509-斐波那契数

LeetCode 509. Fibonacci Number

LeetCode-509

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

method 1: 递归

int fib(int n) {
    if (n < 2) return n;
    return fib(n - 1) + fib(n - 2);
}

method 2: 动态规划

int fib(int n) {
    if (n < 2) return n;
    vector<int> dp(n + 1);
    dp[1] = 1;
    for (int i = 2; i < n + 1; i++) {
        dp[i] = dp[i - 1] + dp[i - 2];
    }
    return dp[n];
}

可以只用2个变量

int fib(int n) {
    if (n < 2) return n;
    int dp0 = 0;
    int dp1 = 1;
    for (int i = 2; i <= n; i++) {
        int res = dp0 + dp1;
        dp0 = dp1;
        dp1 = res;
    }
    return dp1;
}