SOLVE
LATER
You are given an array of numbers \(A_{i}\) which contains positive as well as negative numbers . The cost of the array can be defined as \(C(X)\)
\(C(x) = |A_{1} + T_{1}| + |A_{2}+T_{2}| + ........ |A_{n}+T_{n}|\) , where T is the transfer array which contains N zeros initially.
You need to minimize this cost . You can transfer value from one array element to another if and only if the distance between them is at most K.
Also, transfer value can't be transferred further.
Say array contains \(3, -1 , -2\) and \(K = 1\)
if we transfer 3 from \(1^{st}\) element to \(2^{nd}\) , the array becomes
Original Value \(3, -1,-2\)
Transferred value \(-3 , 3, 0\)
\(C(x) = |3-3| + |-1+3| + ........ |-2+0| = 4 \) which is minimum in this case
Note :
Only positive value can be transferred
It is not necessary to transfer whole value i.e partial transfer is also acceptable. This means that if you have \(A[i] = 5\) then you can distribute the value 5 across many other array elements provided that they finally sum to a number less than equal to 5. For example 5 can be transferred in chunks of smaller values say 2 , 3 but their sum should not exceed 5.
Input:
First line contains N and K separated by space
Second line denotes an array of size N
Output
Minimum value of \(C(X)\)
Constraints
\(1\le N,K \le 10^{5} \)
\( -10^{9}\le A_{i} \le 10^{9} \)
Array contains \(3, -1 , -2\) and \(K = 2\)
if we transfer 1 from \(1^{st}\) element to \(2^{nd}\) and 2 from \(1^{st}\) element to \(3^{rd}\), the array becomes
Original Value \(3, -1,-2\)
Transferred value \(-3 , +1, +2\)
\(C(x) = |3-3| + |-1+1| + |-2+2| = 0 \) which is minimum in this case
Challenge Name
National Instruments Intern Hiring Challenge
National Instruments Intern Hiring Challenge