Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C program to find nth term of given recurrence relation
Suppose we have three numbers a, b, c and a value n. We follow a recurrence formula S(n) −
- S(1) returns a
- S(2) returns b
- S(3) returns c
- S(n) returns S(n-1) + S(n-2) + S(n-3) for all n > 3.
We shall have to find nth term by following this recurrence.
So, if the input is like a = 5, b = 2, c = 3, n = 6, then the output will be 28 because −
- S(6) = S(5) + S(4) + S(3)
- S(5) = S(4) + S(3) + S(2)
- S(4) = S(3) + S(2) + S(1) = 3 + 2 + 5 = 10
- so now S(5) = 10 + 3 + 2 = 15
- and S(6) = 15 + 10 + 3 = 28
To solve this, we will follow these steps −
Define a function solve(), this will take a, b, c, n,
- if n is same as 1, then:
- return a
- if n is same as 2, then:
- return b
- if n is same as 3, then:
- return c
- return solve((a, b, c, n - 1) + solve(a, b, c, n - 2) + solve(a, b, c, n - 3))
Example
Let us see the following implementation to get better understanding −
#include <stdio.h>
int solve(int a, int b, int c, int n){
if(n == 1)
return a;
if(n == 2)
return b;
if(n == 3)
return c;
return solve(a, b, c, n-1) + solve(a, b, c, n-2) + solve(a, b, c, n-3);
}
int main(){
int a = 5, b = 2, c = 3, n = 6;
int res = solve(a, b, c, n);
printf("%d", res);
}
Input
5, 2, 3, 6
Output
28
Updated on: 08-Oct-2021
1K+ Views
Advertisements