Calculating Subarray Sums Using Two Pointers
Efficient computation of subarray sums is a common problem in programming. One effective approach is the two-pointer technique, which allows for efficient sliding-window operations. Below, we explain the implementation of such a method step by step, with a focus on JavaScript.
01. Problem Statement
Given an array of integers nums
and a positive integer subArraySize
, compute the sum of all subarrays of size subArraySize
. The goal is to achieve this efficiently using the two-pointer technique.
02. Understanding the Two-Pointer Technique
The two-pointer technique involves using two indices to represent a sliding window over the array. As the window moves:
- The end pointer adds new elements to the window.
- The start pointer removes elements that are no longer part of the window.
This approach minimizes unnecessary recalculations, maintaining a running sum as the window slides. The technique is both intuitive and efficient for problems requiring operations on contiguous segments of an array.
03. Simplified Implementation
Here is a simplified implementation of the subarray sum calculation using the two-pointer technique in JavaScript:
function calculateSubArraySums(nums, subArraySize) {
let currentSum = 0;
const result = [];
for (let i = 0; i < nums.length; i++) {
currentSum += nums[i]; // Add the current element to the window sum
if (i >= subArraySize - 1) { // Once the window size is reached
result.push(currentSum); // Store the sum
currentSum -= nums[i - subArraySize + 1]; // Remove the first element of the window
}
}
return result;
}
// Example Usage
const nums = [1, 2, 1, 2, 6, 7, 5, 1];
const k = 2;
const result = calculateSubArraySums(nums, k);
console.log(result); // Output: [3, 3, 3, 8, 13, 12, 6]
Explanation of the Code:
- Initialization: The variable
currentSum
keeps track of the sum of the current window, and the arrayresult
stores the sums of all subarrays. - Window Expansion: Each element is added to
currentSum
as the loop progresses. - Window Size Check: When the window reaches the required size (
subArraySize
), the sum is appended toresult
. - Sliding the Window: The first element of the window (
nums[i - subArraySize + 1]
) is subtracted as the window slides forward.
Output:
For nums = [1, 2, 1, 2, 6, 7, 5, 1]
and k = 2
, the output is:
[3, 3, 3, 8, 13, 12, 6]
04. Combining with Two-Pointer Approach
We can refine the logic while explicitly maintaining two pointers (i
and j
) to make the two-pointer mechanism more intuitive:
function calculateSubArraySumsWithPointers(nums, subArraySize) {
let currentSum = 0;
const result = [];
let i = 0; // Start pointer
for (let j = 0; j < nums.length; j++) { // End pointer
currentSum += nums[j]; // Add current element to the window sum
if (j - i + 1 === subArraySize) { // When the window reaches the required size
result.push(currentSum); // Store the sum
currentSum -= nums[i]; // Remove the first element of the window
i++; // Slide the start pointer forward
}
}
return result;
}
// Example Usage
const resultWithPointers = calculateSubArraySumsWithPointers(nums, k);
console.log(resultWithPointers); // Output: [3, 3, 3, 8, 13, 12, 6]
Key Differences in This Approach:
- Explicit Two Pointers:
i
andj
are explicitly defined for clarity. - Sliding the Window: The start pointer
i
moves forward when the window size is met.
Output:
The output remains the same:
[3, 3, 3, 8, 13, 12, 6]
05. Time and Space Complexity
Time Complexity:
- Both implementations iterate through the array once, with each element added and removed from the
currentSum
exactly once. - Overall Time Complexity: $O(n)$, where $n$ is the length of the array.
Space Complexity:
- Only a few variables are used to store intermediate results and the
result
list. - Overall Space Complexity: $O(k)$, where $k$ is the size of the result list.
06. Conclusion
Both implementations efficiently compute subarray sums using the two-pointer technique. The refined approach with explicit pointers provides better clarity, while the simplified implementation is more compact. Choose the one that best suits your coding style and readability preferences. JavaScript's simplicity and flexibility make it an excellent choice for such problems, demonstrating the power of fundamental algorithms.
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