EJOI 2018 A

#include <bits/stdc++.h>

using namespace std;

const int N = 5e3 + 128;
const int K = (N + 1) / 2;
int dp[N][K][2];
int p[N][K][2][3];
int A[N];

const int INF = 1e9;

void solve() {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> A[i];

    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= (n + 1) / 2; j++)
            for (int k = 0; k < 2; k++)
                dp[i][j][k] = INF;

    dp[0][0][0] = dp[0][0][1] = 0;
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= (n + 1) / 2; j++) {
            p[i][j][0][0] = i - 1;
            p[i][j][0][1] = j;
            if (dp[i-1][j][0] < dp[i-1][j][1]) {
                dp[i][j][0] = dp[i-1][j][0];
                p[i][j][0][2] = 0;
            } else {
                dp[i][j][0] = dp[i-1][j][1];
                p[i][j][0][2] = 1;
            }
        }

        int needLeft = 0;
        if (i > 1)
            needLeft += max(0, A[i - 1] - A[i] + 1);
        int needRight = 0;
        if (i < n)
            needRight += max(0, A[i + 1] - A[i] + 1);

        for (int j = 1; j <= (n + 1) / 2; j++) {
            p[i][j][1][0] = i - 1;
            p[i][j][1][1] = j - 1;
            p[i][j][1][2] = 0;
            if (j == 1 || i <= 2 || p[i-1][j-1][0][0] != i - 2 || p[i-1][j-1][0][1] != j - 1 || p[i-1][j-1][0][2] != 1) {
                dp[i][j][1] = dp[i-1][j-1][0] + needLeft + needRight;
            } else {
                int val = min(A[i - 1], A[i - 2] - 1);
                // A[i - 1] = val
                int exNeed = max(0, val - A[i] + 1);
                dp[i][j][1] = dp[i-1][j-1][0] + exNeed + needRight;
            }
        }
    }

    for (int i = 1; i <= (n + 1) / 2; i++) {
        cout << min(dp[n][i][0], dp[n][i][1]) << ' ';
    }
}

main() {
    solve();
    return 0;
}