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.

Difficulty:Medium

Category: Recursion, DP

Analyze

Solution

SOlution 1: 递归方案:

//时间复杂度: O(2^n)
class Solution {
 public:
  int fib(int N) { 
    return N < 2 ? N : fib(N - 1) + fib(N - 2); 
  }
};

Solution 2:

class Solution {
 public:
  int fib(int N) {
    vector<int> m_(N + 1, 0);
    if (N < 2) return N;
    m_[0] = 0, m_[1] = 1;
    for (int i = 2; i <= N; ++i) {
      m_[i] = m_[i - 1] + m_[i - 2];
    }
    return m_[N];
  }
};

Solution 3: DP

class Solution {
 public:
  int fib(int N) {
    if (N < 2) return N;
    int m1 = 0, m2 = 1, m3 = 0;
    for (int i = 2; i <= N; ++i) {
      m3 = m1 + m2;
      m1 = m2;
      m2 = m3;
    }
    return m3;
  }
};