C language: A frog can jump up to 1 steps at a time, you can also jump on level 2. How many hops does the frog have to jump on an n-level stair altogether?

A frog can jump up to 1 steps at a time , or jump up to level 2 . How many hops does the frog have to jump on an n-level stair altogether?

Solution: PutNthe jumping method of the step isf (N), whenn>2, there are two different choices when jumping for the first time: first, jumping only1the number of hops equals the rest of the back.n-1the number of jumps of a step, that isf (n-1);the other is the first jump .2the number of hops equals the rest of the back.n-2the number of jumps of a step, that isf (n-2);soNthe jumping method of the step isf (N) =f (n-1) +f (n-2). It is not hard to see that this is actually a variant application of the Fibonacci sequence, which moves each of the Fibonacci sequence forward.1bit.

Program:

#include <stdio.h>

int Fibonacci (int n)

{

int NUM1 = 1, num2 = 1, num3 = 0, i = 0;

if (n <= 1)

{

return NUM1;

}

for (i = 1; i < n; i++)

{

num3 = Num1 + num2;

NUM1 = num2;

num2 = num3;

}

return num3;

}

int main ()

{

int num = 0, ret = 0;

printf ("Please enter the number of steps:");

scanf ("%d", &num);

ret = Fibonacci (num);

printf ("A total of%d hops!") \ n ", ret);

return 0;

}

Results:

Please enter the number of steps : 3

There are 3 Different kinds of jumping methods!

Please press any key to continue ...

expansion:   Span style= "FONT-FAMILY:CALIBRI;" >1 steps can also jump on 2 level, n class. Ask the frog to jump to the previous n level steps how many kinds of jumping?

Solution: We can obtain a total of f (n) =2^ (n-1) by mathematical induction method

Program:

#include <stdio.h>

#include <math.h>

int Fibonacci (int n)

{

Return pow (2,n-1);

}

int main ()

{

int num = 0, ret = 0;

printf ("Please enter the number of steps:");

scanf ("%d", &num);

ret = Fibonacci (num);

printf ("A total of%d hops!") \ n ", ret);

return 0;

}

Results:

Please enter the number of steps : 3

There are 4 Different kinds of jumping methods!

Please press any key to continue ...

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C: A frog can jump up to 1 steps at a time, or jump up to level 2. How many hops does the frog have to jump on an n-level stair altogether?