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
Find the Minimum Number of Fibonacci Numbers Whose Sum Is K in C++
Suppose we have a number k, we have to find the minimum number of Fibonacci numbers whose sum is equal to the k, whether a Fibonacci number could be used multiple times.
So, if the input is like k = 7, then the output will be 2, as the Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, ... For k = 7 we can use 2 + 5 = 7.
To solve this, we will follow these steps −
Define an array f
insert 0 at the end of f
insert 1 at the end of f
while last element of f <= k, do −
insert (last element of f + second last element of f) into f
ret := 0
j := last index of f
while (j >= 0 and k > 0), do −
if f[j] <= k, then −
k := k - f[j]
(increase ret by 1)
Otherwise
(decrease j by 1)
return ret
Example
Let us see the following implementation to get a better understanding −
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int findMinFibonacciNumbers(int k) {
vector<int> f;
f.push_back(0);
f.push_back(1);
while (f.back() <= k) {
f.push_back(f[f.size() - 1] + f[f.size() - 2]);
}
int ret = 0;
int j = f.size() - 1;
while (j >= 0 && k > 0) {
if (f[j] <= k) {
k -= f[j];
ret++;
}
else
j--;
}
return ret;
}
};
main(){
Solution ob;
cout << (ob.findMinFibonacciNumbers(7));
}Input
7
Output
2
Updated on: 17-Nov-2020
407 Views
Advertisements