#913956 (C++17) No.2474 Empty Quartz

• 問題: No.2474 Empty Quartz
• ユーザー: shobonvip
• 提出日時: 2023-09-18 20:26:40
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 245 ms / 2,000 ms
• コード長: 2,122 bytes
• コンパイル時間: 4,409 ms
• コンパイル使用メモリ: 250,876 KB
• 最終ジャッジ日時: 2025-02-16 23:26:55
• ジャッジサーバーID （参考情報）: judge3 / judge4

ファイルパターン	結果
sample	AC * 2
other	AC * 5

ソースコード

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#include<bits/stdc++.h>
using namespace std;
//* ATCODER
#include<atcoder/all>
using namespace atcoder;
typedef modint998244353 mint;
//*/
/* BOOST MULTIPRECISION
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
//*/
typedef long long ll;
#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}
template <typename T> T max(vector<T> &a){
    assert(!a.empty());
    T ret = a[0];
    for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
    return ret;
}
template <typename T> T min(vector<T> &a){
    assert(!a.empty());
    T ret = a[0];
    for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
    return ret;
}
template <typename T> T sum(vector<T> &a){
    T ret = 0;
    for (int i=0; i<(int)a.size(); i++) ret += a[i];
    return ret;
}
ll floor_sqrt(ll n){
    ll ub = 3e9 + 30;
    ll lb = 0;
    while(ub - lb > 1){
        ll t = (ub + lb) / 2;
        if (t * t <= n){
            lb = t;
        }else{
            ub = t;
        }
    }
    return lb;
}
//defmodfact
const int COMinitMAX = 992844;
mint fact[COMinitMAX+1], factinv[COMinitMAX+1];
void modfact(){
    fact[0] = 1;
    for (int i=1; i<=COMinitMAX; i++){
        fact[i] = fact[i-1] * i;
    }
    factinv[COMinitMAX] = fact[COMinitMAX].inv();
    for (int i=COMinitMAX-1; i>=0; i--){
        factinv[i] = factinv[i+1] * (i+1);
    }
}
mint cmb(int a, int b){
    if (a<b || b<0) return mint(0);
    return fact[a]*factinv[b]*factinv[a-b];
}
//--------
void solve(){
    ll n, k; cin >> n >> k;
    ll v = (n+1)*(n+1)-k*4;
    ll sv = floor_sqrt(v);
    //cout << v << ' ' << sv << endl;
    if (sv * sv != v){
        cout << 0 << '\n';
        return;
    }
    if ((n+1+sv) % 2 != 0){
        cout << 0 << '\n';
        return;
    }
    mint ans = 0;
    {
        ll targ = (n+1-sv) / 2;
        ans += cmb(n, targ-1);
    }
    {
        ll targ = (n+1+sv) / 2;
        if (sv != 0){
            ans += cmb(n, targ-1);
        }
    }
    cout << ans.val() << '\n';
}
int main(){
    modfact();
    int t; cin >> t;
    while(t--) solve();
}
 
 
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