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Suppose we have an array nums and a value k. We have to find number of consecutive subsequences whose sum is divisible by k.

So, if the input is like k = 3 nums = [1,2,3,4,1], then the output will be 4 because the subsequences are [3], [1,2], [1,2,3] and [2,3,4].

To solve this, we will follow these steps −

- x := An array of size k and fill with 0
- x[0] := 1
- r:= 0, s:= 0
- for each elem in nums, do
- s :=(s + elem) mod k
- r := r + x[s]
- x[s] := x[s] + 1

- return r

Let us see the following implementation to get better understanding −

def solve(k, nums): x = [0]*k x[0] = 1 r=s=0 for elem in nums: s = (s+elem) % k r += x[s] x[s] += 1 return r k = 3 nums = [1,2,3,4,1] print(solve(k, nums))

3, [1,2,3,4,1]

4

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