The sliding window pattern is a commonly used algorithmic technique for solving problems that involve arrays or strings.
The basic idea of the sliding window pattern is to maintain a "window" of contiguous elements in the array or string and then slide the window over the array or string one element at a time to solve the problem.
The sliding window pattern typically involves two pointers or indices, one for the beginning of the window and one for the end of the window.The window is initially set to contain the first k elements of the array or string, where k is the size of the window.
The window is then "slid" to the right by one element at a time, and the solution to the problem is updated based on the elements in the current window.
For example, the sliding window pattern can be used to solve problems such as finding the maximum sum of a subarray of length k in an array of integers, or finding the longest substring without repeating characters in a string.
The sliding window pattern can often lead to more efficient solutions than brute force approaches, as it avoids re-computing intermediate results and reduces the time complexity of the algorithm.
In order to understand this pattern let's take a real example: Let's write an algorithm to find the maximum sum of a subarray of length k in an array of integers.Here's the basic algorithm:
- Initialize two pointers, left and right, to the first element of the array.
- Initialize a variable, max_sum, to the sum of the first k elements of the array.
- Initialize a variable, current_sum, to the sum of the first k elements of the array.
- Loop through the array from index k to the end of the array.
- Subtract the element at index left from current_sum and increment left by 1.
- Add the element at index right to current_sum and increment right by 1.
- If current_sum is greater than max_sum, update max_sum to current_sum.
- Return max_sum.
Here's the same algorithm implemented in JavaScript:
In this code, arr is the input array of integers and k is the length of the subarray. The function maxSumSubarray returns the maximum sum of a subarray of length k in arr.
In this example, we have an array arr of integers [4, 2, 1, 7, 8, 1, 2, 8, 1, 0] and we want to find the maximum sum of a subarray of length k = 3.
We pass arr and k as arguments to the maxSumSubarray function, which returns the maximum sum of a subarray of length k in arr.
The function computes the maximum sum of the subarray [7, 8, 1], which has a sum of 16, and returns that value.
I hope this example helps illustrate how the maxSumSubarray function works!