Syntax error Program to find number of operations needed to make pairs from first and last side are with same sum in Python

Program to find number of operations needed to make pairs from first and last side are with same sum in Python

Suppose we have a list of numbers called nums. The length of this list is even. Now consider an operation where we select any number in nums and update it with a value in range [1 and maximum of nums]. We have to find the minimum number of such operations required such that, for every i, nums[i] + nums[n-1-i] equals to the same number.

So, if the input is like nums = [8,6,2,5,9,2], then the output will be 2, because if we change first 2 at nums[2] to 5, and 9 at nums[4] to 4, then the elements will be [8,6,5,5,4,2], then the nums[i] + nums[n-1-i] for each i will be (8+2) = (6+4) = (5+5) = 10.

To solve this, we will follow these steps −

  • N := size of nums
  • mx := maximum of nums
  • events := a new list
  • idx := 0
  • while idx < floor of N / 2, do
    • a := nums[idx]
    • b := nums[N - idx - 1]
    • insert a pair (minimum of (a + 1), (b + 1), 1) at the end of events
    • insert a pair (a + b, 1) at the end of events
    • insert a pair (a + b + 1, -1) at the end of events
    • insert a pair (maximum of (a + mx) and (b + mx + 1), -1) at the end of events
    • idx := idx + 1
  • sort the list events
  • current := 0
  • mx_same := 0
  • for each pair (event, delta) in events, do
    • current := current + delta
    • mx_same := maximum of current and mx_same
  • return N - mx_same

Example

Let us see the following implementation to get better understanding −

def solve(nums):
   N = len(nums)
   mx = max(nums)
   events = []

   idx = 0
   while idx < N // 2:
      a = nums[idx]
      b = nums[N - idx - 1]

      events.append((min(a + 1, b + 1), 1))
      events.append((a + b, 1))
      events.append((a + b + 1, -1))
      events.append((max(a + mx, b + mx) + 1, -1))

   idx += 1

   events.sort()
   current = 0
   mx_same = 0

   for event, delta in events:
      current += delta
      mx_same = max(current, mx_same)

   return N - mx_same

nums = [8,6,2,5,9,2]
print(solve(nums))

Input

[6, 8, 5, 2, 3]

Output

2
Updated on: 2021-10-18T12:49:34+05:30

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