**Table of contents**

Random number generations known as 'RNG' is widely used in different fields from games to apps to websites, to make things unpredictable and natural, in competitive programming RNG is used to create random test data or to solve problems with high probability.

To generate random numbers we usually need to choose a 'seed' (a seed is a base value used to calculate the random values, hence RNG is not really random) in most cases we use the current time as a seed since it is unpredictable, then we can use the random function to get a value in the range \( [0,1) \), now we need to figure out how to generate a value between \( x and y inclusive \).

Let's look at the simpler version first. the range \( [0, x) \), we can see that if we multiply a rangw by some value the range size will change, \( [0,1) * 5 \) we will get \( [0,5)\) so to get \( [0, x) \) we will multiply the range by \( x\).

Now for the general case, the range \( [x, y) \), first we will change the size of the range to \( (length = y - x + 1) \) and we get \( [0, 1) * length = [0, length) = [0,y - x + 1) \), now to fix the left boundary we simply shift the range by \( x \), \( [0, y - x + 1) + x = [0 + x, (y - x + 1) + x) = [x , y + 1) \).

Let's summarize the steps we used to generate a random integer between \(x and y inclusive\):

- Set the seed of the random function (current time is usually used).
- Multiply the random function range by the size of the needed range ( \( random() * (y -x + 1) \) ).
- Shift the random function range by the left boundary ( ( \( (random() * (y -x + 1)) + x \) ).
- Convert the result from float to integer.

```
from random import seed
from random import random
import random #import the random function
#Set the range of values
x = 3
y = 10
#Calculate the length of the needed range
Length = y - x + 1
#Print 10 values between 3 and 10
for _ in range(0,10):
#Change the ranodm function range
currentValuue = random.random() * Length
#Shift the range by x
currentValuue = currentValuue + x
#Convert float to integer
currentValuue = int(currentValuue)
print(currentValuue, end=' ')
```

```
Output:
5 4 4 3 7 8 4 10 9 7
```

## C++ Implementation

```
#include <iostream>
#include <random> //Random function header
#include <time.h> //Current time function header
using namespace std;
int main(){
//Set the random seed as the current time
srand(time(0));
//Set the range of values
int x = 3,y = 10;
//Calculate the length of the needed range
int length = y - x + 1;
//Print 10 values between 3 and 10
for(int i=1;i<=10;i++){
//in c++ the random function return a random integer
//to set the length we take the mod of the random value
//to change the left boundary we simply shift the values by x
int currentValue = rand() % length;
currentValue = currentValue + x;
cout << currentValue << ' ';
}
}
```

```
Output:
10 8 5 4 5 7 10 3 9 7
```