結果

問題 No.1214 Market
ユーザー heno239heno239
提出日時 2020-08-30 16:29:56
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 347 ms / 2,000 ms
コード長 4,351 bytes
コンパイル時間 1,704 ms
コンパイル使用メモリ 125,260 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-15 11:19:33
合計ジャッジ時間 7,993 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 39
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);

ll mod_pow(ll x, ll n, ll m = mod) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1000;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

int gcd(int a, int b) {
	if (a < b)swap(a, b);
	while (b) {
		int r = a % b; a = b; b = r;
	}
	return a;
}

//見てる場所,残り個数,必要個数
modint dp[50][50][50];
void solve() {
	int n, m, k; cin >> n >> m >> k;
	vector<int> a(m), b(m);
	
	rep(i, m)cin >> a[i] >> b[i];
	{
		auto comp = [&](int i, int j)->bool {
			return b[i] > b[j];
		};
		vector<int> ori(m); rep(i, m)ori[i] = i;
		sort(all(ori), comp);
		vector<int> ca = a, cb = b;
		rep(i, m) {
			a[i] = ca[ori[i]];
			b[i] = cb[ori[i]];
		}
		//rep(i, m)cout << "! " << a[i] << " " << b[i] << "\n";
	}
	modint ans = 0;
	rep(i, m) {
		vector<int> locs; locs.push_back(k + 1);
		rep(j, i + 1) {
			locs.push_back(a[j]);
		}
		sort(all(locs));
		int sta = lower_bound(all(locs), a[i]) - locs.begin();
		
		int el = k + 1;
		modint csum = 0;

		rep(j, 50)rep(k, 50)rep(l,50)dp[j][k][l] = 0;
		dp[0][n][0] = 1;
		rep(j, locs.size() - 1) {
			int dif = locs[j + 1] - locs[j];
			rep(k, n + 1) {
				rep(l, j+1) {
					for (int num = 0; num <= k; num++) {
						modint c = comb(k,num) * (modint)mod_pow(dif, num);
						c *= dp[j][k][l];
						if (j < sta) {
							dp[j + 1][k - num][max(0, l + 1 - num)] += c;
						}
						else {
							if (l + 1 - num <= 0) {
								csum += c * (modint)mod_pow(el - dif, k-num);
							}
							else {
								dp[j + 1][k - num][l + 1 - num] += c;
							}
						}
					}
				}
			}
			el -= dif;
		}
		//cout << "valid\n";
		//cout << dp[1][0] << " " << dp[1][1] << "\n";
		//cout << i << " " << csum << "\n";
		ans += csum * (modint)b[i];
	}
	ans = ans / (modint)mod_pow(k + 1, n);
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(15);
	init_f(); 
	//init();
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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