The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,
F(0) = 0
F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.
Given n, calculate F(n).
Constraints
0 <= n <= 30
Approach
Links
GeeksforGeeks
ProgramCreek
YouTube
Examples
Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
Solutions
/**
* Time complexity : O(2^N), The amount of operations needed, for each level
* of recursion, grows exponentially as the depth approaches N.
* Space complexity : O(N), We need space proportionate to N to account for
* the max size of the stack, in memory.
*/
public class Solution {
public int fib(int N) {
if (N <= 1) {
return N;
}
return fib(N-1) + fib(N-2);
}
}
/**
* Time complexity : O(N)
* Space complexity : O(1)
*/
class Solution {
public int fib(int n) {
if(n < 2) {
return n;
}
int prev = 0;
int curr = 1;
for(int i = 2; i <= n; i++) {
int temp = prev + curr;
prev = curr;
curr = temp;
}
return curr;
}
}