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

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