[刷题] 70 Climbing Stairs

Claim

• There are n steps in the staircase. How many ways to go up the stairs each time you go up one or two steps?

Examples

• Input: n = 3
• [1,1,1],[1,2,],[2,1]
• Output: n = 3

achieve

• Top-down (recursive)

Recursive

 1 class Solution {
 2 
 3 private:
 4     int calcWays(int n){
 5         
 6         if( n == 0 || n == 1 )
 7             return 1;    
 8             
 9         return calcWays(n-1) + calcWays(n-2);
10     }
11     
12 public:
13     int climbStairs(int n) {
14         
15         return calcWays(n);
16     }
17 };

View Code

Recursive + memory search

 1 class Solution {
 2 
 3 private:
 4     vector<int> memo;
 5     
 6     int calcWays(int n){
 7         
 8         if( n == 0 || n == 1 )
 9             return 1;    
10         
11         if( memo[n] == -1 )    
12             memo[n] = calcWays(n-1) + calcWays(n-2);
13             
14         return memo[n];
15     }
16     
17 public:
18     int climbStairs(int n) {
19         
20         memo = vector<int>(n+1,-1);
21         return calcWays(n);
22     }
23 };

View Code

• Bottom-up (dynamic programming)

 1 class Solution {
 2     
 3 public:
 4     int climbStairs(int n) {
 5         
 6         vector<int> memo(n+1,-1);
 7         
 8         memo[0] = 1;
 9         memo[1] = 1;
10         for( int i = 2 ; i <= n ; i ++ )
11             memo[i] = memo[i-1]+memo[i-2];
12         return memo[n];
13     }
14 };

View Code

Related

• 120 Triangle
• 64 Minimum Path Sum