# Why start + (end – start)/2 is preferable method for calculating middle of an array over (start + end)/2 ?

• Difficulty Level : Easy
• Last Updated : 27 Jul, 2021

I am very sure that everyone is able to find middle index of array once you know start index and end index of array, but there are certain benefits of using start + (end – start)/2 over (start + end)/2, which are described below :

The very first way of finding middle index is

`mid = (start + end)/2`

But there is problem with this approach, what if value of start or end or both is INT_MAX, it will cause integer overflow.
The better way of calculating mid index is :

`mid = start + (end - start)/2`

Let’s try these both methods in C program :

## C

 `// program for calculating mid of array``#include ``#include ``int` `main()``{``    ``int` `start = INT_MAX, end = INT_MAX;``    ``printf``(``"start = %dn"``, start);``    ``printf``(``"end = %dn"``, end);` `    ``// method 1``    ``int` `mid1 = (start + end) / 2;``    ``printf``(``"mid using (start + end)/2 = %dn"``, mid1);` `    ``// method 2``    ``int` `mid2 = start + (end - start) / 2;``    ``printf``(``"mid using start + (end - start)/2 = %dn"``, mid2);``    ``return` `0;``}`

Output:

```start = 2147483647
end = 2147483647
mid using (start + end)/2 = -1
mid using start + (end - start)/2 = 2147483647```

Note : (end – start) may overflow if end < 0 or start < 0
If you see the output, by using second method you get correct output and first method fails to calculate mid and if you use this index (-1 in this case), it can cause segmentation fault because of invalid index of array.

start + (end – start)/2 also works even if you are using pointers :

Example :
Method 1

## C

 `int` `s = 2, e = 3;``int``* start = &s;``int``* end = &e;``int``* mid = (start + end) / 2;`

Output :

```error: invalid operands of types ‘int*’ and ‘int*’ to binary ‘operator+’
int *mid = (start + end)/2;```

Method 2

## C

 `int` `s = 2, e = 3;``int``* start = &s;``int``* end = &e;``int``* mid = start + (end - start) / 2;`

Output :

`It will compile and give expected results`

Explanation: pointer addition is not supported in C while pointer subtraction is supported, the reason being the result of subtraction is the difference (in array elements) between the operands. The subtraction expression yields a signed integral result of type ptrdiff_t (defined in the standard include file STDDEF.H)(in short subtraction gives memory distance), but addition of two pointers in not meaningful, that’s why not supported

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