feat(algorithms, sliding-window, max sum subarray): max sum subarray

Author: BrianLusina

algorithms/sliding_window/max_sum_of_subarray/README.md

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+# Maximum Sum of Subarray with Size K
+
+Given an array of integers nums and an integer k, find the maximum sum of any contiguous subarray of size k.
+
+## Examples
+
+Example 1
+
+```text
+Input: nums = [2, 1, 5, 1, 3, 2], k = 3
+Output: 9
+Explanation: The subarray with the maximum sum is [5, 1, 3] with a sum of 9.
+```
+
+## Solution
+
+We start by extending the window to size k. Whenever our window is of size k, we first compute the sum of the window and
+update max_sum if it is larger than max_sum. Then, we contract the window by removing the leftmost element to prepare for
+the next iteration. Note how we calculate the sum of the window incrementally by adding the new element and removing from
+the previous sum.
+
+![Solution 1](./images/solutions/max_sum_of_subarray_size_k_solution_1.png)
+![Solution 2](./images/solutions/max_sum_of_subarray_size_k_solution_2.png)
+![Solution 3](./images/solutions/max_sum_of_subarray_size_k_solution_3.png)
+![Solution 4](./images/solutions/max_sum_of_subarray_size_k_solution_4.png)
+![Solution 5](./images/solutions/max_sum_of_subarray_size_k_solution_5.png)
+![Solution 6](./images/solutions/max_sum_of_subarray_size_k_solution_6.png)
+![Solution 7](./images/solutions/max_sum_of_subarray_size_k_solution_7.png)
+![Solution 8](./images/solutions/max_sum_of_subarray_size_k_solution_8.png)
+![Solution 9](./images/solutions/max_sum_of_subarray_size_k_solution_9.png)
+![Solution 10](./images/solutions/max_sum_of_subarray_size_k_solution_10.png)
+![Solution 11](./images/solutions/max_sum_of_subarray_size_k_solution_11.png)
+![Solution 12](./images/solutions/max_sum_of_subarray_size_k_solution_12.png)
+![Solution 13](./images/solutions/max_sum_of_subarray_size_k_solution_13.png)
+![Solution 14](./images/solutions/max_sum_of_subarray_size_k_solution_14.png)
+![Solution 15](./images/solutions/max_sum_of_subarray_size_k_solution_15.png)
+![Solution 16](./images/solutions/max_sum_of_subarray_size_k_solution_16.png)
+![Solution 17](./images/solutions/max_sum_of_subarray_size_k_solution_17.png)

algorithms/sliding_window/max_sum_of_subarray/__init__.py

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+from typing import List
+
+
+def max_sum_subarray(nums: List[int], k: int) -> int:
+    n = len(nums)
+
+    # If the length of the numbers is less than k, we return 0, as we can't get a contiguous subarray of size k from nums
+    if n < k:
+        return 0
+
+    start = 0
+    state = 0
+    max_sum = 0
+
+    for end in range(n):
+        state += nums[end]
+
+        if end - start + 1 == k:
+            max_sum = max(max_sum, state)
+            state -= nums[start]
+            start += 1
+
+    return max_sum
+
+def max_sum_subarray_2(nums: List[int], k: int) -> int:
+    n = len(nums)
+
+    # If the length of the numbers is less than k, we return 0, as we can't get a contiguous subarray of size k from nums
+    if n < k:
+        return 0
+
+    window_sum = sum(nums[:k])
+    max_sum = window_sum
+    start = 0
+
+    for end in range(k, n):
+        window_sum += nums[end] - nums[start]
+        start += 1
+        max_sum = max(max_sum, window_sum)
+
+    return max_sum
+
+
+def max_sum_subarray_3(nums: List[int], k: int) -> int:
+    n = len(nums)
+
+    # If the length of the numbers is less than k, we return 0, as we can't get a contiguous subarray of size k from nums
+    if n < k:
+        return 0
+
+    # Use two points which will act as the boundary of the window. In this window, the sum of the elements will be
+    # checked to get the max sum of the sub array
+    lower_bound = 0
+    upper_bound = k
+    max_sum = 0
+
+    while upper_bound <= n:
+        current_sum = sum(nums[lower_bound:upper_bound])
+        max_sum = max(current_sum, max_sum)
+        lower_bound += 1
+        upper_bound += 1
+
+    return max_sum