oj.uz

Submission #825800

# Submission time Handle Problem Language Result Execution time Memory
825800 2023-08-15T08:14:10 Z GrindMachine Boat (APIO16_boat) C++17
100 / 100
 1775 ms 24140 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];
                choose_ways[i][j] += ways;
                choose_ways[i][j] %= MOD;
            }
        }
    }

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

    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 631 ms 12260 KB Output is correct
2 Correct 617 ms 12264 KB Output is correct
3 Correct 707 ms 12264 KB Output is correct
4 Correct 603 ms 12264 KB Output is correct
5 Correct 611 ms 12264 KB Output is correct
6 Correct 649 ms 12264 KB Output is correct
7 Correct 599 ms 12268 KB Output is correct
8 Correct 615 ms 12268 KB Output is correct
9 Correct 631 ms 12264 KB Output is correct
10 Correct 608 ms 12268 KB Output is correct
11 Correct 621 ms 12264 KB Output is correct
12 Correct 762 ms 12272 KB Output is correct
13 Correct 629 ms 12268 KB Output is correct
14 Correct 651 ms 12268 KB Output is correct
15 Correct 633 ms 12268 KB Output is correct
16 Correct 113 ms 2400 KB Output is correct
17 Correct 120 ms 2644 KB Output is correct
18 Correct 114 ms 2456 KB Output is correct
19 Correct 135 ms 2636 KB Output is correct
20 Correct 115 ms 2460 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 631 ms 12260 KB Output is correct
2 Correct 617 ms 12264 KB Output is correct
3 Correct 707 ms 12264 KB Output is correct
4 Correct 603 ms 12264 KB Output is correct
5 Correct 611 ms 12264 KB Output is correct
6 Correct 649 ms 12264 KB Output is correct
7 Correct 599 ms 12268 KB Output is correct
8 Correct 615 ms 12268 KB Output is correct
9 Correct 631 ms 12264 KB Output is correct
10 Correct 608 ms 12268 KB Output is correct
11 Correct 621 ms 12264 KB Output is correct
12 Correct 762 ms 12272 KB Output is correct
13 Correct 629 ms 12268 KB Output is correct
14 Correct 651 ms 12268 KB Output is correct
15 Correct 633 ms 12268 KB Output is correct
16 Correct 113 ms 2400 KB Output is correct
17 Correct 120 ms 2644 KB Output is correct
18 Correct 114 ms 2456 KB Output is correct
19 Correct 135 ms 2636 KB Output is correct
20 Correct 115 ms 2460 KB Output is correct
21 Correct 1497 ms 20140 KB Output is correct
22 Correct 1201 ms 20356 KB Output is correct
23 Correct 1354 ms 20020 KB Output is correct
24 Correct 1164 ms 20216 KB Output is correct
25 Correct 1181 ms 19908 KB Output is correct
26 Correct 1724 ms 18996 KB Output is correct
27 Correct 1356 ms 19168 KB Output is correct
28 Correct 1264 ms 19032 KB Output is correct
29 Correct 1363 ms 19224 KB Output is correct
30 Correct 1281 ms 22392 KB Output is correct
31 Correct 1114 ms 22304 KB Output is correct
32 Correct 1106 ms 22292 KB Output is correct
33 Correct 1110 ms 22352 KB Output is correct
34 Correct 1147 ms 22132 KB Output is correct
35 Correct 688 ms 12264 KB Output is correct
36 Correct 612 ms 12264 KB Output is correct
37 Correct 598 ms 12264 KB Output is correct
38 Correct 613 ms 12248 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 1236 KB Output is correct
2 Correct 11 ms 1236 KB Output is correct
3 Correct 13 ms 1236 KB Output is correct
4 Correct 15 ms 1236 KB Output is correct
5 Correct 15 ms 1264 KB Output is correct
6 Correct 17 ms 1256 KB Output is correct
7 Correct 14 ms 1252 KB Output is correct
8 Correct 15 ms 1256 KB Output is correct
9 Correct 14 ms 1236 KB Output is correct
10 Correct 15 ms 1252 KB Output is correct
11 Correct 13 ms 1256 KB Output is correct
12 Correct 12 ms 1236 KB Output is correct
13 Correct 14 ms 1256 KB Output is correct
14 Correct 15 ms 1236 KB Output is correct
15 Correct 13 ms 1236 KB Output is correct
16 Correct 7 ms 724 KB Output is correct
17 Correct 5 ms 724 KB Output is correct
18 Correct 5 ms 752 KB Output is correct
19 Correct 6 ms 724 KB Output is correct
20 Correct 6 ms 724 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 631 ms 12260 KB Output is correct
2 Correct 617 ms 12264 KB Output is correct
3 Correct 707 ms 12264 KB Output is correct
4 Correct 603 ms 12264 KB Output is correct
5 Correct 611 ms 12264 KB Output is correct
6 Correct 649 ms 12264 KB Output is correct
7 Correct 599 ms 12268 KB Output is correct
8 Correct 615 ms 12268 KB Output is correct
9 Correct 631 ms 12264 KB Output is correct
10 Correct 608 ms 12268 KB Output is correct
11 Correct 621 ms 12264 KB Output is correct
12 Correct 762 ms 12272 KB Output is correct
13 Correct 629 ms 12268 KB Output is correct
14 Correct 651 ms 12268 KB Output is correct
15 Correct 633 ms 12268 KB Output is correct
16 Correct 113 ms 2400 KB Output is correct
17 Correct 120 ms 2644 KB Output is correct
18 Correct 114 ms 2456 KB Output is correct
19 Correct 135 ms 2636 KB Output is correct
20 Correct 115 ms 2460 KB Output is correct
21 Correct 1497 ms 20140 KB Output is correct
22 Correct 1201 ms 20356 KB Output is correct
23 Correct 1354 ms 20020 KB Output is correct
24 Correct 1164 ms 20216 KB Output is correct
25 Correct 1181 ms 19908 KB Output is correct
26 Correct 1724 ms 18996 KB Output is correct
27 Correct 1356 ms 19168 KB Output is correct
28 Correct 1264 ms 19032 KB Output is correct
29 Correct 1363 ms 19224 KB Output is correct
30 Correct 1281 ms 22392 KB Output is correct
31 Correct 1114 ms 22304 KB Output is correct
32 Correct 1106 ms 22292 KB Output is correct
33 Correct 1110 ms 22352 KB Output is correct
34 Correct 1147 ms 22132 KB Output is correct
35 Correct 688 ms 12264 KB Output is correct
36 Correct 612 ms 12264 KB Output is correct
37 Correct 598 ms 12264 KB Output is correct
38 Correct 613 ms 12248 KB Output is correct
39 Correct 12 ms 1236 KB Output is correct
40 Correct 11 ms 1236 KB Output is correct
41 Correct 13 ms 1236 KB Output is correct
42 Correct 15 ms 1236 KB Output is correct
43 Correct 15 ms 1264 KB Output is correct
44 Correct 17 ms 1256 KB Output is correct
45 Correct 14 ms 1252 KB Output is correct
46 Correct 15 ms 1256 KB Output is correct
47 Correct 14 ms 1236 KB Output is correct
48 Correct 15 ms 1252 KB Output is correct
49 Correct 13 ms 1256 KB Output is correct
50 Correct 12 ms 1236 KB Output is correct
51 Correct 14 ms 1256 KB Output is correct
52 Correct 15 ms 1236 KB Output is correct
53 Correct 13 ms 1236 KB Output is correct
54 Correct 7 ms 724 KB Output is correct
55 Correct 5 ms 724 KB Output is correct
56 Correct 5 ms 752 KB Output is correct
57 Correct 6 ms 724 KB Output is correct
58 Correct 6 ms 724 KB Output is correct
59 Correct 1412 ms 24028 KB Output is correct
60 Correct 1375 ms 24048 KB Output is correct
61 Correct 1361 ms 24024 KB Output is correct
62 Correct 1381 ms 24028 KB Output is correct
63 Correct 1369 ms 24024 KB Output is correct
64 Correct 1553 ms 24040 KB Output is correct
65 Correct 1567 ms 24024 KB Output is correct
66 Correct 1775 ms 24028 KB Output is correct
67 Correct 1608 ms 24028 KB Output is correct
68 Correct 1581 ms 24136 KB Output is correct
69 Correct 1356 ms 24140 KB Output is correct
70 Correct 1493 ms 24028 KB Output is correct
71 Correct 1354 ms 24140 KB Output is correct
72 Correct 1387 ms 24024 KB Output is correct
73 Correct 1358 ms 24140 KB Output is correct
74 Correct 156 ms 2784 KB Output is correct
75 Correct 139 ms 2740 KB Output is correct
76 Correct 139 ms 2788 KB Output is correct
77 Correct 144 ms 2728 KB Output is correct
78 Correct 140 ms 2784 KB Output is correct