# Question: How was the assumption made?

### Jose Ross Barredo γ»1 min read

Hi guys! I have been reading "Cracking the Coding Interview 6th Edition".. On Chapter 0 - Big O, I have problem understanding an assumption made to a problem on Example 3.

```
void printUnorderedPairs(int[] array){
for(int i = 0; i < array.length; i++){
for(int j = i + 1; j < array.length; j++){
...
}
}
}
```

Under *What It Means* section, it assumed that:

There are N

^{2}total pairs. Roughly half of those will have i < j and the remaining half will have i > j. This code goes through roughly n^{2/2}pairs so it does O(N^{2)}work.

My question is, how was the assumption made on ** Roughly half of those will have i < j and the remaining half will have i > j** done? Can someone explain it to me please?

Thanks!