Find n-th element from Stern’s Diatomic Series in C++

C++Server Side ProgrammingProgramming

Here we will see how to find the nth term in Stern’s Diatomic series. The series is like 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, … This is also known as fusc function. This series can be defined as −

𝑝(𝑛)=$p\lgroup\frac{n}{2}\rgroup$ π‘€β„Žπ‘’π‘› 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛

𝑝(𝑛)=$p\lgroup\frac{n-1}{2}\rgroup+p\lgroup\frac{n+1}{2}\rgroup$ π‘€β„Žπ‘’π‘› 𝑛 𝑖𝑠 π‘œπ‘‘π‘‘

𝑝(0)=0 π‘Žπ‘›π‘‘ 𝑝(1)=1

Here we will use the Dynamic programming approach to reduce the number of computations. After saving the base case for p(0) and p(1), we will iterate from index i = 2 to n, and compute p(i)

Example

 Live Demo

#include<iostream>
using namespace std;
int findTerm(int n) {
   int table[n+1];
   table[0] = 0;
   table[1] = 1;
   for (int i = 2; i <= n; i++) {
      if (i % 2 == 0)
         table[i] = table[i / 2];
      else
         table[i] = table[(i - 1) / 2] + table[(i + 1) / 2];
   }
   return table[n];
}
int main() {
   cout << 3 << " rd term is: " << findTerm(3) << endl;
   cout << 15 << " th term is: " << findTerm(15) << endl;
   cout << 20 << " th term is: " << findTerm(20) << endl;
}

Output

3 rd term is: 2
15 th term is: 4
20 th term is: 3
raja
Published on 19-Dec-2019 10:22:29
Advertisements