Interview(DSA+SD) Series Part:- 4 (Array)

Dominate Array Problems with Efficient Solutions & Time Complexities

Arrays are the fundamental building blocks of data structures, and mastering them is vital for coding success. This article delves into three essential array problems, exploring their time complexities and showcasing two effective approaches for each challenge.

Problem 1: Maximum Subarray Sum

Keywords: maximum subarray, Kadane's Algorithm, dynamic programming, divide and conquer

Objective: Given an array of integers, find the contiguous subarray with the largest sum and return its sum.

Time Complexity: O(n)

Approach 1: Kadane's Algorithm (Dynamic Programming)

• Leverage two variables: currentMax and globalMax.

• Traverse the array, updating currentMax with the maximum of the current element or the sum of the current element and currentMax.

• Update globalMax with the maximum of globalMax and currentMax.

Approach 2: Divide and Conquer

• Divide the array into halves and find the maximum subarray sum in each half.

• Combine the results to identify the maximum subarray crossing the midpoint.

  

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Problem 2: Product of Array Except Self

Keywords: product of array except self, prefix product, suffix product, space optimization

Objective: Given an array nums, return an array output where output[i] is the product of all elements in nums except nums[i].

Time Complexity: O(n)

Approach 1: Prefix and Suffix Product Arrays

• Calculate prefix and suffix product arrays, storing the product of elements to the left and right of each element.

• Multiply the corresponding prefix and suffix products for each element to obtain the final result.