update maximum_size_subarray_sum_equals_k.py

Author: kumailn

Python/Maximum_Size_Subarray_Sum_Equals_k.py

@@ -1,15 +1,41 @@
-def maxSubArrayLen(nums, k):
+#Question: Given an array nums and a target value k, find the maximum length of a subarray that sums to k. If there isn't one, return 0 instead.
+#Solution: Keep a hashmap of sums up to that point 
+#Difficulty: Medium
+#Space Complexity: O(n)
+#Time Complexity: O(n)
+
+from typing import List
+
+def maxSubArrayLen(nums: List[int], k: int):
+    #Initialize values for the max sub-array itself and it's value
     answer, accumulator = [], 0
-    sumMap = {0:-1}
-    for i,v in enumerate(nums):
+    
+    #Create a hashmap with keys being sums and values indexes, sum at index -1 is 0
+    #This is important because if the accumulator sums to 0 at any point we can use this 0 and include all numbers from the beginning
+    sumMap = {0: -1}
+
+    for i, v in enumerate(nums):
+        #Increment the accumulator by the number in the array
         accumulator += v
+
+        #If we haven't previously encountered this number, add it to hashmap with index i
         if accumulator not in sumMap: sumMap[accumulator] = i
-        print(sumMap, accumulator-k)
-        if accumulator-k in sumMap: 
-            if (i - sumMap[accumulator - k]) > len(answer): answer = nums[sumMap[accumulator-k]+1:i+1]
+
+        #If the accumulator - the k we're looking for happens to be in our map
+        #This is because accumulator - (accumulator - k) = k. In other words the accumulator up to this point, subtracted by the (accumulator-k) must be k
+        if accumulator - k in sumMap: 
+
+            #If the length of k is greater than the length of our answer, because k spans from index at sum accumulator - k to index at i (from the above comment)
+            if (i - sumMap[accumulator - k]) > len(answer): 
+
+                #Set answer to be the subarray starting from the inde of the sum (accumulator-k) to i inclusively
+                #We want the starting point to be non-inclusive of the last item in the sum (accumulator-k) because we need to subtract this sum completely...
+                #..from the current accumulator in order to obtain k. (Since accumulator - (accumulator - k) = k)
+                answer = nums[sumMap[accumulator-k]+1:i+1]
     return answer
 
 
 def main():
+    print(maxSubArrayLen([1, 1, 2, 3, -1, 0, -1, 1, 2, 3], 5))
     print(maxSubArrayLen([-2, -1, 2, 1, 9], 9))
 main()