CF855B
Marvolo Gaunt's Ring
题面翻译
给了三个数: \(p,q,r(-1e9<=p,q,r<=1e9)\)
然后给了n个数\(a_1,a_2...a_n(-1e9<=a_i<=1e9)\)
求找出三个数\(a_i,a_j,a_k(1<=i<=j<=k<=n)\)使得\(p\times a_i+q\times a_j+r\times a_k\)最大。
分析
这是一道十分简单的“三元组”问题,套路很简单:
- 枚举中心点 \(j,\ O(1)\) 找到最大的 \(i, j\)。
对于这一道题目,需要处理前缀最大值和后缀最大值即可。
#include <bits/stdc++.h>
#define int long long
using namespace std;
const int N = 1e5 + 5;
int n, p, q, r, ans = LONG_LONG_MIN;
int a[N], mxf[N], mxb[N];
signed main(){
cin >> n >> p >> q >> r;
for (int i = 1; i <= n; i++)
cin >> a[i];
mxb[n + 1] = mxf[0] = -1e18 - 1;
for (int i = 1; i <= n; i++)
mxf[i] = max(mxf[i - 1], a[i] * p);
for (int i = n; i >= 1; i--)
mxb[i] = max(mxb[i + 1], a[i] * r);
for (int i = 1; i <= n; i++)
ans = max(ans, mxf[i] + a[i] * q + mxb[i]);
cout << ans;
return 0;
}
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