C++ Programming Code Examples
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Find the maximum subarray sub using Divide and Conquer Approach
/* Find the maximum subarray sub using Divide and Conquer Approach
- This algorithm implements the divide and conquer approach to find the sub-array having a maximum sum.
- The worst case time complexity of the algorithm is O(n*log(n)).
- Take the input of the integer array.
- Using divide and conquer approach break the array.
- Compute the individual sum and combine them, to get the global maximum sum.
- Exit. */
#include<iostream>
using namespace std;
// A function to find the maximum of two integers.
int max(int a, int b)
{
return (a > b)? a:b;
}
// A function to find the maximum sum sub-array which includes mid of the sub-array.
int MaxCrossingSum(int arr[], int low, int mid, int high)
{
// Include elements having index value less than or equal to the mid.
int sum = 0;
int leftpartsum = -1;
for (int i = mid; i >= low; i--)
{
sum = sum + arr[i];
if (sum > leftpartsum)
leftpartsum = sum;
}
// Include elements having index value greater mid.
sum = 0;
int rightpartsum = -1;
for (int i = mid+1; i <= high; i++)
{
sum = sum + arr[i];
if (sum > rightpartsum)
rightpartsum = sum;
}
// Return sum of elements on left and right of mid.
return leftpartsum + rightpartsum;
}
// Returns sum of maxium subarray sum.
int MaxSubArraySum(int arr[], int low, int high)
{
int mid;
// If low index is equal to the high index h then the subarray contains only one element.
if (low == high)
return arr[low];
// Otherwise find the mid index and proceed.
mid = (low + high)/2;
// Maximum sum sub-array can be either in the left part, right part or covering elements from both parts.
return max(max(MaxSubArraySum(arr, low, mid), MaxSubArraySum(arr, mid+1, high)), MaxCrossingSum(arr, low, mid, high));
}
int main()
{
int n, i;
cout<<"Enter 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];
}
// Print the maximum sub-array sum.
cout<<"\nMaximum sub-array sum is: "<<MaxSubArraySum(a, 0, n-1);
return 0;
}
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