oj.uz

Submission #939723

# Submission time Handle Problem Language Result Execution time Memory
939723 2024-03-06T17:04:46 Z sysia Boat (APIO16_boat) C++17
36 / 100
 2000 ms 30024 KB 
//Sylwia Sapkowska
#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;

void __print(int x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << "'" << x << "'";}
void __print(const char *x) {cerr << '"' << x << '"';}
void __print(const string &x) {cerr << '"' << x << '"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef LOCAL
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

#define int long long
typedef pair<int, int> T;
const int oo = 1e18, oo2 = 1e9+7;
const int mod = 1e9+7;

int mul(int a, int b){
    return (a*b)%mod;
}

void add(int &a, int b){
    a += b;
    if (a >= mod) a-=mod;
}

int power(int a, int b){
    if (!b) return 1ll;
    int k = power(a, b/2);
    k = mul(k, k);
    if (b&1) k = mul(k, a);
    return k;
}

void solve(){
    int n; cin >> n;
    vector<int>a(n+1), b(n+1);
    vector<int>s = {0, 1};
    for (int i = 1; i<=n; i++) {
        cin >> a[i] >> b[i];
        s.emplace_back(a[i]);
        s.emplace_back(b[i]);
    }
    sort(s.begin(), s.end());
    s.erase(unique(s.begin(), s.end()), s.end());
    debug(s);
    vector<T>seg;
    for (int i = 0; i<(int)s.size()-1; i++){
        seg.emplace_back(s[i], s[i]);
        if (s[i]+1 <= s[i+1]-1) seg.emplace_back(s[i]+1, s[i+1]-1);
    }
    seg.emplace_back(s.back(), s.back());
    debug(seg);
    vector<int>inv(n+1, 1);
    for (int i = 1; i<=n; i++){
        inv[i] = mul(inv[i-1], power(i, mod-2));
    }
    // auto nck = [&](int N, int K){
    //     if (N < 0 || K < 0 || N < K) return 0ll;
    //     return mul(f[N], mul(inv[K], inv[N-K]));
    // };
    int m = (int)seg.size();
    //len choose k moze byc bardzo dlugie, ale na szczescie dlugosci len jest O(n), wartosci k jest O(n)
    //i mozna uzyc lepszego wzorku by to spreprocessowac
    vector nck(m, vector<int>(n+1, 1)), I(m, vector<int>(n+1));
    for (int j = 0; j<m; j++){
        int len = seg[j].second - seg[j].first+1;
        for (int k = 0; k<=n; k++){
            for (int rep = 0, val = len; rep < k; rep++, val--){
                nck[j][k] = mul(nck[j][k], val);
            }
            nck[j][k] = mul(nck[j][k], inv[k]);
            I[j][k] = power(nck[j][k], mod-2);
        }
    }
    //dp[i][j][k] = na ile sposobow da sie wybrac dzialajace rozwiazanie na prefiksie i, gdzie 
    //ostatnie k elementow nalezy do przedzialu seg[j]
    vector dp(m, vector<int>(n+1, 0));
    dp[0][1] = 1; //zerowy przedzial
    for (int i = 1; i<=n; i++){
        auto new_dp = dp;
        vector<int>pref(m);
        for (int s = 0; s < m; s++){
            if (s) pref[s] += pref[s-1];
            for (int k = 0; k <= n; k++) add(pref[s], dp[s][k]);
        }
        // dp[i] = dp[i-1]; //nic nie dokladamy
        for (int j = 1; j<m; j++){
            if (seg[j].second < a[i] || seg[j].first > b[i]) continue;
            int len = seg[j].second - seg[j].first + 1;
            // dp[i][j][1] = suma po dp[i-1][<j][cokolwiek]
            add(new_dp[j][1], mul(pref[j-1], len)); //dokladamy pierwszy element tego przedzialu
            // for (int s = 0; s < j; s++){
            //     for (int k = 0; k <= n; k++){
            //         if (dp[i-1][s][k]){
            //             debug(dp[i-1][s][k], len);
            //         }
            //         add(dp[i][j][1], mul(dp[i-1][s][k], len));
            //     }
            // } 
            for (int k = 2; k <= min(i, len); k++){
                //dokladamy juz nie pierwszy element tego przedzialu
                // add(new_dp[j][k], mul(dp[j][k-1], mul(power(nck(len, k-1), mod-2), nck(len, k))));
                add(new_dp[j][k], mul(dp[j][k-1], mul(I[j][k-1], nck[j][k])));
            }
        }
        dp.swap(new_dp);
    }
    int ans = mod-1;
    for (int i = 0; i<m; i++){
        for (int j = 0; j<=n; j++){
            add(ans, dp[i][j]);
        }
    }
    cout << ans << "\n";
}

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

    int t = 1;
    //cin >> t;
    while (t--) solve();

    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1060 ms 16476 KB Output is correct
2 Correct 1055 ms 16504 KB Output is correct
3 Correct 1047 ms 16748 KB Output is correct
4 Correct 1043 ms 16400 KB Output is correct
5 Correct 1063 ms 16492 KB Output is correct
6 Correct 1047 ms 16400 KB Output is correct
7 Correct 1058 ms 16604 KB Output is correct
8 Correct 1051 ms 16536 KB Output is correct
9 Correct 1051 ms 16588 KB Output is correct
10 Correct 1056 ms 16632 KB Output is correct
11 Correct 1064 ms 16704 KB Output is correct
12 Correct 1053 ms 16492 KB Output is correct
13 Correct 1063 ms 16472 KB Output is correct
14 Correct 1103 ms 16392 KB Output is correct
15 Correct 1105 ms 16516 KB Output is correct
16 Correct 183 ms 3716 KB Output is correct
17 Correct 196 ms 3492 KB Output is correct
18 Correct 190 ms 3760 KB Output is correct
19 Correct 199 ms 4052 KB Output is correct
20 Correct 192 ms 3396 KB Output is correct

Subtask #2
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1060 ms 16476 KB Output is correct
2 Correct 1055 ms 16504 KB Output is correct
3 Correct 1047 ms 16748 KB Output is correct
4 Correct 1043 ms 16400 KB Output is correct
5 Correct 1063 ms 16492 KB Output is correct
6 Correct 1047 ms 16400 KB Output is correct
7 Correct 1058 ms 16604 KB Output is correct
8 Correct 1051 ms 16536 KB Output is correct
9 Correct 1051 ms 16588 KB Output is correct
10 Correct 1056 ms 16632 KB Output is correct
11 Correct 1064 ms 16704 KB Output is correct
12 Correct 1053 ms 16492 KB Output is correct
13 Correct 1063 ms 16472 KB Output is correct
14 Correct 1103 ms 16392 KB Output is correct
15 Correct 1105 ms 16516 KB Output is correct
16 Correct 183 ms 3716 KB Output is correct
17 Correct 196 ms 3492 KB Output is correct
18 Correct 190 ms 3760 KB Output is correct
19 Correct 199 ms 4052 KB Output is correct
20 Correct 192 ms 3396 KB Output is correct
21 Correct 1932 ms 27052 KB Output is correct
22 Correct 1971 ms 27252 KB Output is correct
23 Correct 1952 ms 26828 KB Output is correct
24 Correct 1934 ms 27476 KB Output is correct
25 Correct 1955 ms 26964 KB Output is correct
26 Correct 1780 ms 25764 KB Output is correct
27 Correct 1822 ms 25720 KB Output is correct
28 Correct 1823 ms 25720 KB Output is correct
29 Correct 1812 ms 25492 KB Output is correct
30 Execution timed out 2069 ms 30024 KB Time limit exceeded
31 Halted 0 ms 0 KB -

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 1780 KB Output is correct
2 Correct 25 ms 1780 KB Output is correct
3 Correct 25 ms 1776 KB Output is correct
4 Correct 25 ms 1780 KB Output is correct
5 Correct 26 ms 1784 KB Output is correct
6 Correct 27 ms 1776 KB Output is correct
7 Correct 26 ms 1780 KB Output is correct
8 Correct 26 ms 1772 KB Output is correct
9 Correct 26 ms 1780 KB Output is correct
10 Correct 26 ms 1776 KB Output is correct
11 Correct 25 ms 1780 KB Output is correct
12 Correct 25 ms 1776 KB Output is correct
13 Correct 25 ms 1772 KB Output is correct
14 Correct 25 ms 1780 KB Output is correct
15 Correct 25 ms 1780 KB Output is correct
16 Correct 10 ms 1032 KB Output is correct
17 Correct 11 ms 1024 KB Output is correct
18 Correct 10 ms 1036 KB Output is correct
19 Correct 10 ms 1036 KB Output is correct
20 Correct 12 ms 1060 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1060 ms 16476 KB Output is correct
2 Correct 1055 ms 16504 KB Output is correct
3 Correct 1047 ms 16748 KB Output is correct
4 Correct 1043 ms 16400 KB Output is correct
5 Correct 1063 ms 16492 KB Output is correct
6 Correct 1047 ms 16400 KB Output is correct
7 Correct 1058 ms 16604 KB Output is correct
8 Correct 1051 ms 16536 KB Output is correct
9 Correct 1051 ms 16588 KB Output is correct
10 Correct 1056 ms 16632 KB Output is correct
11 Correct 1064 ms 16704 KB Output is correct
12 Correct 1053 ms 16492 KB Output is correct
13 Correct 1063 ms 16472 KB Output is correct
14 Correct 1103 ms 16392 KB Output is correct
15 Correct 1105 ms 16516 KB Output is correct
16 Correct 183 ms 3716 KB Output is correct
17 Correct 196 ms 3492 KB Output is correct
18 Correct 190 ms 3760 KB Output is correct
19 Correct 199 ms 4052 KB Output is correct
20 Correct 192 ms 3396 KB Output is correct
21 Correct 1932 ms 27052 KB Output is correct
22 Correct 1971 ms 27252 KB Output is correct
23 Correct 1952 ms 26828 KB Output is correct
24 Correct 1934 ms 27476 KB Output is correct
25 Correct 1955 ms 26964 KB Output is correct
26 Correct 1780 ms 25764 KB Output is correct
27 Correct 1822 ms 25720 KB Output is correct
28 Correct 1823 ms 25720 KB Output is correct
29 Correct 1812 ms 25492 KB Output is correct
30 Execution timed out 2069 ms 30024 KB Time limit exceeded
31 Halted 0 ms 0 KB -