- kaden's algorithm

src/Striver/arrays/kadane-algorithm(medium)/kadane-max-sum-in-array.py

@@ -6,22 +6,25 @@ def maxSubArray(arr: List[int]) -> int:
     maxSumBest = -float('inf')
     maxSumAtIndex = 0
     s = 0
-    subArray = []
+    subArray = ()
     for i in range(len(arr)):
         maxSumAtIndex += arr[i]
         if maxSumAtIndex > maxSumBest:
             maxSumBest = maxSumAtIndex
-            subArray = [s, i]
-        if maxSumAtIndex < 0:
+            subArray = (s, i)
+        # Carrying a subArray which give you negative sum will be of no use because
+        # it will decrease your sum.   
+        if maxSumAtIndex < 0: 
             maxSumAtIndex = 0
             s = i + 1
+
     return (maxSumBest, subArray)
 
 def test(arr):
-    (longest, subArray) = maxSubArray(arr)
+    (longest, (start, end)) = maxSubArray(arr)
     print(f"The longest subArray for {arr} with maximum sum is: ", longest)
-    print("The subArray is: ")
-    for i in range(subArray[0], subArray[1] + 1):
+    print(f"The subArray is: {(start, end)}")
+    for i in range(start, end + 1):
         print(arr[i], end=" ")
     print()
 

src/Striver/arrays/kadane-algorithm(medium)/readme.md

@@ -23,3 +23,11 @@ Output: 1
 
 Explanation: Array has only one element and which is giving positive sum of 1. 
 ```
+
+## Intuition
+
+We carrying only a sub array which gives a positive sum, even if it contains negative numbers inside: `[4, -1, 2]`.
+
+Carrying a subArray which give you negative sum will be of no use. Because you want to maximize the subArray sum. And carrying the negative sum will automatically decrease your sum.
+
+If all elements are negative the greatest sum will come from a single smallest negative element. `start` and `end` indexes of such subArray will be equal.