# Probability that the pieces of a broken stick form a n sided polygon in C++

C++Server Side ProgrammingProgramming

We are given with the stick of any length and that stick can be broken randomly into n pieces which can be of type integer or floating point and the task is to find whether the broken pieces can form a n sided polygon.

We can calculate the probability by applying the formula

$$P(E^{\prime})=1-P(E)=1-\frac{n}{2^{n-1}}$$

Where, n is the number of pieces generated by breaking the stick into parts.

Input

length = 10 , pieces = 4

Output

probability is : 0.5

Explanation − given with length of size 10 cm and it is broken into 4 parts

Input

length = 5 , pieces = 3

Output

probability is : 0.25

Explanation − given with length of size 5 cm and it is broken into 3 parts

## Approach used in the below program is as follows

• Input the length of the stick with number of pieces it can be broken into

• Apply the formula to calculate the probability

• Print the result

## Algorithm

Start
Step 1→ Declare function to calculate the probability
double probab(unsigned len, unsigned pieces)
declare unsigned a = (1 << (pieces-1))
return 1.0 - ((double)pieces) / ((double)a)
step 2→ In main()
Declare unsigned pieces = 4, len = 10
Call probab(len, pieces)
Stop

## Example

Live Demo

#include<iostream>
using namespace std;
//function to calculate probability
double probab(unsigned len, unsigned pieces){
unsigned a = (1 < (pieces-1));
return 1.0 - ((double)pieces) / ((double)a);
}
int main(){
unsigned pieces = 4, len = 10;
cout <<"probability is : "<<probab(len, pieces);
return 0;
}

## Output

If run the above code it will generate the following output −

probability is : 0.5