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ClimbStairs.java
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ClimbStairs.java
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package Leetcode;
/**
* @author kalpak
*
* You are climbing a staircase. It takes n steps to reach the top.
*
* Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
*
* Example 1:
* Input: n = 2
* Output: 2
* Explanation: There are two ways to climb to the top.
* 1. 1 step + 1 step
* 2. 2 steps
*
*
* Example 2:
* Input: n = 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
*
* Constraints:
*
* 1 <= n <= 45
*
*/
public class ClimbStairs {
public static int climbStairs(int n) {
int[] dp = new int[n + 1];
return countNumberOfStairsTopDown(dp, n);
}
private static int countNumberOfStairsTopDown(int[] dp, int n) {
if(n < 2)
return 1;
if (dp[n] != 0)
return dp[n];
dp[n] = countNumberOfStairsTopDown(dp, n - 1) + countNumberOfStairsTopDown(dp, n - 2);
return dp[n];
}
public static int countNumberOfStairsBottomsUp(int n) {
int[] dp = new int[n + 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];
}
public static int countNumberOfStairsBottomsUpSpaceOptimized(int n) {
if (n < 2)
return 1;
int num1 = 1;
int num2 = 1;
int temp = 0;
for(int i = 2; i <= n; i++) {
temp = num1 + num2;
num1 = num2;
num2 = temp;
}
return temp;
}
public static void main(String[] args) {
System.out.println(countNumberOfStairsBottomsUpSpaceOptimized(13));
}
}