Fibonacci Number LT509

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).

Example 1:

Input: 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

Example 2:

Input: 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

Example 3:

Input: 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

Note:

0 ≤ N ≤ 30.

Idea 1. dynamic programming, 经典的入门dp,

dp[i] = dp[i-2] + dp[i-1] (i >= 2)

Time complexity: O(n)

Space complexity: O(n)

 class Solution {
     public int fib(int N) {
        if(N <= 1) {
            return N;
        }

         int[] dp = new int[N+1];
         dp[0] = 0;
         dp[1] = 1;

         for(int i = 2; i <= N; ++i) {
             dp[i] = dp[i-1] + dp[i-2];
         }

         return dp[N];
     }
 }

Idea 1.b, 从上面的公式可以看出只需要前2位dp[i-2] and dp[i-1], 可以不用array dp[].

Time complxity: O(n)

Space complexity: O(1)

 class Solution {
     public int fib(int N) {
         int first = 0;
         int second = 1;
         int result = N;

         for(int i = 2; i <= N; ++i) {
             result = first + second;
             first = second;
             second = result;
         }

         return result;
     }
 }