Leetcode – Search Insert Position Solution in Python

LeetCode offers numerous challenges to help programmers enhance their coding skills and the ‘Search Insert Position’ problem is one of them. This problem, falling under the array manipulation category, is a common one asked during interviews and coding tests. It not only tests a candidate’s basic understanding of array manipulation but also evaluates their grasp of searching algorithms, particularly binary search.

In this article, we’ll be discussing this problem in detail, the approach to tackle it, and a Pythonic solution to solve it.

Understanding the Problem Statement

The problem statement is as follows:

Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.

The objective of this problem is to find the position of a target element in a sorted array. If the element doesn’t exist, we need to find the position where it can be inserted while maintaining the sorted order of the array.

Approach to the Problem

The problem is essentially a search problem in a sorted array, and it is tempting to use a simple linear search to solve it. However, since the array is sorted, we can take advantage of this property to perform a binary search, which has a better time complexity than a linear search.

Binary search works by repeatedly dividing the search space in half. If the target value is equal to the middle element of the array, we’ve found the target. If the target is less than the middle element, it must lie in the lower half of the array. If the target is greater, it must lie in the upper half. We thus discard the other half and repeat the process until we find the target or exhaust the search space.

Python Solution for Search Insert Position

Now let’s implement this approach in Python:

class Solution:
    def searchInsert(self, nums, target):
        left, right = 0, len(nums) - 1
        while left <= right:
            mid = left + (right - left) // 2
            if nums[mid] == target:
                return mid
            elif nums[mid] < target:
                left = mid + 1
            else:
                right = mid - 1
        return left

In this solution, we start with the entire array as our search space. We calculate the middle index and compare the middle element with the target. If the target is found, we return the middle index. If the target is larger, we discard the lower half of the array by setting left to mid + 1. If the target is smaller, we discard the upper half by setting right to mid - 1.

The while loop continues as long as left is less than or equal to right. If we don’t find the target and the loop ends, left would be the index where the target can be inserted to maintain the sorted order. This is why we return left at the end.

This binary search algorithm has a time complexity of O(log n), making it more efficient than a linear search (O(n)) for large inputs. The space complexity is O(1), as we only use a few variables and don’t allocate any new data structures.

Conclusion

The ‘Search Insert Position’ problem is a classic example of a binary search problem. Solving this problem requires an understanding of how to manipulate indices in an array and how to implement a binary search algorithm. This problem serves as an excellent practice for anyone looking to master binary search and other similar search algorithms. Once you understand how binary search works, this problem becomes a straightforward task.