Partition Array into Disjoint Intervals in Python

Suppose we have an array nums, we have to partition it into two different subarrays called left and right such that −

• Each element in left subarray is less than or equal to each element in right subarray.

• left and right subarrays are non-empty.

• left subarray has the smallest possible size.

We have to find the length of left after such a partitioning.

So, if the input is like nums = [5,0,3,8,6], then the output will be 3 because left array will be [5,0,3] and right subarray will be [8,6].

To solve this, we will follow these steps −

• mx := null, temp := null, nmx := null

• temp2 := 0

• for each i in nums, do

  • if mx is same as null, then

    • mx := i

    • nmx := i

    • temp := temp2

    • temp2 := temp2 + 1

    • go for next iteration

  • if i>=mx, then

    • temp2 := temp2 + 1

    • if i>nmx, then

      • nmx := i

    • go for next iteration

  • otherwise,

    • temp := temp2

    • temp2 := temp2 + 1

    • mx := nmx

    • go for next iteration

• return temp+1

Example

Let us see the following implementation to get better understanding −

def solve(nums):
   mx = None
   temp = None
   nmx = None
   temp2 = 0

   for i in nums:

      if(mx==None):
         mx = i
         nmx = i
         temp = temp2
         temp2+=1
         continue

      if(i>=mx):
         temp2+=1
         if(i>nmx):
            nmx = i
         continue

      else:
         temp = temp2
         temp2+=1
         mx = nmx
         continue

   return temp+1

nums = [5,0,3,8,6]
print(solve(nums))

Input

[5,0,3,8,6]

Output

3