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Program to find maximum in generated array in Python
Suppose we have a number n. We have to generate an array A of length n + 1 in the following way −
A[0] = 0
A[1] = 1
A[2 * i] = A[i] if 2 <= 2 * i <= n
A[2 * i + 1] = A[i] + A[i + 1] if 2 <= 2 * i + 1 <= n
Finally we have to find the maximum number in the array nums.
So, if the input is like n = 5, then the output will be 3 because
A[0] = 0
A[1] = 1
A[2] = A[1] = 1
A[3] = A[1] + A[2] = 1 + 1 = 2
A[4] = A[2]= 1
A[5] = A[2] + A[3] = 1 + 2 = 3
A[6] = A[3] = 2
So the maximum is 3
To solve this, we will follow these steps −
A := a new list from 0 to n
for each element i in A, do
if i is same as 0 or i is same as 1, then
go to next iteration
otherwise when i is even, then
A[i] := A[integer of i/2]
otherwise,
A[i] := A[integer of i/2] + A[(integer of i/2) + 1]
return maximum element of A
Example (Python)
Let us see the following implementation to get better understanding −
def solve(n): A = list(range(0,n+1)) for i in A: if i == 0 or i == 1: continue elif i%2 == 0: A[i] = A[i//2] else: A[i] = A[i//2] + A[(i//2) + 1] return max(A) n = 5 print(solve(n))
Input
5
Output
3
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