Hello! In this post, we will cover the second part of the job interview algorithm problem-solving lecture, focusing on the range sum problem using C#. This problem may seem simple, as it involves calculating the sum of consecutive numbers, but it requires an efficient approach.<\/p>\n<\/header>\n Given an integer array The length of the array is between 1 and 10^5, and Here, the range sum is There are two approaches to solve this problem:<\/p>\n First, the simplest method is to iterate over the range using a loop and calculate the sum. However, this method has a time complexity of O(n) when the range is large, making it inefficient.<\/p>\n To solve this problem more efficiently, we can use a prefix sum array. A prefix sum array stores the cumulative sum at each index of the given array, reducing the number of loops.<\/p>\n The process of constructing a prefix sum array is as follows:<\/p>\n By utilizing this constructed prefix sum array, we can calculate the range sum in O(1) time complexity. The range sum is calculated as follows:<\/p>\n Now, let’s write the C# code based on the methods explained above. The code below calculates the range sum based on the given array and range.<\/p>\n This code takes the given array Now, let’s analyze the time and space complexity of the code we wrote.<\/p>\n The process of initializing the prefix array has a time complexity of O(n), while the range sum calculation has a time complexity of O(1). Therefore, the overall time complexity is O(n).<\/p>\nProblem Definition<\/h2>\n
nums<\/code> and two integers left<\/code> and right<\/code>, we need to solve the problem of calculating the range sum from index left<\/code> to right<\/code> within nums<\/code>. The range sum<\/code> is defined as follows:<\/p>\nsum = nums[left] + nums[left + 1] + ... + nums[right]<\/code><\/p>\nleft<\/code> and right<\/code> are values between 0 and nums.Length - 1<\/code>.<\/p>\n<\/section>\nExample<\/h2>\n
Input<\/h3>\n
nums = [1, 2, 3, 4, 5]\nleft = 1\nright = 3<\/code><\/pre>\nOutput<\/h3>\n
sum = 9<\/code><\/pre>\n2 + 3 + 4 = 9<\/code>.<\/p>\n<\/section>\nApproach to the Problem<\/h2>\n
\n
1. Using a Direct Loop<\/h3>\n
2. Using a Prefix Sum Array<\/h3>\n
prefix[0] = nums[0]\nprefix[i] = prefix[i - 1] + nums[i] (1 \u2264 i < nums.Length)<\/code><\/pre>\nsum = prefix[right] - prefix[left - 1] (left > 0)\nsum = prefix[right] (left == 0)<\/code><\/pre>\n<\/section>\nC# Code Implementation<\/h2>\n
Code<\/h3>\n
using System;\n\nclass Program {\n static void Main(string[] args) {\n int[] nums = { 1, 2, 3, 4, 5 };\n int left = 1;\n int right = 3;\n\n int result = GetRangeSum(nums, left, right);\n Console.WriteLine(result);\n }\n\n static int GetRangeSum(int[] nums, int left, int right) {\n int n = nums.Length;\n int[] prefix = new int[n];\n prefix[0] = nums[0];\n\n \/\/ Initialize the prefix array\n for (int i = 1; i < n; i++) {\n prefix[i] = prefix[i - 1] + nums[i];\n }\n\n \/\/ Calculate the range sum\n if (left == 0) {\n return prefix[right];\n }\n return prefix[right] - prefix[left - 1];\n }\n}<\/code><\/pre>\nnums<\/code> and the range left<\/code> and right<\/code> as inputs and returns the range sum. It efficiently calculates the range sum using a prefix sum array.<\/p>\n<\/section>\nComplexity Analysis<\/h2>\n
Time Complexity<\/h3>\n
Space Complexity<\/h3>\n