Overview

Searching and sorting are fundamental algorithms in computer science, essential for organizing data and optimizing operations across diverse applications. These techniques form the backbone of efficient data manipulation and retrieval, making them critical for performance in software development and technical interviews. Among these, binary search and merge sort are two of the most likely algorithms you might be asked to implement in a coding challenge

Key Algorithms

🔍 Binary Search

Binary search is an efficient algorithm for finding an item in a sorted list of items. It works by repeatedly dividing the search interval in half. If the value of the search key is less than the item in the middle of the interval, the search continues in the lower half, or if greater, in the upper half. This approach reduces the search time to O(logn), making it highly efficient for large data sets.

Now let’s solve this problem Example Problem: Merge Sorted Array

Problem: Merge Sorted Arrays

We are given two integer arrays nums1 and nums2, both sorted in non-decreasing order. The task is to merge nums2 into nums1 such that nums1 becomes a single sorted array (Do not return anything).

The first m elements of nums1 are valid elements, and the rest of the nums1 array is filled with zeros to accommodate the elements from nums2. The length of nums1 is m + n, where n is the length of nums2.

Brainstorming the Approach

1. Binary Search Technique: This technique helps efficiently find the correct insertion points for each element from nums2 into nums1. Binary search is used to find the appropriate index to insert elements from nums2.
2. Key Observations:
   • Both nums1 and nums2 are already sorted.
   • The largest elements are at the end of both arrays. By merging from the end of nums1, we can avoid overwriting valid elements.
   • Binary search can quickly find the position in nums1 where each element from nums2 should go.
3. Edge Cases:
   • Empty nums2: If nums2 has no elements (n = 0), nums1 remains unchanged.
   • Empty nums1: If nums1 initially contains no valid elements (m = 0), nums1 should become exactly nums2.
   • All elements of nums2 are smaller/larger than nums1: Ensure the remaining elements are properly handled.

Pseudocode

1. Binary Search Function:
   • Finds the insertion position for a given element from nums2 in nums1.
2. Merging Process:
   • For each element in nums2, use binary search to find the correct insertion position in nums1.
   • Shift elements in nums1 to create space for the new element.
   • Insert the element from nums2 into the identified position.

Code Implementation

class Solution(object):
    def merge(self, nums1, m, nums2, n):
        
        def binary_search(nums1, left, right, target):
            
            while left <= right:
                mid = (left + right) // 2
                if nums1[mid] < target:
                    left = mid + 1
                else:
                    right = mid - 1
            return left

        # Process each element in nums2
        for i in range(n):
            # Find the position to insert nums2[i] into nums1
            position = binary_search(nums1, 0, m + i - 1, nums2[i])
            # Shift elements in nums1 to make space for nums2[i]
            nums1[position + 1:m + i + 1] = nums1[position:m + i]
            # Insert nums2[i] into nums1
            nums1[position] = nums2[i]

Explanation