P1255——数楼梯

思路：高精+动态规划+滚动数组
高精不必再提，f[i]表示第i层楼梯走法，那么状态转移方程为f[i]=f[i-1]+f[i-2]，也就是斐波那契数列。当然，不同的是f[n]=n(n<=2)
代码：

#include<iostream>
using namespace std;
const int MAXN = 2001;
int last[MAXN] = { 1,1 }, now[MAXN] = { 1,2 };
int temp[MAXN] = { 1,1 };
int len = 1;
int N;
int main()
{
 cin >> N;
 if (N <= 2) {
  cout << N;
  return 0;
 }
 for (int i = 3; i <= N; i++) {
  int k = 1;
  for (int i = 1; i <= len; i++)
   temp[i] = now[i];
  while (k <= len) {
   now[k] += last[k];
   if (now[k] >= 10) {
    now[k] %= 10;
    now[k + 1] += 1;
   }
   k++;
  }
  for (int i = 1; i <= len; i++)
   last[i] = temp[i];
  if (now[len + 1] > 0)
   len++;
 }
 for (int i = len; i >= 1; i--)
  cout << now[i];
 return 0;
}