Given a number k, find the required minimum number of Fibonacci terms whose sum equal to k. We can choose a Fibonacci number multiple times.
Input : k = 4 Output : 2 Fibonacci term added twice that is 2 + 2 = 4. Other combinations are 1 + 1 + 2. 1 + 1 + 1 + 1 Among all cases first case has the minimum number of terms = 2. Input : k = 17 Output : 3
We can get any sum using Fibonacci numbers as 1 is a Fibonacci number. For example, to get n, we can n times add 1. Here we need to minimize the count of Fibonacci numbers that contribute to sum. So this problem is basically coin change problem with coins having Fibonacci values. By taking some examples, we can notice that With Fibonacci coin values Greedy approach works.
Firstly we calculate Fibonacci terms till less than or equal to k. then start from the last term and keep subtracting that term from k until k >(nth term). Also along with this keep increasing the count of the number of terms.
When k < (nth Fibonacci term) move to next Fibonacci term which is less than or Equal to k. at last, print the value of count.
The stepwise algorithm is:
1. Find all Fibonacci Terms less than or equal to K. 2. Initialize count = 0. 3. j = Index of last calculated Fibonacci Term. 4. while K > 0 do: // Greedy step count += K / (fibo[j]) // Note that division // is repeated subtraction. K = K % (fibo[j]) j--; 5. Print count.
Below is the implementation of the above approach.
- Find n terms of Fibonacci type series with given first two terms
- Sum of Fibonacci numbers at even indexes upto N terms
- Sum of nth terms of Modified Fibonacci series made by every pair of two arrays
- Deriving the expression of Fibonacci Numbers in terms of golden ratio
- Minimum number of Fibonacci jumps to reach end
- Minimum number of elements to be replaced to make the given array a Fibonacci Sequence
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- Minimum increment by k operations to make all elements equal
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- Make array elements equal in Minimum Steps
- Minimum value of X to make all array elements equal by either decreasing or increasing by X
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