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?
Constraints
n >= 1
Approach
Fibonacci
Links
ProgramCreek
Examples
Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1 step + 1 step
2 steps
Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1 step + 1 step + 1 step
1 step + 2 steps
2 steps + 1 step
Solutions
/**
* Time complexity : O(2^n).Size of recursion tree will be 2^n.
*
*/
public class Solution {
public int climbStairs(int n) {
return climb_Stairs(0, n);
}
public int climb_Stairs(int i, int n) {
if (i > n) {
return 0;
}
if (i == n) {
return 1;
}
return climb_Stairs(i + 1, n) + climb_Stairs(i + 2, n);
}
}
/**
* Time complexity : O(n). Single loop upto n.
* Space complexity : O(n). dp array of size n is used.
*/
public class Solution {
public int climbStairs(int n) {
if (n == 1) {
return 1;
}
int[] dp = new int[n + 1];
dp[1] = 1;
dp[2] = 2;
for (int i = 3; i <= n; i++) {
dp[i] = dp[i - 1] + dp[i - 2];
}
return dp[n];
}
}
/**
* Time complexity : O(n). Single loop upto n is required to calculate nth fibonacci number.
* Space complexity : O(1). Constant space is used.
*/
class Solution {
public int climbStairs(int n) {
int first = 1;
int second = 1;
while(--n > 0) {
int t = first;
first = second;
second += t;
}
return second;
}
}