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Submission #1027545

# Submission time Handle Problem Language Result Execution time Memory
1027545 2024-07-19T07:26:09 Z _8_8_ Boat (APIO16_boat) C++17
100 / 100
 1567 ms 19092 KB 
#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
const int  N = 1e3 + 20, MOD = (int)1e9+7;

ll binpow(ll a,ll b) {
    ll ans = 1,k = a;
    while(b) {
        if(b % 2)ans *= k;
        ans %= MOD;
        k *= k;
        k %= MOD;
        b /= 2ll;
    }
    return ans;
}
ll bp[N];
ll ceis(ll n,ll k){
    if(k > n) return 0;     
    ll d = 1;
    for(ll i = n - k + 1;i <= n;i++){
        d = i % MOD * d % MOD;
    }
    for(ll i = 2;i <= k;i++){   
        d = d * bp[i]%MOD;
    }
    return d;
}
int n;
array<int,2> a[N];
vector<int> b;
vector<array<int,2>> o;
ll dp[N][N],pref[N][N],c[N][N],prec[N/2][N/2];
int m;
void test(){
    cin >> n;
    for(int i = 1;i <= n;i++){
        cin >> a[i][0] >> a[i][1];
        b.push_back(a[i][0]);
        b.push_back(a[i][1] + 1);
        bp[i] = binpow(i,MOD-2);
    }
    sort(b.begin(),b.end());
    b.resize(unique(b.begin(),b.end()) - b.begin()); 
    for(int i = 1;i < (int)b.size();i++){
        o.push_back({b[i-1],b[i]-1});
    }
    int m = (int)o.size();
    for(int i = 0;i <= m;i++){
        pref[0][i] = 1;
    }
    for(int i = 0;i <= n;i++){
        for(int j = 0;j <= i;j++){
            prec[i][j] = ceis(i,j);
        }
    }
    for(int i = 1;i <= m;i++){
        int s = (o[i - 1][1] - o[i - 1][0]+1);
        c[i][1] = s;
        vector<int> C(n+1,0);
        for(int j = 0;j <= n;++j){
            C[j] = ceis(s,j);
        }
        for(int j = 2;j <= n;j++){
            for(int k = 0;k <= j-2;k++){
                c[i][j] = (c[i][j] + prec[j-2][k]*1ll*C[j-k]%MOD);
                if(c[i][j] >= MOD) c[i][j] -= MOD;
            }
        }
    }
    for(int i = 1;i <= n;i++){
        pref[i][0] = 1;
        for(int j = 1;j <= m;j++){
            dp[i][j] = dp[i - 1][j];
            if(a[i][0] <= o[j - 1][0] && a[i][1] >= o[j-1][1]){
                for(int k = i,col = 0;k >= 1;k--){
                    if(a[k][0] <= o[j-1][0] && a[k][1] >= o[j-1][1]){
                        ++col;
                        dp[i][j] += pref[k-1][j-1]*1ll*c[j][col]%MOD;
                        if(dp[j][j] >= MOD) dp[i][j] -= MOD;
                    }
                }
            }
        }
        for(int j = 1;j <= m;j++){
            pref[i][j] = (pref[i][j - 1] + dp[i][j])%MOD;
        }
    }
    cout << (pref[n][m]-1+MOD)%MOD << '\n';
}
signed main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1; 
    // cin >> t;
    while(t--){
        test();
    }
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 865 ms 18772 KB Output is correct
2 Correct 938 ms 19084 KB Output is correct
3 Correct 928 ms 18836 KB Output is correct
4 Correct 919 ms 18836 KB Output is correct
5 Correct 943 ms 19028 KB Output is correct
6 Correct 940 ms 18832 KB Output is correct
7 Correct 873 ms 18772 KB Output is correct
8 Correct 888 ms 18836 KB Output is correct
9 Correct 926 ms 18836 KB Output is correct
10 Correct 888 ms 18836 KB Output is correct
11 Correct 910 ms 18836 KB Output is correct
12 Correct 898 ms 19092 KB Output is correct
13 Correct 878 ms 18832 KB Output is correct
14 Correct 909 ms 18832 KB Output is correct
15 Correct 846 ms 18832 KB Output is correct
16 Correct 293 ms 14480 KB Output is correct
17 Correct 301 ms 14420 KB Output is correct
18 Correct 318 ms 14416 KB Output is correct
19 Correct 322 ms 14480 KB Output is correct
20 Correct 315 ms 14468 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 865 ms 18772 KB Output is correct
2 Correct 938 ms 19084 KB Output is correct
3 Correct 928 ms 18836 KB Output is correct
4 Correct 919 ms 18836 KB Output is correct
5 Correct 943 ms 19028 KB Output is correct
6 Correct 940 ms 18832 KB Output is correct
7 Correct 873 ms 18772 KB Output is correct
8 Correct 888 ms 18836 KB Output is correct
9 Correct 926 ms 18836 KB Output is correct
10 Correct 888 ms 18836 KB Output is correct
11 Correct 910 ms 18836 KB Output is correct
12 Correct 898 ms 19092 KB Output is correct
13 Correct 878 ms 18832 KB Output is correct
14 Correct 909 ms 18832 KB Output is correct
15 Correct 846 ms 18832 KB Output is correct
16 Correct 293 ms 14480 KB Output is correct
17 Correct 301 ms 14420 KB Output is correct
18 Correct 318 ms 14416 KB Output is correct
19 Correct 322 ms 14480 KB Output is correct
20 Correct 315 ms 14468 KB Output is correct
21 Correct 476 ms 18768 KB Output is correct
22 Correct 492 ms 18840 KB Output is correct
23 Correct 471 ms 18772 KB Output is correct
24 Correct 469 ms 19028 KB Output is correct
25 Correct 434 ms 18840 KB Output is correct
26 Correct 488 ms 18768 KB Output is correct
27 Correct 552 ms 18836 KB Output is correct
28 Correct 469 ms 19024 KB Output is correct
29 Correct 506 ms 18768 KB Output is correct
30 Correct 803 ms 18828 KB Output is correct
31 Correct 830 ms 18768 KB Output is correct
32 Correct 874 ms 18836 KB Output is correct
33 Correct 820 ms 18840 KB Output is correct
34 Correct 829 ms 18848 KB Output is correct
35 Correct 829 ms 18840 KB Output is correct
36 Correct 846 ms 18844 KB Output is correct
37 Correct 887 ms 18836 KB Output is correct
38 Correct 884 ms 18836 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 9308 KB Output is correct
2 Correct 14 ms 9308 KB Output is correct
3 Correct 14 ms 9308 KB Output is correct
4 Correct 15 ms 9360 KB Output is correct
5 Correct 14 ms 9308 KB Output is correct
6 Correct 15 ms 9308 KB Output is correct
7 Correct 15 ms 9308 KB Output is correct
8 Correct 14 ms 9308 KB Output is correct
9 Correct 14 ms 9360 KB Output is correct
10 Correct 14 ms 9356 KB Output is correct
11 Correct 14 ms 9308 KB Output is correct
12 Correct 13 ms 9308 KB Output is correct
13 Correct 13 ms 9364 KB Output is correct
14 Correct 15 ms 9308 KB Output is correct
15 Correct 14 ms 9308 KB Output is correct
16 Correct 8 ms 9352 KB Output is correct
17 Correct 8 ms 9308 KB Output is correct
18 Correct 8 ms 9308 KB Output is correct
19 Correct 8 ms 9304 KB Output is correct
20 Correct 9 ms 9612 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 865 ms 18772 KB Output is correct
2 Correct 938 ms 19084 KB Output is correct
3 Correct 928 ms 18836 KB Output is correct
4 Correct 919 ms 18836 KB Output is correct
5 Correct 943 ms 19028 KB Output is correct
6 Correct 940 ms 18832 KB Output is correct
7 Correct 873 ms 18772 KB Output is correct
8 Correct 888 ms 18836 KB Output is correct
9 Correct 926 ms 18836 KB Output is correct
10 Correct 888 ms 18836 KB Output is correct
11 Correct 910 ms 18836 KB Output is correct
12 Correct 898 ms 19092 KB Output is correct
13 Correct 878 ms 18832 KB Output is correct
14 Correct 909 ms 18832 KB Output is correct
15 Correct 846 ms 18832 KB Output is correct
16 Correct 293 ms 14480 KB Output is correct
17 Correct 301 ms 14420 KB Output is correct
18 Correct 318 ms 14416 KB Output is correct
19 Correct 322 ms 14480 KB Output is correct
20 Correct 315 ms 14468 KB Output is correct
21 Correct 476 ms 18768 KB Output is correct
22 Correct 492 ms 18840 KB Output is correct
23 Correct 471 ms 18772 KB Output is correct
24 Correct 469 ms 19028 KB Output is correct
25 Correct 434 ms 18840 KB Output is correct
26 Correct 488 ms 18768 KB Output is correct
27 Correct 552 ms 18836 KB Output is correct
28 Correct 469 ms 19024 KB Output is correct
29 Correct 506 ms 18768 KB Output is correct
30 Correct 803 ms 18828 KB Output is correct
31 Correct 830 ms 18768 KB Output is correct
32 Correct 874 ms 18836 KB Output is correct
33 Correct 820 ms 18840 KB Output is correct
34 Correct 829 ms 18848 KB Output is correct
35 Correct 829 ms 18840 KB Output is correct
36 Correct 846 ms 18844 KB Output is correct
37 Correct 887 ms 18836 KB Output is correct
38 Correct 884 ms 18836 KB Output is correct
39 Correct 14 ms 9308 KB Output is correct
40 Correct 14 ms 9308 KB Output is correct
41 Correct 14 ms 9308 KB Output is correct
42 Correct 15 ms 9360 KB Output is correct
43 Correct 14 ms 9308 KB Output is correct
44 Correct 15 ms 9308 KB Output is correct
45 Correct 15 ms 9308 KB Output is correct
46 Correct 14 ms 9308 KB Output is correct
47 Correct 14 ms 9360 KB Output is correct
48 Correct 14 ms 9356 KB Output is correct
49 Correct 14 ms 9308 KB Output is correct
50 Correct 13 ms 9308 KB Output is correct
51 Correct 13 ms 9364 KB Output is correct
52 Correct 15 ms 9308 KB Output is correct
53 Correct 14 ms 9308 KB Output is correct
54 Correct 8 ms 9352 KB Output is correct
55 Correct 8 ms 9308 KB Output is correct
56 Correct 8 ms 9308 KB Output is correct
57 Correct 8 ms 9304 KB Output is correct
58 Correct 9 ms 9612 KB Output is correct
59 Correct 1553 ms 18840 KB Output is correct
60 Correct 1394 ms 18832 KB Output is correct
61 Correct 1400 ms 18772 KB Output is correct
62 Correct 1433 ms 18772 KB Output is correct
63 Correct 1402 ms 18772 KB Output is correct
64 Correct 1536 ms 18832 KB Output is correct
65 Correct 1484 ms 18848 KB Output is correct
66 Correct 1405 ms 18844 KB Output is correct
67 Correct 1481 ms 18860 KB Output is correct
68 Correct 1567 ms 18856 KB Output is correct
69 Correct 1463 ms 19028 KB Output is correct
70 Correct 1530 ms 18860 KB Output is correct
71 Correct 1501 ms 18844 KB Output is correct
72 Correct 1531 ms 18848 KB Output is correct
73 Correct 1422 ms 18860 KB Output is correct
74 Correct 330 ms 14420 KB Output is correct
75 Correct 344 ms 14496 KB Output is correct
76 Correct 324 ms 14420 KB Output is correct
77 Correct 333 ms 14480 KB Output is correct
78 Correct 309 ms 14480 KB Output is correct