[CF479E] Riding in a Lift

[CF479E] Riding in a Lift - dp

Description

一个楼有N层，由于你很无聊，你开始玩电梯。你的初始位置在A层，有个神秘实验室在B层，所以你的移动会受到如下限制：假设你在x层，你能走到的y层都要满足 |x - y| < |x - b|. 你不能走到B层或者留在原地。问一共走K次，有多少种走法。(n,k le 5000)

Solution

前缀和优化 dp

#include <bits/stdc++.h>
using namespace std;

#define int long long
int n, a, b, k;
int f[5005], s[5005];

const int mod = 1e9 + 7;

signed main()
{
    ios::sync_with_stdio(false);
    cin >> n >> a >> b >> k;
    s[a] = 1;
    for (int i = 1; i <= k; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            if (j < b)
                f[max(1ll, 2 * j - b + 1)] += s[j];
            if (j < b)
                f[b] -= s[j];
            if (j > b)
                f[b + 1] += s[j];
            if (j > b && 2 * j - b <= n)
                f[2 * j - b] -= s[j];
        }
        for (int j = 1; j <= n; j++)
            f[j] = (f[j] % mod + mod) % mod;
        for (int j = 1; j <= n; j++)
            f[j] += f[j - 1];
        for (int j = 1; j <= n; j++)
            f[j] -= s[j];
        for (int j = 1; j <= n; j++)
            f[j] = (f[j] % mod + mod) % mod;
        for (int j = 0; j <= n; j++)
            s[j] = f[j], f[j] = 0;
    }
    int ans = 0;
    for (int i = 1; i <= n; i++)
        ans += s[i];
    cout << ans % mod << endl;
}