Swift Coding Test Course, Finding the Product of an Interval

One of the common problems encountered in programming interviews or coding tests is ‘Calculating the Product of an Interval’. This problem requires a deep understanding of data structures and algorithms through the efficient calculation of the product over a specific interval of a given array. In this chapter, we will understand this problem and explore efficient solutions.

Problem Definition

Given an integer array nums and multiple queries queries, the task is to return the product of the interval defined by each query. The product of an interval refers to the result of multiplying all the numbers within that interval.

Example Problem

Example: 
Input: nums = [1, 2, 3, 4, 5]
Queries: queries = [[0, 1], [1, 3], [2, 4]]
Output: [2, 24, 60]
Explanation:
- The first query [0, 1] returns nums[0] * nums[1] = 1 * 2 = 2.
- The second query [1, 3] returns nums[1] * nums[2] * nums[3] = 2 * 3 * 4 = 24.
- The third query [2, 4] returns nums[2] * nums[3] * nums[4] = 3 * 4 * 5 = 60.

Solution Approach

The problem of calculating the product of an interval can be solved using a basic double loop. However, if the number of queries is large and the array is big, a double loop is inefficient, and we should consider other methods. Particularly, if the number of queries is N and each query takes O(M) time to calculate the interval product, the worst-case time complexity is O(N * M). Therefore, we need to find a method that can solve it in O(N + Q) time.

Calculating Interval Products in Linear Time Complexity

We can solve this problem using a technique called prefix product (pre-computation). This method helps to quickly calculate the product of an interval using the starting and ending indices of each query.

Calculating Prefix Product

First, we construct a prefix product array. The prefix product array is defined with the name prefixProduct, where prefixProduct[i] represents nums[0] * nums[1] * ... * nums[i]. This way, the product of the interval [i, j] can be simply calculated as prefixProduct[j] / prefixProduct[i-1].

Swift Code Implementation

import Foundation

func rangeProduct(_ nums: [Int], _ queries: [[Int]]) -> [Int] {
    var prefixProduct = [Int](repeating: 1, count: nums.count + 1)
    
    // Create the prefix product array
    for i in 0..

Code Analysis

The code above works through the following procedures:

1. Creating the Prefix Product Array: It iterates through the nums array to calculate the cumulative product at each position. The time complexity of this process is O(N).
2. Processing Queries: It checks each given query one by one and calculates the interval product. The time complexity for processing each query is O(1).
3. Therefore, the overall time complexity is O(N + Q).

Conclusion

Through this tutorial, we have learned how to efficiently solve the problem of calculating the product of an interval. Moving away from the basic double loop approach to utilizing prefix products is a method that can be applied beneficially in many algorithmic problems. Such problems are also used in various applications for data processing in reality, so it is important to understand and utilize this problem well.

I wish you success in taking on more coding challenges and building your skills!

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