Added Maximum Subarray Sum

Author: nandikeshsingh

Competitive Coding/Dynamic Programming/Maximum Subarray Sum/Maximum Subarray Sum Readme.md

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+Problem : To find the maximum subarray sum.
+
+Language used : C++
+
+Input : An integer array given by the user.
+
+Output : A single integer denoting the maximum subarray sum.
+
+Algorithm Paradigm : Dynamic Programming.
+
+Time Complexity : Linear
+
+Space Complexity : Constant
+
+Working :- 
+
+We are traversing the array and storing the sum of contiguous elements in sum variable.
+As the value of sum reaches its maximum value that value is stored in max_so_far variable.
+And as the value of sum becomes negative,we are setting the value of sum again to 0 as now its time to look for another subarray as the net sum of the elements of the previous subarray became negative. 
+

Competitive Coding/Dynamic Programming/Maximum Subarray Sum/Maximum Subarray Sum.cpp

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+//Code to find the maximum subarray sum using dynamin programming in c++.
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int main()
+{
+	int n;
+	cout<<"Enter the size of the array : ";//Inputting the size of the array.
+	cin>>n;
+	cout<<endl;
+
+	int arr[n];
+	for(int i=0;i<n;i++)
+	{
+		cout<<"Enter the value of element "<<i+1<<" : ";
+		cin>>arr[i];//Inputting the values in the array.
+	} 
+
+	int max_so_far=-99999;//It will store the maximum subarray sum.
+	int sum=0;//It will store the sum of the different subarrays.
+
+	for(int i=0;i<n;i++)//Implementing the kadane's Algorithm.
+	{
+		sum+=arr[i];
+		if(sum>max_so_far)
+			max_so_far=sum;
+		if(sum<0)
+			sum=0;
+	}
+
+	cout<<"The maximum subarray sum is : "<<max_so_far<<endl;//Printing the answer i.e the maximum subarray sum.
+
+	return 0;
+}