---
tags: leetcode
---

# [509. Fibonacci Number](https://leetcode.com/problems/fibonacci-number/)
---
# My Solution
## Solution 1
### The Key Idea for Solving This Coding Question
Brute Force
### C++ Code

class Solution {
public:
    int fib(int n) {
        if (n == 0 || n == 1) {
            return n;
        }
        
        return fib(n - 1) + fib(n - 2);
    }
};

### Time Complexity
$O(2^{n})$
### Space Complexity
$O(n)$
## Solution 2
### The Key Idea for Solving This Coding Question
Top-down DP (memoization)
### C++ Code

class Solution {
public:
    int fib(int n) {
        if (n == 0 || n == 1) {
            return n;
        }
        
        if (memo.find(n) == memo.end()) {
            memo[n] = fib(n - 1) + fib(n - 2);
            return memo[n];
        }
        return memo[n];
    }
    
private:
    unordered_map<int, int> memo;
};

### Time Complexity
$O(n)$
### Space Complexity
$O(n)$
## Solution 3
### The Key Idea for Solving This Coding Question
Bottom-up DP (tabulation)
### C++ Code

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

### Time Complexity
$O(n)$
### Space Complexity
$O(n)$
## Solution 4
### The Key Idea for Solving This Coding Question
Bottom-up DP (iteration)
### C++ Code

class Solution {
public:
    int fib(int n) {
        if (n == 0 || n == 1) {
            return n;
        }
        
        int a = 0, b = 1, c;
        for (int i = 2; i <= n; ++i) {
            c = a + b;
            a = b;
            b = c;
        }
        
        return c;
    }
};

### Time Complexity
$O(n)$
### Space Complexity
$O(1)$
# Miscellane
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