P5124 Teamwork(DP)

题目：

p5124 [usaco18dec]teamwork

解析：

动态规划，设\(f[i]\)表示到第\(i\)位的最大值，我们枚举i之前的j个位置\((j<k)\)，记录一下这\(j+1\)个数（包括自己）的最大值\(mx\)，转移方程就是\(f[i]=max(f[i],f[i-j-1]+mx\times (j+1))\)

代码：

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

const int n = 1e6 + 10;

int n, m, num;
int a[n], f[n];

template<class t>void read(t &x) {
    x = 0; int f = 0; char ch = getchar();
    while (!isdigit(ch)) f |= (ch == '-'), ch = getchar();
    while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
    x = f ? -x : x;
    return;
}

int main() {
    read(n), read(m);
    for (int i = 1; i <= n; ++i) read(a[i]);
    for (int i = 1; i <= n; ++i) {
        int mx = -1;
        f[i] = f[i - 1] + a[i];
        for (int j = 0; j < m && i - j > 0; ++j) {
            mx = max(mx, a[i - j]);
            f[i] = max(f[i], f[i - j - 1] + mx * (j + 1));
        }
    }
    cout << f[n];
}