oj.uz

Submission #825767

# Submission time Handle Problem Language Result Execution time Memory
825767 2023-08-15T07:49:57 Z GrindMachine Boat (APIO16_boat) C++17
58 / 100
 2000 ms 24152 KB 
// Om Namah Shivaya

#pragma GCC optimize("O3,unroll-loops")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a, b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a, b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*



*/

const int MOD = 1e9 + 7;
const int N = 500 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

ll fact[N], ifact[N];

ll bexp(ll a, ll b) {
    a %= MOD;
    if (a == 0) return 0;

    ll res = 1;

    while (b) {
        if (b & 1) res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }

    return res;
}

ll invmod(ll a) {
    return bexp(a, MOD - 2);
}

ll ncr(ll n, ll r) {
    if (n < 0 or r < 0 or n < r) return 0;
    return fact[n] * ifact[r] % MOD * ifact[n - r] % MOD;
}

ll npr(ll n, ll r) {
    if (n < 0 or r < 0 or n < r) return 0;
    return fact[n] * ifact[n - r] % MOD;
}

void precalc(ll n) {
    fact[0] = 1;
    rep1(i, n) fact[i] = fact[i - 1] * i % MOD;

    ifact[n] = invmod(fact[n]);
    rev(i, n - 1, 0) ifact[i] = ifact[i + 1] * (i + 1) % MOD;
}

void solve(int test_case)
{
    precalc(N-1);

    ll n; cin >> n;
    vector<pll> a(n+5);
    rep1(i,n) cin >> a[i].ff >> a[i].ss;

    vector<ll> b;
    rep1(i,n) b.pb(a[i].ff), b.pb(a[i].ss);
    sort(all(b));
    b.resize(unique(all(b))-b.begin());

    vector<pll> ranges;
    ranges.pb({0,0});
    rep(i,sz(b)){
        ranges.pb({b[i],b[i]});
        if(i+1 < sz(b)){
            if(b[i]+1 <= b[i+1]-1){
                ranges.pb({b[i]+1,b[i+1]-1});
            }   
        }
    }

    ll m = sz(ranges);

    ll choose[m+5][n+5];
    memset(choose,0,sizeof choose);

    rep(i,m){
        auto [l,r] = ranges[i];
        ll len = r-l+1;
        choose[i][0] = 1;
        ll curr = 1;

        rep1(r,n){
            if(len < r) break;
            curr = curr * (len-r+1) % MOD;
            choose[i][r] = curr * ifact[r] % MOD;
        }
    }

    auto isect = [&](pll p1, pll p2){
        return max(p1.ff,p2.ff) <= min(p1.ss,p2.ss);
    };

    ll choose_ways[m+5][n+5];
    memset(choose_ways,0,sizeof choose_ways);

    rep(i,m){
        choose_ways[i][0] = 1;
        choose_ways[i][1] = choose[i][1];

        for(int j = 2; j <= n; ++j){
            // endpoints fixed i.e 2 of these j guys are always chosen
            // decide pick/ignore for rest j-2 guys
            rep(more,j-2+1){
                ll ways = ncr(j-2,more)*choose[i][more+2]%MOD;
                choose_ways[i][j] += ways;
                choose_ways[i][j] %= MOD;
            }
        }
    }

    // debug(ranges);
    // debug(choose[2][1]);

    ll dp[n+5][m+5];
    memset(dp,0,sizeof dp);
    rep(j,m+5) dp[0][j] = 1;

    rep1(i,n){
        dp[i][0] = 1;
        rep1(j,m-1){
            dp[i][j] = (dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1]+MOD)%MOD;
            if(!isect(a[i],ranges[j])) conts;

            dp[i][j] += choose[j][1]*dp[i-1][j-1];
            dp[i][j] %= MOD;

            ll good = 1;

            rev(k,i-1,1){
                // i and k fixed
                // few more in between
                if(isect(a[k],ranges[j])){
                    good++;
                    dp[i][j] += choose_ways[j][good]*dp[k-1][j-1];
                    dp[i][j] %= MOD;
                    // rep(more,good-2+1){
                    //     ll choose_guys = ncr(good-2,more);
                    //     ll choose_points = choose[j][more+2];
                    //     ll choose_ways = choose_guys*choose_points % MOD;
                    //     dp[i][j] += choose_ways*dp[k-1][j-1];
                    //     dp[i][j] %= MOD;
                    // }
                }
            }
        }
    }

    ll ans = (dp[n][m-1]-1+MOD)%MOD;
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Compilation message

boat.cpp: In function 'void solve(int)':
boat.cpp:32:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   32 | #define rep(i, n) for(int i = 0; i < n; ++i)
      |                                    ^
boat.cpp:118:5: note: in expansion of macro 'rep'
  118 |     rep(i,sz(b)){
      |     ^~~
boat.cpp:120:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  120 |         if(i+1 < sz(b)){
      |                ^

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 923 ms 12264 KB Output is correct
2 Correct 880 ms 12264 KB Output is correct
3 Correct 862 ms 12268 KB Output is correct
4 Correct 871 ms 12268 KB Output is correct
5 Correct 846 ms 12268 KB Output is correct
6 Correct 851 ms 12264 KB Output is correct
7 Correct 845 ms 12264 KB Output is correct
8 Correct 858 ms 12264 KB Output is correct
9 Correct 835 ms 12260 KB Output is correct
10 Correct 824 ms 12268 KB Output is correct
11 Correct 806 ms 12272 KB Output is correct
12 Correct 878 ms 12264 KB Output is correct
13 Correct 871 ms 12264 KB Output is correct
14 Correct 821 ms 12268 KB Output is correct
15 Correct 851 ms 12264 KB Output is correct
16 Correct 151 ms 2396 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 174 ms 2444 KB Output is correct
19 Correct 170 ms 2636 KB Output is correct
20 Correct 151 ms 2476 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 923 ms 12264 KB Output is correct
2 Correct 880 ms 12264 KB Output is correct
3 Correct 862 ms 12268 KB Output is correct
4 Correct 871 ms 12268 KB Output is correct
5 Correct 846 ms 12268 KB Output is correct
6 Correct 851 ms 12264 KB Output is correct
7 Correct 845 ms 12264 KB Output is correct
8 Correct 858 ms 12264 KB Output is correct
9 Correct 835 ms 12260 KB Output is correct
10 Correct 824 ms 12268 KB Output is correct
11 Correct 806 ms 12272 KB Output is correct
12 Correct 878 ms 12264 KB Output is correct
13 Correct 871 ms 12264 KB Output is correct
14 Correct 821 ms 12268 KB Output is correct
15 Correct 851 ms 12264 KB Output is correct
16 Correct 151 ms 2396 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 174 ms 2444 KB Output is correct
19 Correct 170 ms 2636 KB Output is correct
20 Correct 151 ms 2476 KB Output is correct
21 Correct 1539 ms 20140 KB Output is correct
22 Correct 1605 ms 20348 KB Output is correct
23 Correct 1583 ms 20040 KB Output is correct
24 Correct 1547 ms 20324 KB Output is correct
25 Correct 1491 ms 19800 KB Output is correct
26 Correct 1531 ms 18932 KB Output is correct
27 Correct 1584 ms 19168 KB Output is correct
28 Correct 1551 ms 19032 KB Output is correct
29 Correct 1600 ms 19348 KB Output is correct
30 Correct 1517 ms 22396 KB Output is correct
31 Correct 1504 ms 22300 KB Output is correct
32 Correct 1481 ms 22288 KB Output is correct
33 Correct 1491 ms 22356 KB Output is correct
34 Correct 1475 ms 22128 KB Output is correct
35 Correct 806 ms 12264 KB Output is correct
36 Correct 812 ms 12264 KB Output is correct
37 Correct 831 ms 12264 KB Output is correct
38 Correct 835 ms 12256 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 1216 KB Output is correct
2 Correct 17 ms 1256 KB Output is correct
3 Correct 15 ms 1256 KB Output is correct
4 Correct 15 ms 1256 KB Output is correct
5 Correct 15 ms 1236 KB Output is correct
6 Correct 17 ms 1332 KB Output is correct
7 Correct 17 ms 1260 KB Output is correct
8 Correct 17 ms 1256 KB Output is correct
9 Correct 16 ms 1236 KB Output is correct
10 Correct 17 ms 1332 KB Output is correct
11 Correct 15 ms 1236 KB Output is correct
12 Correct 15 ms 1236 KB Output is correct
13 Correct 15 ms 1236 KB Output is correct
14 Correct 15 ms 1236 KB Output is correct
15 Correct 15 ms 1260 KB Output is correct
16 Correct 7 ms 724 KB Output is correct
17 Correct 7 ms 724 KB Output is correct
18 Correct 7 ms 748 KB Output is correct
19 Correct 7 ms 724 KB Output is correct
20 Correct 7 ms 724 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 923 ms 12264 KB Output is correct
2 Correct 880 ms 12264 KB Output is correct
3 Correct 862 ms 12268 KB Output is correct
4 Correct 871 ms 12268 KB Output is correct
5 Correct 846 ms 12268 KB Output is correct
6 Correct 851 ms 12264 KB Output is correct
7 Correct 845 ms 12264 KB Output is correct
8 Correct 858 ms 12264 KB Output is correct
9 Correct 835 ms 12260 KB Output is correct
10 Correct 824 ms 12268 KB Output is correct
11 Correct 806 ms 12272 KB Output is correct
12 Correct 878 ms 12264 KB Output is correct
13 Correct 871 ms 12264 KB Output is correct
14 Correct 821 ms 12268 KB Output is correct
15 Correct 851 ms 12264 KB Output is correct
16 Correct 151 ms 2396 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 174 ms 2444 KB Output is correct
19 Correct 170 ms 2636 KB Output is correct
20 Correct 151 ms 2476 KB Output is correct
21 Correct 1539 ms 20140 KB Output is correct
22 Correct 1605 ms 20348 KB Output is correct
23 Correct 1583 ms 20040 KB Output is correct
24 Correct 1547 ms 20324 KB Output is correct
25 Correct 1491 ms 19800 KB Output is correct
26 Correct 1531 ms 18932 KB Output is correct
27 Correct 1584 ms 19168 KB Output is correct
28 Correct 1551 ms 19032 KB Output is correct
29 Correct 1600 ms 19348 KB Output is correct
30 Correct 1517 ms 22396 KB Output is correct
31 Correct 1504 ms 22300 KB Output is correct
32 Correct 1481 ms 22288 KB Output is correct
33 Correct 1491 ms 22356 KB Output is correct
34 Correct 1475 ms 22128 KB Output is correct
35 Correct 806 ms 12264 KB Output is correct
36 Correct 812 ms 12264 KB Output is correct
37 Correct 831 ms 12264 KB Output is correct
38 Correct 835 ms 12256 KB Output is correct
39 Correct 16 ms 1216 KB Output is correct
40 Correct 17 ms 1256 KB Output is correct
41 Correct 15 ms 1256 KB Output is correct
42 Correct 15 ms 1256 KB Output is correct
43 Correct 15 ms 1236 KB Output is correct
44 Correct 17 ms 1332 KB Output is correct
45 Correct 17 ms 1260 KB Output is correct
46 Correct 17 ms 1256 KB Output is correct
47 Correct 16 ms 1236 KB Output is correct
48 Correct 17 ms 1332 KB Output is correct
49 Correct 15 ms 1236 KB Output is correct
50 Correct 15 ms 1236 KB Output is correct
51 Correct 15 ms 1236 KB Output is correct
52 Correct 15 ms 1236 KB Output is correct
53 Correct 15 ms 1260 KB Output is correct
54 Correct 7 ms 724 KB Output is correct
55 Correct 7 ms 724 KB Output is correct
56 Correct 7 ms 748 KB Output is correct
57 Correct 7 ms 724 KB Output is correct
58 Correct 7 ms 724 KB Output is correct
59 Correct 1843 ms 24036 KB Output is correct
60 Correct 1770 ms 24140 KB Output is correct
61 Correct 1781 ms 24032 KB Output is correct
62 Correct 1812 ms 24140 KB Output is correct
63 Correct 1835 ms 24136 KB Output is correct
64 Correct 1970 ms 24132 KB Output is correct
65 Correct 1989 ms 24152 KB Output is correct
66 Execution timed out 2050 ms 24152 KB Time limit exceeded
67 Halted 0 ms 0 KB -