Cover

The sliding window technique is a powerful approach used to solve a variety of problems, especially those involving subarrays or substrings. Here are the key characteristics and criteria to identify if a problem can be effectively solved using the sliding window technique:

Characteristics of Sliding Window Problems

  • Contiguous Subarrays or Subsequences:

    • The problem involves finding a subarray or substring with certain properties, such as a fixed length or a sum within a range.

  • Optimal Subarray/Subsequence:

    • The problem requires finding an optimal subarray/subsequence, such as the longest, shortest, or one with the maximum/minimum sum/product.

  • Fixed or Variable Window Size:

    • The sliding window can be either fixed in size (e.g., finding all subarrays of length k) or variable (e.g., finding the smallest subarray with a sum greater than a target).

Common Scenarios for Sliding Window Technique

  • Maximum/Minimum Sum Subarray of Fixed Length:

    • Problems where you need to find the maximum or minimum sum of a subarray of a fixed length.

      def maxSumSubarray(nums, k):
    max_sum = current_sum = sum(nums[:k])
    for i in range(k, len(nums)):
        current_sum += nums[i] - nums[i - k]
        max_sum = max(max_sum, current_sum)
    return max_sum

  • Longest Substring with K Distinct Characters:

    • Problems where you need to find the longest substring containing at most k distinct characters.

      def lengthOfLongestSubstringKDistinct(s, k):
    char_map = {}
    left = 0
    max_length = 0
    for right in range(len(s)):
        char_map[s[right]] = char_map.get(s[right], 0) + 1
        while len(char_map) > k:
            char_map[s[left]] -= 1
            if char_map[s[left]] == 0:
                del char_map[s[left]]
            left += 1
        max_length = max(max_length, right - left + 1)
    return max_length

  • Smallest Subarray with Sum Greater than a Given Value:

    • Problems where you need to find the smallest subarray with a sum greater than a given target.

      def minSubArrayLen(target, nums):
    left = 0
    current_sum = 0
    min_length = float('inf')
    for right in range(len(nums)):
        current_sum += nums[right]
        while current_sum >= target:
            min_length = min(min_length, right - left + 1)
            current_sum -= nums[left]
            left += 1
    return min_length if min_length != float('inf') else 0

Steps to Identify and Apply the Sliding Window Technique

  1. Determine if the Problem Involves Subarrays or Subsequences:

    • Check if the problem requires examining or optimizing properties of contiguous subarrays or subsequences.

  2. Identify the Window Size:

    • Determine if the window size is fixed or variable.
    • For fixed-size windows, the problem often involves a specific length k.
    • For variable-size windows, the problem usually has a condition to expand or contract the window.

  3. Use a Two-Pointer Approach:

    • Typically, the sliding window technique uses two pointers, left and right, to represent the current window.
    • Adjust the pointers to expand or contract the window based on the problem’s requirements.

  4. Maintain a Running Calculation:

    • Keep track of the current state of the window (e.g., sum, product, or character count) as you slide the window across the array or string.
    • Update the running calculation efficiently to reflect changes in the window.

Example Problem: Maximum Sum Subarray of Size K

Problem Statement: Given an array of integers and a number k, find the maximum sum of a subarray of size k.

Solution Using Sliding Window Technique:

def maxSumSubarray(nums, k):
    max_sum = current_sum = sum(nums[:k])  # Step 1: Initialize window and calculate initial sum
    for i in range(k, len(nums)):  # Step 2: Slide the window across the array
        current_sum += nums[i] - nums[i - k]  # Step 3: Update the window sum
        max_sum = max(max_sum, current_sum)  # Step 4: Track the maximum sum found
    return max_sum

# Sample Input
nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
k = 3

# Expected Output: 27 (subarray [8, 9, 10])
print(maxSumSubarray(nums, k))

By analyzing the problem’s characteristics and determining if the sliding window technique is applicable, you can effectively use this technique to solve a wide range of problems efficiently.