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Entringer Number in C++
Entringer Number is a special number which is equal to the number of permutations of {1, 2, 3, … n+1}, starting with K+1 which is updated by decreasing then increasing the values alternatively.
The value of Entringer Number is formulated using,
The recurrence relation,
E(n, k) = E(n, k-1) + E(n-1, n-k)
The base value is,
E(0,0) = 1
E(n, 0) = 0
We can find the Entringer number using,
Let’s take an example to see values
N = 5, k = 3
E(5, 3) = 14
Program to illustrate the working of our solution,
Example
#include <iostream>
using namespace std;
int EntringerNumber(int n, int k)
{
if (n == 0 && k == 0)
return 1;
if (k == 0)
return 0;
return EntringerNumber(n, k - 1) + EntringerNumber(n - 1, n - k);
}
int main() {
int n = 5, k = 3;
cout<<"The value of E("<<n<<", "<<k<<") = "<<EntringerNumber(n, k);
return 0;
}Output −
The value of E(5, 3) = 14
Updated on: 22-Jan-2021
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