

	ll res = ok * ginv(all) % p;

	if (res < 0) res += p;

	res = res * fa[n] % p;

	// res is the posibility

	DE(all, ok, fa[n]);

	cout << res << '\n';

}

Compilation message

asceticism.cpp: In function 'int32_t main()':
asceticism.cpp:14:17: warning: statement has no effect [-Wunused-value]
   14 | #define DE(...) 0
      |                 ^
asceticism.cpp:88:2: note: in expansion of macro 'DE'
   88 |  DE(all, ok, fa[n]);
      |  ^~

Subtask #1
4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	364 KB	Output is correct
2	Correct	1 ms	364 KB	Output is correct
3	Correct	1 ms	364 KB	Output is correct
4	Correct	1 ms	364 KB	Output is correct
5	Correct	1 ms	364 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	364 KB	Output is correct
8	Correct	1 ms	364 KB	Output is correct
9	Correct	1 ms	364 KB	Output is correct
10	Correct	1 ms	364 KB	Output is correct

Subtask #2
20.0 / 20.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	364 KB	Output is correct
2	Correct	1 ms	364 KB	Output is correct
3	Correct	1 ms	364 KB	Output is correct
4	Correct	1 ms	364 KB	Output is correct
5	Correct	1 ms	364 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	364 KB	Output is correct
8	Correct	1 ms	364 KB	Output is correct
9	Correct	1 ms	364 KB	Output is correct
10	Correct	1 ms	364 KB	Output is correct
11	Correct	1 ms	364 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	1 ms	364 KB	Output is correct
14	Correct	1 ms	364 KB	Output is correct
15	Correct	1 ms	364 KB	Output is correct
16	Correct	1 ms	364 KB	Output is correct
17	Correct	1 ms	364 KB	Output is correct
18	Correct	1 ms	364 KB	Output is correct
19	Correct	1 ms	364 KB	Output is correct
20	Correct	1 ms	364 KB	Output is correct

Subtask #3
25.0 / 25.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	364 KB	Output is correct
2	Correct	1 ms	364 KB	Output is correct
3	Correct	1 ms	364 KB	Output is correct
4	Correct	1 ms	364 KB	Output is correct
5	Correct	1 ms	364 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	364 KB	Output is correct
8	Correct	1 ms	364 KB	Output is correct
9	Correct	1 ms	364 KB	Output is correct
10	Correct	1 ms	364 KB	Output is correct
11	Correct	1 ms	364 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	1 ms	364 KB	Output is correct
14	Correct	1 ms	364 KB	Output is correct
15	Correct	1 ms	364 KB	Output is correct
16	Correct	1 ms	364 KB	Output is correct
17	Correct	1 ms	364 KB	Output is correct
18	Correct	1 ms	364 KB	Output is correct
19	Correct	1 ms	364 KB	Output is correct
20	Correct	1 ms	364 KB	Output is correct
21	Correct	1 ms	364 KB	Output is correct
22	Correct	1 ms	364 KB	Output is correct
23	Correct	1 ms	364 KB	Output is correct
24	Correct	1 ms	364 KB	Output is correct
25	Correct	1 ms	364 KB	Output is correct
26	Correct	1 ms	364 KB	Output is correct
27	Correct	1 ms	364 KB	Output is correct
28	Correct	1 ms	364 KB	Output is correct
29	Correct	1 ms	364 KB	Output is correct
30	Correct	1 ms	384 KB	Output is correct

Subtask #4
51.0 / 51.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	364 KB	Output is correct
2	Correct	1 ms	364 KB	Output is correct
3	Correct	1 ms	364 KB	Output is correct
4	Correct	1 ms	364 KB	Output is correct
5	Correct	1 ms	364 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	364 KB	Output is correct
8	Correct	1 ms	364 KB	Output is correct
9	Correct	1 ms	364 KB	Output is correct
10	Correct	1 ms	364 KB	Output is correct
11	Correct	1 ms	364 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	1 ms	364 KB	Output is correct
14	Correct	1 ms	364 KB	Output is correct
15	Correct	1 ms	364 KB	Output is correct
16	Correct	1 ms	364 KB	Output is correct
17	Correct	1 ms	364 KB	Output is correct
18	Correct	1 ms	364 KB	Output is correct
19	Correct	1 ms	364 KB	Output is correct
20	Correct	1 ms	364 KB	Output is correct
21	Correct	1 ms	364 KB	Output is correct
22	Correct	1 ms	364 KB	Output is correct
23	Correct	1 ms	364 KB	Output is correct
24	Correct	1 ms	364 KB	Output is correct
25	Correct	1 ms	364 KB	Output is correct
26	Correct	1 ms	364 KB	Output is correct
27	Correct	1 ms	364 KB	Output is correct
28	Correct	1 ms	364 KB	Output is correct
29	Correct	1 ms	364 KB	Output is correct
30	Correct	1 ms	384 KB	Output is correct
31	Correct	12 ms	2668 KB	Output is correct
32	Correct	12 ms	2688 KB	Output is correct
33	Correct	13 ms	2668 KB	Output is correct
34	Correct	16 ms	2760 KB	Output is correct
35	Correct	26 ms	2668 KB	Output is correct
36	Correct	28 ms	2668 KB	Output is correct
37	Correct	30 ms	2668 KB	Output is correct
38	Correct	4 ms	748 KB	Output is correct
39	Correct	14 ms	2028 KB	Output is correct
40	Correct	19 ms	2796 KB	Output is correct

Submission #366711

Compilation message

Subtask #1 4.0 / 4.0

Subtask #2 20.0 / 20.0

Subtask #3 25.0 / 25.0

Subtask #4 51.0 / 51.0

Subtask #1
4.0 / 4.0

Subtask #2
20.0 / 20.0

Subtask #3
25.0 / 25.0

Subtask #4
51.0 / 51.0