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C++ Program to Find the maximum subarray sum O(n^2) time(naive method)
/* C++ Program to Find the maximum subarray sum O(n^2) time(naive method)
- Implement the naive method to find the sub-array having a maximum sum.
- The worst case time complexity of the algorithm is O(n*n).
- Take the input of the integer array.
- Compare the sum of elements of every sub-array of length 1 to n.
- Print the sub-array with maximum sum.
- Exit. */
#include<iostream>
using namespace std;
int main()
{
int n, i, j, max=-1, sum, imax, fmax;
cout<<"\nEnter the number of data element in the array: ";
cin>>n;
int a[n];
for(i = 0; i < n; i++)
{
cout<<"Enter element "<<i+1<<": ";
cin>>a[i];
}
// Loop for the length of the sub-array.
for(i = 1; i < n+1; i++)
{
sum = 0;
// Loop for the maximizing the sum of the element of the sub array of length 'i'.
for(j = 0; j < n; j++)
{
// First pick the first sub array of 'i' length.
if(j < i)
sum += a[j];
// Add the next element and subtract the first element from the sub-array.
else
sum = sum+a[j]-a[j-i];
// Compare the sum with the global maximum of each length.
if(max < sum )
{
// Assign the initial and the final indexes to the imax and the fmax variables and update the max, if condition satisfies.
imax = j-i+1;
fmax = j;
max = sum;
}
}
}
// Print the maximum sum sub-array and their sum.
cout<<"\nThe maximum sub array is: ";
for(i = imax; i <= fmax; i++)
cout<<a[i]<<" ";
cout<<"\nThe maximum sub-array sum is: "<<max;
}
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