斐波那契dp

You are climbing a stair case. It takes n steps to reach to the top.
Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
Note: Given n will be a positive integer.
题目来源于https://leetcode.com/problems/climbing-stairs/#/description
题目的意思是给你n级台阶，每次只能上1，2级台阶，总共有多少种方法？
测试数据n=70结果696897233

简单的递归

long long dfs(int n){    if(n==0)return 1;    if(n==1)return 1;    return dfs(n-1)+dfs(n-2);}

数据量大，递归的次数太多，内存容易爆炸

增量化模型

int dp[100];long long dfs(int n){    if(n==1)return 1;    dp[0]=1;    dp[1]=1;    for(int i=2;i<=n;i++)    {        dp[i]=dp[i-1]+dp[i-2];    }    return dp[n];}

滚动数组

long long climbStairs(int n){    if (n <= 2) {        return n;    }    int num1 = 1;    int num2 = 2;    int res = 0;    for (int i = 2; i < n; i++)    {        res = num1 + num2;        num1 = num2;        num2 = res;    }    return res;}