oj.uz

Submission #825797

# Submission time Handle Problem Language Result Execution time Memory
825797 2023-08-15T08:11:47 Z GrindMachine Boat (APIO16_boat) C++17
100 / 100
 1618 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;
}

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 609 ms 14152 KB Output is correct
2 Correct 601 ms 14120 KB Output is correct
3 Correct 603 ms 14192 KB Output is correct
4 Correct 608 ms 14272 KB Output is correct
5 Correct 610 ms 14164 KB Output is correct
6 Correct 599 ms 14156 KB Output is correct
7 Correct 612 ms 14284 KB Output is correct
8 Correct 605 ms 14176 KB Output is correct
9 Correct 610 ms 14240 KB Output is correct
10 Correct 605 ms 14120 KB Output is correct
11 Correct 651 ms 14180 KB Output is correct
12 Correct 607 ms 14156 KB Output is correct
13 Correct 610 ms 14124 KB Output is correct
14 Correct 597 ms 14144 KB Output is correct
15 Correct 606 ms 14196 KB Output is correct
16 Correct 108 ms 4412 KB Output is correct
17 Correct 115 ms 4592 KB Output is correct
18 Correct 116 ms 4388 KB Output is correct
19 Correct 120 ms 4552 KB Output is correct
20 Correct 113 ms 4452 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 609 ms 14152 KB Output is correct
2 Correct 601 ms 14120 KB Output is correct
3 Correct 603 ms 14192 KB Output is correct
4 Correct 608 ms 14272 KB Output is correct
5 Correct 610 ms 14164 KB Output is correct
6 Correct 599 ms 14156 KB Output is correct
7 Correct 612 ms 14284 KB Output is correct
8 Correct 605 ms 14176 KB Output is correct
9 Correct 610 ms 14240 KB Output is correct
10 Correct 605 ms 14120 KB Output is correct
11 Correct 651 ms 14180 KB Output is correct
12 Correct 607 ms 14156 KB Output is correct
13 Correct 610 ms 14124 KB Output is correct
14 Correct 597 ms 14144 KB Output is correct
15 Correct 606 ms 14196 KB Output is correct
16 Correct 108 ms 4412 KB Output is correct
17 Correct 115 ms 4592 KB Output is correct
18 Correct 116 ms 4388 KB Output is correct
19 Correct 120 ms 4552 KB Output is correct
20 Correct 113 ms 4452 KB Output is correct
21 Correct 1154 ms 21440 KB Output is correct
22 Correct 1148 ms 21536 KB Output is correct
23 Correct 1127 ms 21364 KB Output is correct
24 Correct 1151 ms 21536 KB Output is correct
25 Correct 1143 ms 21228 KB Output is correct
26 Correct 1241 ms 20636 KB Output is correct
27 Correct 1259 ms 20740 KB Output is correct
28 Correct 1251 ms 20764 KB Output is correct
29 Correct 1245 ms 20848 KB Output is correct
30 Correct 1159 ms 22868 KB Output is correct
31 Correct 1125 ms 22796 KB Output is correct
32 Correct 1139 ms 22848 KB Output is correct
33 Correct 1141 ms 22856 KB Output is correct
34 Correct 1128 ms 22916 KB Output is correct
35 Correct 605 ms 14144 KB Output is correct
36 Correct 601 ms 14156 KB Output is correct
37 Correct 598 ms 14152 KB Output is correct
38 Correct 634 ms 14092 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 4180 KB Output is correct
2 Correct 13 ms 4100 KB Output is correct
3 Correct 13 ms 4108 KB Output is correct
4 Correct 13 ms 4180 KB Output is correct
5 Correct 13 ms 4104 KB Output is correct
6 Correct 14 ms 4128 KB Output is correct
7 Correct 14 ms 4160 KB Output is correct
8 Correct 14 ms 4188 KB Output is correct
9 Correct 14 ms 4160 KB Output is correct
10 Correct 14 ms 4176 KB Output is correct
11 Correct 13 ms 4196 KB Output is correct
12 Correct 13 ms 4212 KB Output is correct
13 Correct 13 ms 4180 KB Output is correct
14 Correct 13 ms 4184 KB Output is correct
15 Correct 13 ms 4180 KB Output is correct
16 Correct 6 ms 2132 KB Output is correct
17 Correct 6 ms 2132 KB Output is correct
18 Correct 6 ms 2132 KB Output is correct
19 Correct 7 ms 2132 KB Output is correct
20 Correct 6 ms 2284 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 609 ms 14152 KB Output is correct
2 Correct 601 ms 14120 KB Output is correct
3 Correct 603 ms 14192 KB Output is correct
4 Correct 608 ms 14272 KB Output is correct
5 Correct 610 ms 14164 KB Output is correct
6 Correct 599 ms 14156 KB Output is correct
7 Correct 612 ms 14284 KB Output is correct
8 Correct 605 ms 14176 KB Output is correct
9 Correct 610 ms 14240 KB Output is correct
10 Correct 605 ms 14120 KB Output is correct
11 Correct 651 ms 14180 KB Output is correct
12 Correct 607 ms 14156 KB Output is correct
13 Correct 610 ms 14124 KB Output is correct
14 Correct 597 ms 14144 KB Output is correct
15 Correct 606 ms 14196 KB Output is correct
16 Correct 108 ms 4412 KB Output is correct
17 Correct 115 ms 4592 KB Output is correct
18 Correct 116 ms 4388 KB Output is correct
19 Correct 120 ms 4552 KB Output is correct
20 Correct 113 ms 4452 KB Output is correct
21 Correct 1154 ms 21440 KB Output is correct
22 Correct 1148 ms 21536 KB Output is correct
23 Correct 1127 ms 21364 KB Output is correct
24 Correct 1151 ms 21536 KB Output is correct
25 Correct 1143 ms 21228 KB Output is correct
26 Correct 1241 ms 20636 KB Output is correct
27 Correct 1259 ms 20740 KB Output is correct
28 Correct 1251 ms 20764 KB Output is correct
29 Correct 1245 ms 20848 KB Output is correct
30 Correct 1159 ms 22868 KB Output is correct
31 Correct 1125 ms 22796 KB Output is correct
32 Correct 1139 ms 22848 KB Output is correct
33 Correct 1141 ms 22856 KB Output is correct
34 Correct 1128 ms 22916 KB Output is correct
35 Correct 605 ms 14144 KB Output is correct
36 Correct 601 ms 14156 KB Output is correct
37 Correct 598 ms 14152 KB Output is correct
38 Correct 634 ms 14092 KB Output is correct
39 Correct 13 ms 4180 KB Output is correct
40 Correct 13 ms 4100 KB Output is correct
41 Correct 13 ms 4108 KB Output is correct
42 Correct 13 ms 4180 KB Output is correct
43 Correct 13 ms 4104 KB Output is correct
44 Correct 14 ms 4128 KB Output is correct
45 Correct 14 ms 4160 KB Output is correct
46 Correct 14 ms 4188 KB Output is correct
47 Correct 14 ms 4160 KB Output is correct
48 Correct 14 ms 4176 KB Output is correct
49 Correct 13 ms 4196 KB Output is correct
50 Correct 13 ms 4212 KB Output is correct
51 Correct 13 ms 4180 KB Output is correct
52 Correct 13 ms 4184 KB Output is correct
53 Correct 13 ms 4180 KB Output is correct
54 Correct 6 ms 2132 KB Output is correct
55 Correct 6 ms 2132 KB Output is correct
56 Correct 6 ms 2132 KB Output is correct
57 Correct 7 ms 2132 KB Output is correct
58 Correct 6 ms 2284 KB Output is correct
59 Correct 1417 ms 24060 KB Output is correct
60 Correct 1379 ms 24052 KB Output is correct
61 Correct 1370 ms 24024 KB Output is correct
62 Correct 1421 ms 24060 KB Output is correct
63 Correct 1380 ms 24076 KB Output is correct
64 Correct 1597 ms 24152 KB Output is correct
65 Correct 1584 ms 24108 KB Output is correct
66 Correct 1586 ms 24044 KB Output is correct
67 Correct 1618 ms 24124 KB Output is correct
68 Correct 1576 ms 24088 KB Output is correct
69 Correct 1366 ms 24124 KB Output is correct
70 Correct 1349 ms 24136 KB Output is correct
71 Correct 1361 ms 24084 KB Output is correct
72 Correct 1342 ms 24052 KB Output is correct
73 Correct 1370 ms 24080 KB Output is correct
74 Correct 144 ms 4724 KB Output is correct
75 Correct 140 ms 4796 KB Output is correct
76 Correct 140 ms 4624 KB Output is correct
77 Correct 144 ms 4708 KB Output is correct
78 Correct 141 ms 4744 KB Output is correct