Create longest_sum_contigous_array.py

algorithms/arrays/longest_sum_contigous_array.py

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+"""
+Find the sum of contiguous subarray within a one-dimensional array of numbers which has the largest sum.
+
+The idea of algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this).
+And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). 
+Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far
+
+Example)
+Let input array = [-2,-3,4,-1,-2,1,5,3]
+
+max_so_far = max_ending_here = 0
+
+for i=0,  a[0] =  -2
+max_ending_here = max_ending_here + (-2)
+Set max_ending_here = 0 because max_ending_here < 0
+
+for i=1,  a[1] =  -3
+max_ending_here = max_ending_here + (-3)
+Set max_ending_here = 0 because max_ending_here < 0
+
+for i=2,  a[2] =  4
+max_ending_here = max_ending_here + (4)
+max_ending_here = 4
+max_so_far is updated to 4 because max_ending_here greater 
+than max_so_far which was 0 till now
+
+for i=3,  a[3] =  -1
+max_ending_here = max_ending_here + (-1)
+max_ending_here = 3
+
+for i=4,  a[4] =  -2
+max_ending_here = max_ending_here + (-2)
+max_ending_here = 1
+
+for i=5,  a[5] =  1
+max_ending_here = max_ending_here + (1)
+max_ending_here = 2
+
+for i=6,  a[6] =  5
+max_ending_here = max_ending_here + (5)
+max_ending_here = 7
+max_so_far is updated to 7 because max_ending_here is 
+greater than max_so_far
+
+for i=7,  a[7] =  -3
+max_ending_here = max_ending_here + (-3)
+max_ending_here = 4
+
+4+(-1)+(-2)+1+5 = 7
+hence,maximum contiguous array sum is 7
+"""
+def max_subarray_sum(a,size): 
+
+    max_so_far = 0
+    max_ending_here = 0
+
+    for i in range(0, size): 
+        max_ending_here = max_ending_here + a[i] 
+        if max_ending_here < 0: 
+            max_ending_here = 0
+        elif (max_so_far < max_ending_here): 
+            max_so_far = max_ending_here 
+
+    return max_so_far