oj.uz

Submission #380609

# Submission time Handle Problem Language Result Execution time Memory
380609 2021-03-22T12:46:36 Z smjleo Skyscraper (JOI16_skyscraper) C++14
100 / 100
 100 ms 77292 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
using namespace std;
#define int long long
#define nl '\n'
#define io ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
mt19937 rng((unsigned)chrono::steady_clock::now().time_since_epoch().count());
const int mod = 1000000007, mod2 = 998244353;

// change this
const int N = 105;
const int L = 1005;

int n, l, arr[N], dp[N][N][L][3];

signed main() {
    io;
    cin >> n >> l;
    for (int i=1; i<=n; i++) cin >> arr[i];

    if (n == 1) {
        cout << 1 << nl;
        return 0;
    }

    sort(arr, arr+n+1);
    arr[n+1] = 1e9;

    dp[0][0][0][0] = 1;
    
    for (int i=1; i<=n; i++) {
        for (int j=1; j<=i; j++) {
            for (int k=0; k<=l; k++) {
                for (int m=0; m<3; m++) {
                    // i: index, j: components, k: sum, m: ends
                    int dc = (2*j-m) * (arr[i+1] - arr[i]);
                    // difference in cost. each component contributes 2*j except for the m ones which contribute 1

                    if (dc > k) continue;   // cost too much lol

                    // we can create a new component that isn't the end
                    dp[i][j][k][m] += dp[i-1][j-1][k-dc][m];

                    // we can create a new component that is the end
                    if (m) dp[i][j][k][m] += (3-m) * dp[i-1][j-1][k-dc][m-1];

                    // we can join an existing component but not combine
                    dp[i][j][k][m] += (2*j-m) * dp[i-1][j][k-dc][m];

                    // we can join two existing components [[...]X[...]]
                    if (m == 0) {
                        dp[i][j][k][m] += j*(j+1)*dp[i-1][j+1][k-dc][m];
                        // for each of the j+1 i can match with j
                    } else if (m == 1) {
                        dp[i][j][k][m] += j*j*dp[i-1][j+1][k-dc][m];
                        // for each of the j (because end cannot) i can match with j
                    } else {
                        if (i == n) dp[i][j][k][m] += dp[i-1][j+1][k-dc][m];
                        else dp[i][j][k][m] += j*(j-1)*dp[i-1][j+1][k-dc][m];
                        // for each of the j-1 (because ends cannot) i can match with j
                    }

                    // we can bring an existing component to the end
                    if (m == 1) {
                        dp[i][j][k][m] += (2*j) * dp[i-1][j][k-dc][m-1];    // 2j components to select from (two ends of each)
                    } else if (m == 2) {
                        if (i == n) dp[i][j][k][m] += dp[i-1][j][k-dc][m-1];    // only one thing to select from
                        else if (j) dp[i][j][k][m] += (j-1) * dp[i-1][j][k-dc][m-1];   // j-1 components to select from (one end of each except other end)
                    }

                    dp[i][j][k][m] %= mod;
                }       
            }
        }
    }
    int ans = 0;
    for (int i=0; i<=l; i++) {
        ans += dp[n][1][i][2];
        ans %= mod;
    }

    cout << ans << nl;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 492 KB Output is correct
5 Correct 1 ms 876 KB Output is correct
6 Correct 1 ms 748 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 2 ms 876 KB Output is correct
10 Correct 1 ms 492 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 748 KB Output is correct
2 Correct 1 ms 748 KB Output is correct
3 Correct 1 ms 876 KB Output is correct
4 Correct 1 ms 748 KB Output is correct
5 Correct 1 ms 748 KB Output is correct
6 Correct 1 ms 876 KB Output is correct
7 Correct 1 ms 748 KB Output is correct
8 Correct 1 ms 876 KB Output is correct
9 Correct 1 ms 876 KB Output is correct
10 Correct 1 ms 748 KB Output is correct

Subtask #3
80.0 / 80.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 492 KB Output is correct
5 Correct 1 ms 876 KB Output is correct
6 Correct 1 ms 748 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 2 ms 876 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 748 KB Output is correct
12 Correct 1 ms 748 KB Output is correct
13 Correct 1 ms 876 KB Output is correct
14 Correct 1 ms 748 KB Output is correct
15 Correct 1 ms 748 KB Output is correct
16 Correct 1 ms 876 KB Output is correct
17 Correct 1 ms 748 KB Output is correct
18 Correct 1 ms 876 KB Output is correct
19 Correct 1 ms 876 KB Output is correct
20 Correct 1 ms 748 KB Output is correct
21 Correct 3 ms 3180 KB Output is correct
22 Correct 88 ms 65516 KB Output is correct
23 Correct 97 ms 76396 KB Output is correct
24 Correct 92 ms 74988 KB Output is correct
25 Correct 99 ms 77036 KB Output is correct
26 Correct 93 ms 71788 KB Output is correct
27 Correct 44 ms 41324 KB Output is correct
28 Correct 52 ms 47852 KB Output is correct
29 Correct 87 ms 72776 KB Output is correct
30 Correct 100 ms 77292 KB Output is correct