给定一个数 k，找出总和等于 k 的所需的最小斐波那契项数。我们可以多次选择一个斐波那契数。
例子：
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推荐：请先在 IDE 上尝试您的方法，然后再查看解决方案
我们可以使用斐波那契数获得任何和，因为 1 是斐波那契数。例如，要得到 n，我们可以 n 次加 1。这里我们需要最小化对总和有贡献的斐波那契数的数量。所以这个问题基本上是具有斐波那契值的硬币的硬币找零问题。通过举一些例子，我们可以注意到使用斐波那契硬币价值贪婪方法是有效的。
首先我们计算斐波那契项直到小于或等于 k。然后从最后一项开始，不断地从 k 中减去那个项，直到 k >(nth term)。与此同时，不断增加术语的数量。
当 k <（第 n 个斐波那契项）移动到下一个小于或等于 k 的斐波那契项时。最后，打印count的值。
逐步算法是：
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.下面是上述方法的实现。
C++
// C++ code to find minimum number of fibonacci
// terms that sum to K.
#include
using namespace std;
// Function to calculate Fibonacci Terms
void calcFiboTerms(vector& fiboTerms, int K)
{
int i = 3, nextTerm;
fiboTerms.push_back(0);
fiboTerms.push_back(1);
fiboTerms.push_back(1);
// Calculate all Fibonacci terms
// which are less than or equal to K.
while (1) {
nextTerm = fiboTerms[i - 1] + fiboTerms[i - 2];
// If next term is greater than K
// do not push it in vector and return.
if (nextTerm > K)
return;
fiboTerms.push_back(nextTerm);
i++;
}
}
// Function to find the minimum number of
// Fibonacci terms having sum equal to K.
int findMinTerms(int K)
{
// Vector to store Fibonacci terms.
vector fiboTerms;
calcFiboTerms(fiboTerms, K);
int count = 0, j = fiboTerms.size() - 1;
// Subtract Fibonacci terms from sum K
// until sum > 0.
while (K > 0) {
// Divide sum K by j-th Fibonacci term to find
// how many terms it contribute in sum.
count += (K / fiboTerms[j]);
K %= (fiboTerms[j]);
j--;
}
return count;
}
// driver code
int main()
{
int K = 17;
cout << findMinTerms(K);
return 0;
} Java
// Java code to find the minimum number of Fibonacci terms
// that sum to k.
import java.util.*;
class GFG
{
// Function to calaculate Fibonacci Terms
public static void calcFiboTerms(ArrayList fiboterms,
int k)
{
int i = 3, nextTerm = 0;
fiboterms.add(0);
fiboterms.add(1);
fiboterms.add(1);
// Calculate all Fibonacci terms
// which are less than or equal to k.
while(true)
{
nextTerm = fiboterms.get(i - 1) + fiboterms.get(i - 2);
// If next term is greater than k
// do not add in arraylist and return.
if(nextTerm>k)
return;
fiboterms.add(nextTerm);
i++;
}
}
// Function to find the minimum number of
// Fibonacci terms having sum equal to k.
public static int fibMinTerms(int k)
{
// ArrayList to store Fibonacci terms.
ArrayList fiboterms = new ArrayList();
calcFiboTerms(fiboterms,k);
int count = 0, j = fiboterms.size() - 1;
// Subtract Fibonacci terms from sum k
// until sum > 0.
while(k > 0)
{
// Divide sum k by j-th Fibonacci term to find
// how many terms it contribute in sum.
count += (k / fiboterms.get(j));
k %= (fiboterms.get(j));
j--;
}
return count;
}
// driver code
public static void main (String[] args) {
int k = 17;
System.out.println(fibMinTerms(k));
}
}
/* This code is contributed by Akash Singh*/ Python3
# Python3 code to find minimum number
# of Fibonacci terms that sum to K.
# Function to calculate Fibonacci Terms
def calcFiboTerms(fiboTerms, K):
i = 3
fiboTerms.append(0)
fiboTerms.append(1)
fiboTerms.append(1)
# Calculate all Fibonacci terms
# which are less than or equal to K.
while True:
nextTerm = (fiboTerms[i - 1] +
fiboTerms[i - 2])
# If next term is greater than K
# do not push it in vector and return.
if nextTerm > K:
return
fiboTerms.append(nextTerm)
i += 1
# Function to find the minimum number of
# Fibonacci terms having sum equal to K.
def findMinTerms(K):
# Vector to store Fibonacci terms.
fiboTerms = []
calcFiboTerms(fiboTerms, K)
count, j = 0, len(fiboTerms) - 1
# Subtract Fibonacci terms from
# sum K until sum > 0.
while K > 0:
# Divide sum K by j-th Fibonacci
# term to find how many terms it
# contribute in sum.
count += K // fiboTerms[j]
K %= fiboTerms[j]
j -= 1
return count
# Driver code
if __name__ == "__main__":
K = 17
print(findMinTerms(K))
# This code is contributed
# by Rituraj JainC#
// C# code to find the minimum number
// of Fibonacci terms that sum to k.
using System;
using System.Collections.Generic;
class GFG
{
// Function to calaculate Fibonacci Terms
public static void calcFiboTerms(List fiboterms,
int k)
{
int i = 3, nextTerm = 0;
fiboterms.Add(0);
fiboterms.Add(1);
fiboterms.Add(1);
// Calculate all Fibonacci terms
// which are less than or equal to k.
while(true)
{
nextTerm = fiboterms[i - 1] +
fiboterms[i - 2];
// If next term is greater than k
// do not add in arraylist and return.
if(nextTerm > k)
return;
fiboterms.Add(nextTerm);
i++;
}
}
// Function to find the minimum number of
// Fibonacci terms having sum equal to k.
public static int fibMinTerms(int k)
{
// List to store Fibonacci terms.
List fiboterms = new List();
calcFiboTerms(fiboterms, k);
int count = 0, j = fiboterms.Count - 1;
// Subtract Fibonacci terms from sum k
// until sum > 0.
while(k > 0)
{
// Divide sum k by j-th Fibonacci term to find
// how many terms it contribute in sum.
count += (k / fiboterms[j]);
k %= (fiboterms[j]);
j--;
}
return count;
}
// Driver Code
public static void Main (String[] args)
{
int k = 17;
Console.WriteLine(fibMinTerms(k));
}
}
// This code is contributed by PrinciRaj1992 Javascript
输出：
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