509. Fibonacci Number

Question

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.

Solutions

Method 1: DP

class Solution {
      public int fib(int N) {
          if(N < 2) 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];
      }
  }