Merge pull request #1310 from zahinekbal/zahinekbal

Added kadane's_algorithm By zahinekbal

data structures/array/Maximum-Subarray-Sum/KADANE'S_ALGORITHM/C++/Kadane's_algorithm.c++

@@ -0,0 +1,101 @@
+/*Largest Sum Contiguous Subarray
+Write an efficient program to find the sum of contiguous subarray within a one-dimensional 
+array of numbers which has the largest sum.
+
+Largest Subarray Sum Problem:-
+
+-2  -3  4  -1  -2  1  5  -3 
+
+=>4 + (-1) + (-2) + 1 + 5 = 7
+
+Maximum contiguous array sum is = 7;
+
+Kadane’s Algorithm:
+
+Initialize:
+    max_so_far = 0
+    max_ending_here = 0
+Loop for each element of the array
+  (a) max_ending_here = max_ending_here + a[i]
+  (b) if(max_so_far < max_ending_here)
+            max_so_far = max_ending_here
+  (c) if(max_ending_here < 0)
+            max_ending_here = 0
+return max_so_far
+
+Explanation:
+
+Simple idea of the Kadane’s 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
+
+ Lets take the example:
+
+    {-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 */
+
+//Program:
+
+//KADANE'S algorithm is able to find the MaximumSum of a Contiguous Subarray in array with the runtime of O(n)...
+// C++ program to print largest contiguous array sum 
+#include<iostream> 
+#include<climits> 
+using namespace std; 
+
+int maxSubArraySum(int a[], int size) 
+{ 
+    int max_so_far = INT_MIN, max_ending_here = 0; 
+
+    for (int i = 0; i < size; i++) 
+    { 
+        max_ending_here = max_ending_here + a[i]; 
+        if (max_so_far < max_ending_here) 
+            max_so_far = max_ending_here; 
+
+        if (max_ending_here < 0) 
+            max_ending_here = 0; 
+    } 
+    return max_so_far; 
+} 
+
+/*Driver program to test maxSubArraySum*/
+int main() 
+{ 
+    int a[] = {-2, -3, 4, -1, -2, 1, 5, -3}; 
+    int n = sizeof(a)/sizeof(a[0]); 
+    int max_sum = maxSubArraySum(a, n); 
+    cout << "Maximum contiguous sum is " << max_sum; 
+    return 0; 
+} 
+
+//Output:
+//Maximum contiguous sum is 7
+