Program to find index, where we can insert element to keep list sorted in Python

Suppose we have a list of numbers called nums, they are sorted in ascending order, we also have another number target, we have to find the index where target should be inserted to keep nums sorted. If target already present in nums, then return the largest index where target can be inserted. We have to solve this without using library functions and solve it in O(log n) time.

So, if the input is like nums = [1,5,6,6,8,9] target = 6, then the output will be 4, because 6 is already there, so to insert it, the largest possible index is 4, so the array will be like [1,5,6,6,6,8,9].

To solve this, we will follow these steps −

• left := 0
• right :=
• size of nums - 1
• ans := 0
• while left <= right, do
  • mid := floor of (left + right) / 2
  • if target >= nums[mid], then
    • ans := mid + 1
    • left := mid + 1
  • otherwise,
    • right := mid - 1
• return ans

Example

Let us see the following implementation to get better understanding −

def solve(nums, target):
   left, right = 0, len(nums) - 1
   ans = 0
   while left <= right:
      mid = (left + right) // 2
      if target >= nums[mid]:
         ans = mid + 1
         left = mid + 1
      else:
         right = mid - 1
   return ans

nums = [1,5,6,6,8,9]
target = 6
print(solve(nums, target))

Input

[1,5,6,6,8,9], 6

Output

4