[Leetcode] Climbing Stairs

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?

DP启蒙啊，做完这题终于对DP有个大概的认识了，自底向上检表，建完也就ok了，复杂度是O(n)

void iter(int acc, int n, vector<int> &table) {
    if (acc < 0) return;
    if (acc == n+1) return;
    int a = acc-1 < 0? 0 : acc-1;
    int b = acc-2 <0? 0 : acc-2;
    table.push_back(table[a] + table[b]);
    iter(acc+1, n, table);
}

int climbStairs(int n) {
    vector<int> table;
    table.push_back(0);
    table.push_back(1);
    table.push_back(2);
    if (n < 3) return table[n];
    iter(3, n,table);
    return table[n];
}

另附纯递归版，当然是TLE的

int climbstairs_TLE(int n) {
    if (n == 1) return 1;
    if (n == 2) return 2;
    return climbstairs_TLE(n-1) + climbstairs_TLE(n-2);
}