Update max_sub_array.py

TheAlgorithms#8609

Author: snehanjaligvs

Diff for: dynamic_programming/max_sub_array.py

@@ -1,44 +1,11 @@
 """
 author : Mayank Kumar Jha (mk9440)
+author(after editing) : Snehanjali G V S
 """
 from __future__ import annotations
 
 
-def find_max_sub_array(a, low, high):
-    if low == high:
-        return low, high, a[low]
-    else:
-        mid = (low + high) // 2
-        left_low, left_high, left_sum = find_max_sub_array(a, low, mid)
-        right_low, right_high, right_sum = find_max_sub_array(a, mid + 1, high)
-        cross_left, cross_right, cross_sum = find_max_cross_sum(a, low, mid, high)
-        if left_sum >= right_sum and left_sum >= cross_sum:
-            return left_low, left_high, left_sum
-        elif right_sum >= left_sum and right_sum >= cross_sum:
-            return right_low, right_high, right_sum
-        else:
-            return cross_left, cross_right, cross_sum
-
-
-def find_max_cross_sum(a, low, mid, high):
-    left_sum, max_left = -999999999, -1
-    right_sum, max_right = -999999999, -1
-    summ = 0
-    for i in range(mid, low - 1, -1):
-        summ += a[i]
-        if summ > left_sum:
-            left_sum = summ
-            max_left = i
-    summ = 0
-    for i in range(mid + 1, high + 1):
-        summ += a[i]
-        if summ > right_sum:
-            right_sum = summ
-            max_right = i
-    return max_left, max_right, (left_sum + right_sum)
-
-
-def max_sub_array(nums: list[int]) -> int:
+def max_sub_array(a: list[int]) -> int:
     """
     Finds the contiguous subarray which has the largest sum and return its sum.
 
@@ -58,36 +25,20 @@ def max_sub_array(nums: list[int]) -> int:
     >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
     187
     """
-    best = 0
-    current = 0
-    for i in nums:
-        current += i
-        current = max(current, 0)
-        best = max(best, current)
-    return best
+    sol = [0]* (len(a) + 1)
+    for i in range(1, len(sol)):
+        sol[i] = max(sol[i - 1] + a[i -1], a[i - 1])
+        
+    answer  = sol[0]
+    for i in range(1, len(sol)):
+        if answer < sol[i]:
+            answer = sol[i]
+    return answer
 
 
 if __name__ == "__main__":
     """
     A random simulation of this algorithm.
     """
-    import time
-    from random import randint
-
-    from matplotlib import pyplot as plt
-
-    inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
-    tim = []
-    for i in inputs:
-        li = [randint(1, i) for j in range(i)]
-        strt = time.time()
-        (find_max_sub_array(li, 0, len(li) - 1))
-        end = time.time()
-        tim.append(end - strt)
-    print("No of Inputs       Time Taken")
-    for i in range(len(inputs)):
-        print(inputs[i], "\t\t", tim[i])
-    plt.plot(inputs, tim)
-    plt.xlabel("Number of Inputs")
-    plt.ylabel("Time taken in seconds ")
-    plt.show()
+    inputs = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    print(max_sub_array(inputs))