_70.java

package com.fishercoder.solutions;

/**
 * 70. 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?

 Note: Given n will be a positive integer.

 Example 1:

 Input: 2
 Output:  2
 Explanation:  There are two ways to climb to the top.

 1. 1 step + 1 step
 2. 2 steps

 Example 2:

 Input: 3
 Output:  3
 Explanation:  There are three ways to climb to the top.

 1. 1 step + 1 step + 1 step
 2. 1 step + 2 steps
 3. 2 steps + 1 step

 */

public class _70 {
  public static class Solution1 {
    //classical dp problem
    public int climbStairs(int n) {
      if (n < 1) {
        return 0;
      } else if (n < 4) {
        return n;
      } else {
        int[] dp = new int[n + 1];
        //the number of ways to reach step n could be calculated from n-1 and n-2
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; i++) {
          dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
      }
    }
  }
}