oj.uz

Submission #825798

# Submission time Handle Problem Language Result Execution time Memory
825798 2023-08-15T08:13:35 Z GrindMachine Boat (APIO16_boat) C++17
100 / 100
 1976 ms 24148 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;
}

// ll choose[N*4][N], choose_ways[N*4][N], dp[N][N*4];

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:120:5: note: in expansion of macro 'rep'
  120 |     rep(i,sz(b)){
      |     ^~~
boat.cpp:122:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  122 |         if(i+1 < sz(b)){
      |                ^

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 626 ms 12264 KB Output is correct
2 Correct 607 ms 12280 KB Output is correct
3 Correct 600 ms 12264 KB Output is correct
4 Correct 602 ms 12264 KB Output is correct
5 Correct 604 ms 12272 KB Output is correct
6 Correct 597 ms 12268 KB Output is correct
7 Correct 610 ms 12268 KB Output is correct
8 Correct 608 ms 12268 KB Output is correct
9 Correct 598 ms 12264 KB Output is correct
10 Correct 599 ms 12264 KB Output is correct
11 Correct 606 ms 12264 KB Output is correct
12 Correct 604 ms 12268 KB Output is correct
13 Correct 594 ms 12268 KB Output is correct
14 Correct 598 ms 12268 KB Output is correct
15 Correct 604 ms 12268 KB Output is correct
16 Correct 106 ms 2400 KB Output is correct
17 Correct 115 ms 2636 KB Output is correct
18 Correct 113 ms 2448 KB Output is correct
19 Correct 114 ms 2640 KB Output is correct
20 Correct 110 ms 2476 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 626 ms 12264 KB Output is correct
2 Correct 607 ms 12280 KB Output is correct
3 Correct 600 ms 12264 KB Output is correct
4 Correct 602 ms 12264 KB Output is correct
5 Correct 604 ms 12272 KB Output is correct
6 Correct 597 ms 12268 KB Output is correct
7 Correct 610 ms 12268 KB Output is correct
8 Correct 608 ms 12268 KB Output is correct
9 Correct 598 ms 12264 KB Output is correct
10 Correct 599 ms 12264 KB Output is correct
11 Correct 606 ms 12264 KB Output is correct
12 Correct 604 ms 12268 KB Output is correct
13 Correct 594 ms 12268 KB Output is correct
14 Correct 598 ms 12268 KB Output is correct
15 Correct 604 ms 12268 KB Output is correct
16 Correct 106 ms 2400 KB Output is correct
17 Correct 115 ms 2636 KB Output is correct
18 Correct 113 ms 2448 KB Output is correct
19 Correct 114 ms 2640 KB Output is correct
20 Correct 110 ms 2476 KB Output is correct
21 Correct 1149 ms 20152 KB Output is correct
22 Correct 1153 ms 20356 KB Output is correct
23 Correct 1139 ms 20040 KB Output is correct
24 Correct 1144 ms 20208 KB Output is correct
25 Correct 1129 ms 19912 KB Output is correct
26 Correct 1224 ms 18932 KB Output is correct
27 Correct 1246 ms 19168 KB Output is correct
28 Correct 1271 ms 19032 KB Output is correct
29 Correct 1279 ms 19224 KB Output is correct
30 Correct 1155 ms 22396 KB Output is correct
31 Correct 1117 ms 22300 KB Output is correct
32 Correct 1098 ms 22288 KB Output is correct
33 Correct 1100 ms 22352 KB Output is correct
34 Correct 1097 ms 22272 KB Output is correct
35 Correct 601 ms 12268 KB Output is correct
36 Correct 600 ms 12268 KB Output is correct
37 Correct 620 ms 12268 KB Output is correct
38 Correct 608 ms 12120 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 12 ms 1236 KB Output is correct
3 Correct 12 ms 1236 KB Output is correct
4 Correct 12 ms 1336 KB Output is correct
5 Correct 13 ms 1248 KB Output is correct
6 Correct 13 ms 1236 KB Output is correct
7 Correct 14 ms 1236 KB Output is correct
8 Correct 13 ms 1336 KB Output is correct
9 Correct 14 ms 1260 KB Output is correct
10 Correct 13 ms 1236 KB Output is correct
11 Correct 12 ms 1256 KB Output is correct
12 Correct 15 ms 1248 KB Output is correct
13 Correct 12 ms 1260 KB Output is correct
14 Correct 12 ms 1256 KB Output is correct
15 Correct 13 ms 1236 KB Output is correct
16 Correct 5 ms 724 KB Output is correct
17 Correct 5 ms 724 KB Output is correct
18 Correct 7 ms 724 KB Output is correct
19 Correct 6 ms 768 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 626 ms 12264 KB Output is correct
2 Correct 607 ms 12280 KB Output is correct
3 Correct 600 ms 12264 KB Output is correct
4 Correct 602 ms 12264 KB Output is correct
5 Correct 604 ms 12272 KB Output is correct
6 Correct 597 ms 12268 KB Output is correct
7 Correct 610 ms 12268 KB Output is correct
8 Correct 608 ms 12268 KB Output is correct
9 Correct 598 ms 12264 KB Output is correct
10 Correct 599 ms 12264 KB Output is correct
11 Correct 606 ms 12264 KB Output is correct
12 Correct 604 ms 12268 KB Output is correct
13 Correct 594 ms 12268 KB Output is correct
14 Correct 598 ms 12268 KB Output is correct
15 Correct 604 ms 12268 KB Output is correct
16 Correct 106 ms 2400 KB Output is correct
17 Correct 115 ms 2636 KB Output is correct
18 Correct 113 ms 2448 KB Output is correct
19 Correct 114 ms 2640 KB Output is correct
20 Correct 110 ms 2476 KB Output is correct
21 Correct 1149 ms 20152 KB Output is correct
22 Correct 1153 ms 20356 KB Output is correct
23 Correct 1139 ms 20040 KB Output is correct
24 Correct 1144 ms 20208 KB Output is correct
25 Correct 1129 ms 19912 KB Output is correct
26 Correct 1224 ms 18932 KB Output is correct
27 Correct 1246 ms 19168 KB Output is correct
28 Correct 1271 ms 19032 KB Output is correct
29 Correct 1279 ms 19224 KB Output is correct
30 Correct 1155 ms 22396 KB Output is correct
31 Correct 1117 ms 22300 KB Output is correct
32 Correct 1098 ms 22288 KB Output is correct
33 Correct 1100 ms 22352 KB Output is correct
34 Correct 1097 ms 22272 KB Output is correct
35 Correct 601 ms 12268 KB Output is correct
36 Correct 600 ms 12268 KB Output is correct
37 Correct 620 ms 12268 KB Output is correct
38 Correct 608 ms 12120 KB Output is correct
39 Correct 12 ms 1236 KB Output is correct
40 Correct 12 ms 1236 KB Output is correct
41 Correct 12 ms 1236 KB Output is correct
42 Correct 12 ms 1336 KB Output is correct
43 Correct 13 ms 1248 KB Output is correct
44 Correct 13 ms 1236 KB Output is correct
45 Correct 14 ms 1236 KB Output is correct
46 Correct 13 ms 1336 KB Output is correct
47 Correct 14 ms 1260 KB Output is correct
48 Correct 13 ms 1236 KB Output is correct
49 Correct 12 ms 1256 KB Output is correct
50 Correct 15 ms 1248 KB Output is correct
51 Correct 12 ms 1260 KB Output is correct
52 Correct 12 ms 1256 KB Output is correct
53 Correct 13 ms 1236 KB Output is correct
54 Correct 5 ms 724 KB Output is correct
55 Correct 5 ms 724 KB Output is correct
56 Correct 7 ms 724 KB Output is correct
57 Correct 6 ms 768 KB Output is correct
58 Correct 6 ms 724 KB Output is correct
59 Correct 1412 ms 24140 KB Output is correct
60 Correct 1514 ms 24136 KB Output is correct
61 Correct 1381 ms 24136 KB Output is correct
62 Correct 1441 ms 24132 KB Output is correct
63 Correct 1413 ms 24136 KB Output is correct
64 Correct 1563 ms 24140 KB Output is correct
65 Correct 1826 ms 24024 KB Output is correct
66 Correct 1670 ms 24136 KB Output is correct
67 Correct 1976 ms 24148 KB Output is correct
68 Correct 1783 ms 24140 KB Output is correct
69 Correct 1526 ms 24028 KB Output is correct
70 Correct 1349 ms 24032 KB Output is correct
71 Correct 1878 ms 24028 KB Output is correct
72 Correct 1366 ms 24140 KB Output is correct
73 Correct 1639 ms 24028 KB Output is correct
74 Correct 139 ms 2732 KB Output is correct
75 Correct 143 ms 2736 KB Output is correct
76 Correct 158 ms 2740 KB Output is correct
77 Correct 190 ms 2732 KB Output is correct
78 Correct 147 ms 2732 KB Output is correct