Overview

Arrays are linear data structures that store elements in consecutive memory locations, enabling efficient access using indices. Each element in an array can be accessed directly with its index in constant time, making them ideal for any application that requires frequent retrieval or modification of data. Arrays are particularly beneficial for tasks that involve sorting, searching, and optimization. Due to their fundamental nature and versatility, arrays are a common feature in a lot of coding challenges, understanding arrays is crucial for doing well in online tests and technical interviews.

Important Techniques

➡️🪟 ➡️  Sliding Window

The sliding window technique is a method often applied to arrays and other linear data structures like strings or lists. It involves forming a 'window', defined by two indices for its start and end, over the data structure and sliding it to explore different subsets. This technique proves valuable when you need to find a specific subset of elements that satisfies a certain condition. It's a go-to approach for problems that involve contiguous sequences or continuous segments in an array, like finding or calculating features among all subarrays of a specific size.

To identify when to use the sliding window technique, look out for problem scenarios that involve contiguous sequences or continuous segments in a data structure. If you encounter problems where you're asked to find or calculate something among all subarrays or substrings of a specific size, the sliding window technique is likely a suitable strategy.

Now let’s try to solve this problem! Example Problem: Minimum Size Subarray Sum

Before going to write the code, let’s think how we can solve the problem 🤔

Problem: Minimum Size Subarray Sum

We are given an array of positive integers nums and a positive integer target. The task is to find the minimal length of a subarray whose sum is greater than or equal to target. If no such subarray exists, return 0.

Brainstorming the Approach

1. Sliding Window Technique:
   • This problem can be approached using the sliding window technique because we are dealing with a contiguous subarray.
   • We want to maintain a window that keeps track of the sum of elements. The idea is to expand the window by adding elements from the right until the sum meets or exceeds the target. Then, we'll try to contract the window from the left to find the minimal subarray length.
2. Key Observations:
   • If the sum of the current window is less than the target, expand the window by adding the next element.
   • If the sum is greater than or equal to the target, we calculate the length of the current window and try to minimize it by shrinking the window from the left.
   • We repeat this process until we traverse the entire array.
3. Don’t forget the Edge Cases:
   • If the array is empty, return 0.
   • If all elements in the array are smaller than the target, check whether any subarray can meet the condition.
   • If the sum of the entire array is still less than the target, return 0.

Pseudocode

• Initialize variables:
  • left to track the left boundary of the window.
  • current_sum to keep track of the sum of the current window.
  • min_length to store the minimum length of subarray that meets the condition.
• Loop through each element of the array using an index right for the right boundary of the window:
  • Add the current element to current_sum.
  • While current_sum is greater than or equal to target:
    • Update min_length to be the minimum of min_length and the current window length (right - left + 1).
    • Subtract the element at left from current_sum and increment left to shrink the window.
• If min_length remains unchanged (i.e., no valid subarray was found), return 0; otherwise, return min_length.