Merge pull request #412 from inimitable034/inimitable034-patch-1

Kadane's algorithm

Author: smv1999

Arrays/kadanes.java

@@ -0,0 +1,97 @@
+// Java program for Kadane's Algorithms
+
+//### Description :-
+
+//The  idea behind the implementation of Kadane’s algorithm is to peek for all positive contiguous segments of the array (max_ending_here is used for this).
+//Keep track of  the 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.
+
+
+class algo{
+
+	static void Kadanes(int a[], int size)
+	{
+		int max_so_far = Integer.MIN_VALUE,
+		max_ending_here = 0,start = 0,
+		end = 0, s = 0;
+
+		for (int i = 0; i < size; i++)
+		{
+		// loop to iterate and find the max_ending_here.
+			max_ending_here += a[i];
+
+			if (max_so_far < max_ending_here)
+		//condition to find the start and end indexes of the sub-array
+			{
+				max_so_far = max_ending_here;
+				start = s;
+				end = i;
+			}
+
+			if (max_ending_here < 0)
+			{
+				max_ending_here = 0;
+				s = i + 1;
+			}
+		}
+		// PRINT THE MAXIMUM CONTIGUOUS SUM WITH THE STARTING AND ENDING INDEXES.
+		System.out.println("Maximum contiguous sum is "
+						+ max_so_far);
+		System.out.println("Starting index " + start);
+		System.out.println("Ending index " + end);
+	}
+
+
+	public static void main(String[] args)
+	{
+		int a[] = { 10, 16, -2, 8, 5, 9, -7, 3 };
+		int n = a.length;
+	// CALLING OUR FUNCTION TO IMPLEMENT THE ALGORITH ON THE ABOVE ARRAY a[] 
+		Kadanes(a, n);
+	}
+}
+//     A SAMPLE TEST CASE  :-
+
+//     Here is a test cases to show the implementation of the above stated Algorithm:-
+
+//     Lets take the below set of elements in an array as 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
+