Question: I am trying to understand how the following algorithms works.

```
#include <iostream>
using namespace std;
int maxsimum(int a[], int l, int r) {
    if (l == r)  
        return a[l];
    int m = (l+r)/2;
    int u = maxsimum(a,l,m);
    int v = maxsimum(a,m+1,r);
    return u>v?u:v;    
}

int main() {
    int a[] = {34,23,45,56,30,31,57,33,55,10};
    int n = sizeof(a)/sizeof(int);
    cout << maxsimum(a,0,n) << endl;         
    return 0;
}

```

First, what I am interested in is that in spite of algorithm's working correctly, it is mysterious for me how it finds the maximum element. I will show how I understood this algorithm:

Step 1: we say that in case of an array, `l=0` and `r=10`, it checks `if (l>r)` which does not hold of course so it calculates `m=(0+10)/2;`. Then do again the procedure for new bounds. The first pair is (0,5), the second is (6,10) and after the final operation it compares two returned values and finally returns the maximum element between them.

Does this algorithm always work? In each iteration it does not do any comparison, only the final step. How can it determine the maximum element at each recursive iteration? It checks only what. For example: take pair(0,5), is (0 more than 5)? No, so repeat again and divide these bounds into two so get new average value m1=(0+5)/2 then again again and return some element but not the maximum. Also for second subarray we can say the same.

What is the main idea of this algorithm?

Answer: 
Your error is here:

> 
> In each iteration it does not do any comparison, only the final step.
> 
> 
> 

This is wrong. In fact, it does a comparison in *every* step of the recursion (except in the base cases, i.e. where the array size is 1).
Error in `main()` function, test array has 10 elements, should be:

```
cout << maxsimum(a,0,n-1) << endl;

```