結果
問題 | No.1039 Project Euler でやれ |
ユーザー |
|
提出日時 | 2020-04-24 23:11:16 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 18 ms / 2,000 ms |
コード長 | 2,797 bytes |
コンパイル時間 | 2,458 ms |
コンパイル使用メモリ | 210,784 KB |
最終ジャッジ日時 | 2025-01-10 00:32:17 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 18 |
ソースコード
#include <bits/stdc++.h>using namespace std;const int64_t MOD = 1e9+7;void add(int64_t& a, int64_t b){a = (a+b) % MOD;}void mul(int64_t& a, int64_t b){a = a*b % MOD;}int64_t power_mod(int64_t num, int64_t power){int64_t prod = 1;num %= MOD;while(power > 0){if(power&1) prod = prod * num % MOD;num = num * num % MOD;power >>= 1;}return prod;}int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y){int64_t d = a;if(b != 0){d = extgcd(b, a%b, y, x);y -= (a/b) * x;}else{x = 1; y = 0;}return d;}int64_t inv_mod(int64_t a){int64_t x, y;extgcd(a, MOD, x, y);return (MOD + x%MOD) % MOD;}vector<int64_t> fact, fact_inv;void create_mod_tables(int num){fact.assign(num+1, 1);fact_inv.assign(num+1, 1);for(int i=1; i<=num; i++) fact[i] = fact[i-1] * i % MOD;fact_inv[num] = inv_mod(fact[num]);for(int i=num; i>0; i--) fact_inv[i-1] = fact_inv[i] * i % MOD;}int64_t comb_mod(int n, int k){return fact[n] * fact_inv[n-k] % MOD * fact_inv[k] % MOD;}int64_t perm_mod(int n, int k){return fact[n] * fact_inv[n-k] % MOD;}vector<pair<int64_t, int>> prime_division(int64_t n){vector<pair<int64_t, int>> ret;for(int64_t i=2; i*i<=n; i++){int cnt = 0;while(n % i == 0){n /= i;cnt++;}if(cnt) ret.emplace_back(i, cnt);}if(n > 1) ret.emplace_back(n, 1);return ret;}int main(){vector<vector<int>> G[20];G[0].push_back({0});for(int s=0; s<20; s++) for(auto v : G[s]){int tail = max(1, v.back());for(int a=tail; a+s<20; a++){auto v2 = v;v2.push_back(a);G[a+s].push_back(v2);}}int M;cin >> M;create_mod_tables(M);auto prs = prime_division(M);int64_t ans = fact[M];for(auto [p, num] : prs){int64_t sum = 0;for(auto& e : G[num]){int64_t res = 1;int n = e.size()-1;vector<int> d(n+1), c(n+1);for(int i=1; i<=n; i++) d[i] = c[i] = i;for(int i=1; i<=n; i++) for(int j=1; j<=n; j++) if(e[i] == e[j]){d[i] = max(d[i], j);c[i] = min(c[i], j);}for(int k=1; k<=n; k++){mul(res, power_mod(p, d[k]) - power_mod(p, k-1));}for(int j=1; j<=n; j++){mul(res, power_mod(p, e[j]*(n-d[j])));}for(int i=1; i<=n; i++){mul(res, power_mod(p, (e[i]-1)*(n-c[i]+1)));}add(sum, inv_mod(res));}mul(ans, sum);}cout << ans << endl;return 0;}