【动态规划专练-01背包】CF189A (1500)

Marvolo Gaunt's Ring

Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. Professor Snape is helping Dumbledore remove the curse. For this, he wants to give Dumbledore exactly x drops of the potion he made.

Value of x is calculated as maximum of p·ai + q·aj + r·ak for given p, q, r and array a1, a2, ... an such that 1 ≤ i ≤ j ≤ k ≤ n. Help Snape find the value of x. Do note that the value of x may be negative.

Input
First line of input contains 4 integers n, p, q, r ( - 109 ≤ p, q, r ≤ 109, 1 ≤ n ≤ 105).

Next line of input contains n space separated integers a1, a2, ... an ( - 109 ≤ ai ≤ 109).

Output
Output a single integer the maximum value of p·ai + q·aj + r·ak that can be obtained provided 1 ≤ i ≤ j ≤ k ≤ n.

Examples
inputCopy
5 1 2 3
1 2 3 4 5
outputCopy
30
inputCopy
5 1 2 -3
-1 -2 -3 -4 -5
outputCopy
12
Note
In the first sample case, we can take i = j = k = 5, thus making the answer as 1·5 + 2·5 + 3·5 = 30.

In second sample case, selecting i = j = 1 and k = 5 gives the answer 12.

ll a[N],b[4],f[N][4];
int main(){
    int n;
    cin>>n>>b[1]>>b[2]>>b[3];
    for(int i=1;i<=n;i++) cin>>a[i];
    for(int i=0;i<=n;i++)
    {
        f[i][0]=0;
        for(int j=1;j<=3;j++)
            f[i][j]=-INF;
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=3;j++){
            f[i][j] = max(f[i][j],max(f[i-1][j],f[i][j-1]+(a[i]*b[j])));
        }
    }

    cout<<f[n][3]<<endl;
    return 0;
}