# | 제출 시각 | 아이디 | 문제 | 언어 | 결과 | 실행 시간 | 메모리 |
---|---|---|---|---|---|---|---|
1275379 | vibeduck | Trains (BOI24_trains) | C++20 | 603 ms | 11268 KiB |
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define pf push_front
#define mp make_pair
#define fi first
#define se second
#define int long long
#define all(x) (x).begin(), (x).end()
typedef long double ld;
typedef long long ll;
typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<bool> vb;
typedef vector<vector<int>> vvi;
typedef vector<vector<bool>> vvb;
typedef vector<vector<ll>> vvll;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;
typedef vector<char> vc;
typedef vector<vector<char>> vvc;
typedef map<int, int> mii;
typedef unordered_map<int, int> umii;
const int mod = 1e9 + 7;
const int inf = INTMAX_MAX;
const bool tc = false;
inline void solve() {
int n; cin >> n;
vi d(n + 1), x(n + 1);
for (int i = 1; i <= n; i++) cin >> d[i] >> x[i];
vi dp(n + 1); dp[1] = 1;
// O(n^2) dp
// for (int i = 2; i <= n; i++) {
// for (int j = i - 1; j >= 0; j--) {
// if (a[j].fi == 0) continue;
// if (((i - j) % a[j].fi) == 0 && (i - j) / a[j].fi <= a[j].se) {
// dp[i] += dp[j];
// dp[i] %= mod;
// }
// }
// }
// x[i] = 1e9
// unordered_map<int, umii> m; // m[number][mod]
// for (int i = 1; i <= n; i++) {
// // add necessary
// for (int j = 1; j <= (int)sqrt(n); j++) {
// dp[i] += m[j][(i % j)];
// dp[i] %= mod;
// }
// if (!d[i]) continue;
// if (d[i] <= (int)(sqrt(n))) {
// m[d[i]][i % d[i]] += dp[i];
// m[d[i]][i % d[i]] %= mod;
// } else {
// for (int j = i + d[i]; j <= n; j += d[i]) {
// dp[j] += dp[i];
// dp[j] %= mod;
// }
// }
// }
// 100 points
unordered_map<int, umii> m; // m[number][mod]
set<pii> q;
for (int i = 1; i <= n; i++) {
if (q.size()) {
auto it = *q.begin();
while (i > it.fi) {
int j = it.se;
m[d[j]][j % d[j]] -= dp[j];
m[d[j]][j % d[j]] += mod * 10000;
m[d[j]][j % d[j]] %= mod;
q.erase(q.begin());
if (q.size()) {
it = *q.begin();
} else {
break;
}
}
}
// add necessary
for (int j = 1; j <= (int)sqrt(n); j++) {
dp[i] += m[j][(i % j)];
dp[i] %= mod;
}
if (!d[i]) continue;
if (d[i] <= (int)(sqrt(n))) {
m[d[i]][i % d[i]] += dp[i];
m[d[i]][i % d[i]] %= mod;
q.insert({i + d[i] * x[i], i});
} else {
for (int j = i + d[i]; j <= n; j += d[i]) {
if ((j - i) / d[i] > x[i]) break;
dp[j] += dp[i];
dp[j] %= mod;
}
}
}
cout << accumulate(all(dp), (int)0) % mod << '\n';
}
void setIO(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
signed main() {
ios::sync_with_stdio(false);
cout.tie(0);
cin.tie(0);
//setIO();
int t = 1;
if (tc) {
cin >> t;
}
while (t--) {
solve();
}
}
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