oj.uz

Submission #825755

# Submission time Handle Problem Language Result Execution time Memory
825755 2023-08-15T07:42:52 Z GrindMachine Boat (APIO16_boat) C++17
58 / 100
 2000 ms 24156 KB 
// Om Namah Shivaya

#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:30:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   30 | #define rep(i, n) for(int i = 0; i < n; ++i)
      |                                    ^
boat.cpp:116:5: note: in expansion of macro 'rep'
  116 |     rep(i,sz(b)){
      |     ^~~
boat.cpp:118:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  118 |         if(i+1 < sz(b)){
      |                ^

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 799 ms 12268 KB Output is correct
2 Correct 795 ms 12264 KB Output is correct
3 Correct 803 ms 12268 KB Output is correct
4 Correct 831 ms 12268 KB Output is correct
5 Correct 798 ms 12268 KB Output is correct
6 Correct 822 ms 12264 KB Output is correct
7 Correct 805 ms 12268 KB Output is correct
8 Correct 794 ms 12264 KB Output is correct
9 Correct 822 ms 12268 KB Output is correct
10 Correct 811 ms 12264 KB Output is correct
11 Correct 797 ms 12264 KB Output is correct
12 Correct 821 ms 12268 KB Output is correct
13 Correct 815 ms 12268 KB Output is correct
14 Correct 853 ms 12264 KB Output is correct
15 Correct 863 ms 12268 KB Output is correct
16 Correct 148 ms 2400 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 145 ms 2448 KB Output is correct
19 Correct 151 ms 2520 KB Output is correct
20 Correct 149 ms 2464 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 799 ms 12268 KB Output is correct
2 Correct 795 ms 12264 KB Output is correct
3 Correct 803 ms 12268 KB Output is correct
4 Correct 831 ms 12268 KB Output is correct
5 Correct 798 ms 12268 KB Output is correct
6 Correct 822 ms 12264 KB Output is correct
7 Correct 805 ms 12268 KB Output is correct
8 Correct 794 ms 12264 KB Output is correct
9 Correct 822 ms 12268 KB Output is correct
10 Correct 811 ms 12264 KB Output is correct
11 Correct 797 ms 12264 KB Output is correct
12 Correct 821 ms 12268 KB Output is correct
13 Correct 815 ms 12268 KB Output is correct
14 Correct 853 ms 12264 KB Output is correct
15 Correct 863 ms 12268 KB Output is correct
16 Correct 148 ms 2400 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 145 ms 2448 KB Output is correct
19 Correct 151 ms 2520 KB Output is correct
20 Correct 149 ms 2464 KB Output is correct
21 Correct 1507 ms 20240 KB Output is correct
22 Correct 1566 ms 20360 KB Output is correct
23 Correct 1531 ms 20024 KB Output is correct
24 Correct 1526 ms 20336 KB Output is correct
25 Correct 1479 ms 19924 KB Output is correct
26 Correct 1585 ms 19008 KB Output is correct
27 Correct 1613 ms 19052 KB Output is correct
28 Correct 1616 ms 19036 KB Output is correct
29 Correct 1666 ms 19232 KB Output is correct
30 Correct 1560 ms 22404 KB Output is correct
31 Correct 1566 ms 22312 KB Output is correct
32 Correct 1554 ms 22304 KB Output is correct
33 Correct 1588 ms 22364 KB Output is correct
34 Correct 1469 ms 22140 KB Output is correct
35 Correct 799 ms 12288 KB Output is correct
36 Correct 811 ms 12284 KB Output is correct
37 Correct 806 ms 12280 KB Output is correct
38 Correct 811 ms 12260 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 1236 KB Output is correct
2 Correct 15 ms 1236 KB Output is correct
3 Correct 16 ms 1264 KB Output is correct
4 Correct 16 ms 1332 KB Output is correct
5 Correct 16 ms 1332 KB Output is correct
6 Correct 19 ms 1228 KB Output is correct
7 Correct 17 ms 1236 KB Output is correct
8 Correct 17 ms 1264 KB Output is correct
9 Correct 19 ms 1364 KB Output is correct
10 Correct 17 ms 1236 KB Output is correct
11 Correct 18 ms 1260 KB Output is correct
12 Correct 15 ms 1256 KB Output is correct
13 Correct 15 ms 1260 KB Output is correct
14 Correct 16 ms 1256 KB Output is correct
15 Correct 15 ms 1256 KB Output is correct
16 Correct 7 ms 724 KB Output is correct
17 Correct 7 ms 724 KB Output is correct
18 Correct 8 ms 724 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 799 ms 12268 KB Output is correct
2 Correct 795 ms 12264 KB Output is correct
3 Correct 803 ms 12268 KB Output is correct
4 Correct 831 ms 12268 KB Output is correct
5 Correct 798 ms 12268 KB Output is correct
6 Correct 822 ms 12264 KB Output is correct
7 Correct 805 ms 12268 KB Output is correct
8 Correct 794 ms 12264 KB Output is correct
9 Correct 822 ms 12268 KB Output is correct
10 Correct 811 ms 12264 KB Output is correct
11 Correct 797 ms 12264 KB Output is correct
12 Correct 821 ms 12268 KB Output is correct
13 Correct 815 ms 12268 KB Output is correct
14 Correct 853 ms 12264 KB Output is correct
15 Correct 863 ms 12268 KB Output is correct
16 Correct 148 ms 2400 KB Output is correct
17 Correct 153 ms 2636 KB Output is correct
18 Correct 145 ms 2448 KB Output is correct
19 Correct 151 ms 2520 KB Output is correct
20 Correct 149 ms 2464 KB Output is correct
21 Correct 1507 ms 20240 KB Output is correct
22 Correct 1566 ms 20360 KB Output is correct
23 Correct 1531 ms 20024 KB Output is correct
24 Correct 1526 ms 20336 KB Output is correct
25 Correct 1479 ms 19924 KB Output is correct
26 Correct 1585 ms 19008 KB Output is correct
27 Correct 1613 ms 19052 KB Output is correct
28 Correct 1616 ms 19036 KB Output is correct
29 Correct 1666 ms 19232 KB Output is correct
30 Correct 1560 ms 22404 KB Output is correct
31 Correct 1566 ms 22312 KB Output is correct
32 Correct 1554 ms 22304 KB Output is correct
33 Correct 1588 ms 22364 KB Output is correct
34 Correct 1469 ms 22140 KB Output is correct
35 Correct 799 ms 12288 KB Output is correct
36 Correct 811 ms 12284 KB Output is correct
37 Correct 806 ms 12280 KB Output is correct
38 Correct 811 ms 12260 KB Output is correct
39 Correct 16 ms 1236 KB Output is correct
40 Correct 15 ms 1236 KB Output is correct
41 Correct 16 ms 1264 KB Output is correct
42 Correct 16 ms 1332 KB Output is correct
43 Correct 16 ms 1332 KB Output is correct
44 Correct 19 ms 1228 KB Output is correct
45 Correct 17 ms 1236 KB Output is correct
46 Correct 17 ms 1264 KB Output is correct
47 Correct 19 ms 1364 KB Output is correct
48 Correct 17 ms 1236 KB Output is correct
49 Correct 18 ms 1260 KB Output is correct
50 Correct 15 ms 1256 KB Output is correct
51 Correct 15 ms 1260 KB Output is correct
52 Correct 16 ms 1256 KB Output is correct
53 Correct 15 ms 1256 KB Output is correct
54 Correct 7 ms 724 KB Output is correct
55 Correct 7 ms 724 KB Output is correct
56 Correct 8 ms 724 KB Output is correct
57 Correct 7 ms 724 KB Output is correct
58 Correct 7 ms 724 KB Output is correct
59 Correct 1831 ms 24048 KB Output is correct
60 Correct 1819 ms 24040 KB Output is correct
61 Correct 1766 ms 24036 KB Output is correct
62 Correct 1841 ms 24056 KB Output is correct
63 Correct 1844 ms 24156 KB Output is correct
64 Execution timed out 2024 ms 24040 KB Time limit exceeded
65 Halted 0 ms 0 KB -