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Submission #947710

# Submission time Handle Problem Language Result Execution time Memory
947710 2024-03-16T22:36:59 Z vjudge1 Skyscraper (JOI16_skyscraper) C++17
100 / 100
 479 ms 192048 KB 
#include <bits/stdc++.h>
using namespace std;

using LL = long long;
using PII = pair<int, int>;

const int N = 105, V = 3005;
const int M = 1e9 + 7;

LL dp[N][N][V][2][2], a[N];

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int n, L;
    cin >> n >> L;

    for(int i = 1; i <= n; i++) cin >> a[i];
    sort(a + 1, a + 1 + n), a[n + 1] = 2004;
    int d = a[2] - a[1];

    dp[1][1][0][0][0] = 1, dp[1][1][d][1][0] = 1;
    dp[1][1][d][0][1] = 1, dp[1][1][d * 2][1][1] = 1;

    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= i; j++) {
            for(int sum = 0; sum <= L; sum++) {
                for(int l = 0; l <= 1; l++) {
                    for(int r = 0; r <= 1; r++) {

                        // place a new component in the middle
                        int new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                        dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1) % M;
                        dp[i + 1][j + 1][new_sum][l][r] %= M;

                        //place a new component in the left , don't block it
                        if(l > 0){
                            new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][r] %= M;
                        }

                        //place a new component in the left and block it
                        if(l > 0){
                            new_sum = sum + (j * 2 + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][0][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][0][r] %= M;
                        }

                        //place a new component in the right, don't block it
                        if(r > 0){
                            new_sum = sum + (j * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][r] %= M;
                        }

                        //place a new component in the right and block it
                        if(r > 0){
                            new_sum = sum + (j * 2 + l) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j + 1][new_sum][l][0] += dp[i][j][sum][l][r];
                            dp[i + 1][j + 1][new_sum][l][0] %= M;
                        }

                        //add to existing component but not at the end of permutation
                        new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                        dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1 ) * 2 % M;
                        dp[i + 1][j][new_sum][l][r] %= M;

                        //adding to left of the leftmost component but do not block it
                        if(l > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][r] %= M;
                        }

                        //adding to left of the leftmost component and block it
                        if(l > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r - 1) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][0][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][0][r] %= M;
                        }

                        //adding to right of the rightmost component but do not block it
                        if(r > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][r] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][r] %= M;
                        }

                        //adding to right of the rightmost component and block it
                        if(r > 0){
                            new_sum = sum + ((j - 1) * 2  + l + r - 1) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j][new_sum][l][0] += dp[i][j][sum][l][r];
                            dp[i + 1][j][new_sum][l][0] %= M;
                        }

                        //merging two components
                        if(j > 1 ) {
                            new_sum = sum + ((j - 2 ) * 2 + l + r) * (a[i + 2] - a[i + 1]);
                            dp[i + 1][j - 1][new_sum][l][r] += dp[i][j][sum][l][r] * (j - 1)%M;
                            dp[i + 1][j - 1][new_sum][l][r] %= M;
                        }

                    }
                }
            }
        }
    }

    LL ans = 0;
    for(int sum = 0; sum <= L; sum++) ans = (ans + dp[n][1][sum][0][0]) % M;
    cout << ans; 
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 4 ms 4700 KB Output is correct
6 Correct 4 ms 4700 KB Output is correct
7 Correct 1 ms 2908 KB Output is correct
8 Correct 1 ms 2908 KB Output is correct
9 Correct 4 ms 4700 KB Output is correct
10 Correct 1 ms 2908 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 3416 KB Output is correct
2 Correct 2 ms 3676 KB Output is correct
3 Correct 1 ms 3164 KB Output is correct
4 Correct 2 ms 3676 KB Output is correct
5 Correct 2 ms 3676 KB Output is correct
6 Correct 3 ms 3420 KB Output is correct
7 Correct 1 ms 3164 KB Output is correct
8 Correct 2 ms 3252 KB Output is correct
9 Correct 2 ms 3416 KB Output is correct
10 Correct 2 ms 3420 KB Output is correct

Subtask #3
80.0 / 80.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 4 ms 4700 KB Output is correct
6 Correct 4 ms 4700 KB Output is correct
7 Correct 1 ms 2908 KB Output is correct
8 Correct 1 ms 2908 KB Output is correct
9 Correct 4 ms 4700 KB Output is correct
10 Correct 1 ms 2908 KB Output is correct
11 Correct 1 ms 3416 KB Output is correct
12 Correct 2 ms 3676 KB Output is correct
13 Correct 1 ms 3164 KB Output is correct
14 Correct 2 ms 3676 KB Output is correct
15 Correct 2 ms 3676 KB Output is correct
16 Correct 3 ms 3420 KB Output is correct
17 Correct 1 ms 3164 KB Output is correct
18 Correct 2 ms 3252 KB Output is correct
19 Correct 2 ms 3416 KB Output is correct
20 Correct 2 ms 3420 KB Output is correct
21 Correct 6 ms 7772 KB Output is correct
22 Correct 240 ms 100924 KB Output is correct
23 Correct 467 ms 189452 KB Output is correct
24 Correct 348 ms 149500 KB Output is correct
25 Correct 475 ms 191428 KB Output is correct
26 Correct 413 ms 167208 KB Output is correct
27 Correct 133 ms 66124 KB Output is correct
28 Correct 149 ms 75344 KB Output is correct
29 Correct 271 ms 120660 KB Output is correct
30 Correct 479 ms 192048 KB Output is correct