常见算法：斐波那契（Fibonacci）数列

class Solution {
public:

    map<int, int> cache;
    int fib(int n) {
        if (n == 0 || n == 1) {
            return n;
        }

        if (cache.find(n) != cache.end()) {
            return cache[n];
        }

        int res = (fib(n - 1) + fib(n - 2)) % 1000000007;
        cache[n] = res;

        return res;
    }
};

class Solution {
public:

    int fib(int n) {
        if (n == 0 || n == 1) {
            return n;
        }
        
       if(n == 2) {
            return 1;
        }

        vector<int> dp(n + 1, 0);
        // base case
        dp[1] = dp[2] = 1;
        for (int i = 3; i < n + 1; i++) {
            dp[i] = dp[i - 2] + dp[i - 1];
        }
        
        return dp[n];
    }
};