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.
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| 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
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Recursive Solution:#
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| class Solution {
public int climbStairs(int n) {
return climbStairs(0, n);
}
int climbStairs(int i, int n) {
if (i > n) return 0;
if (i == n) return 1;
return climbStairs(i + 1, n) + climbStairs(i + 2, n);
}
}
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Recursive Solution with Memo#
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| class Solution {
public int climbStairs(int n) {
int[] memo = new int[n + 1];
return climbStairs(0, n, memo);
}
int climbStairs(int i, int n, int[] memo) {
if (i > n) return 0;
if (i == n) return 1;
if (memo[i] > 0) {
return memo[i];
}
return memo[i] = climbStairs(i + 1, n, memo) + climbStairs(i + 2, n, memo);
}
}
|