Zeckendorf 定理的Java程序(非相邻斐波那契表示)
给定一个数字,找到一个数字表示为非连续斐波那契数的总和。
例子:
Input: n = 10
Output: 8 2
8 and 2 are two non-consecutive Fibonacci Numbers
and sum of them is 10.
Input: n = 30
Output: 21 8 1
21, 8 and 1 are non-consecutive Fibonacci Numbers
and sum of them is 30.
这个想法是使用贪心算法。
1) Let n be input number
2) While n >= 0
a) Find the greatest Fibonacci Number smaller than n.
Let this number be 'f'. Print 'f'
b) n = n - f
// Java program for Zeckendorf's theorem. It finds representation
// of n as sum of non-neighbouring Fibonacci Numbers.
class GFG {
public static int nearestSmallerEqFib(int n)
{
// Corner cases
if (n == 0 || n == 1)
return n;
// Find the greatest Fibonacci Number smaller
// than n.
int f1 = 0, f2 = 1, f3 = 1;
while (f3 <= n) {
f1 = f2;
f2 = f3;
f3 = f1 + f2;
}
return f2;
}
// Prints Fibonacci Representation of n using
// greedy algorithm
public static void printFibRepresntation(int n)
{
while (n > 0) {
// Find the greates Fibonacci Number smaller
// than or equal to n
int f = nearestSmallerEqFib(n);
// Print the found fibonacci number
System.out.print(f + " ");
// Reduce n
n = n - f;
}
}
// Driver method to test
public static void main(String[] args)
{
int n = 30;
System.out.println("Non-neighbouring Fibonacci Representation of " + n + " is");
printFibRepresntation(n);
}
}
输出:
Non-neighbouring Fibonacci Representation of 30 is
21 8 1
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