K-Subarrays solution codechef

K-Subarrays solution codechef

You are given two integers NN and KK, and an array AA of NN integers. You have to choose KK disjoint non-empty subarrays such that the score is maximized.

The score is calculated as follows:

Score=i=1KSum[i]i,Score=∑i=1KSum[i]⋅i,

where Sum[i]Sum[i] denotes sum of elements of ii-th subarray. By the ii-th subarray, we mean the ii-th one in the order from left to right.

Find the maximum score that can be achieved.

Note: The subarrays are not required to cover the whole array. It is allowed for some elements of AA to belong to none of the subarrays.

Input K-Subarrays solution codechef

• The first line of the input contains a single integer TT denoting the number of test cases. The description of TT test cases follows.
• The first line of each test case contains two space-separated integers NN and KK.
• The second line of each test case contains NN space-separated integers A1,A2,,ANA1,A2,…,AN.

Output K-Subarrays solution codechef

For each test case, print a single line containing one integer ― the maximum score.

Constraints K-Subarrays solution codechef

• 1T10001≤T≤1000
• 1N1051≤N≤105
• 1Kmin(100,N)1≤K≤min(100,N)
• 106Ai106−106≤Ai≤106
• The sum of NN over all test cases does not exceed 105105

• Subtask #2 (35 points): K=2K=2
• Subtask #3 (50 points): Original constraints

Sample Input v K-Subarrays solution codechef

2
5 2
1 2 -1 3 1
5 2
-1 2 11 -23 12


Sample Output K-Subarrays solution codechef

11
37


Explanation

• Test Case 1: One way to choose 22 disjoint non-empty subarrays is:

S1=[1,2]S1=[1,2] and S2=[3,1]S2=[3,1]

The score is 31+42=113⋅1+4⋅2=11, which is the maximum possible.

• Test Case 2: One way to choose 22 disjoint non-empty subarrays is:

S1=[2,11]S1=[2,11] and S2=[12]S2=[12]

The score is 131+122=3713⋅1+12⋅2=37, which is the maximum possible.

SOLUTION

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