[LeetCode] 121: Unique Binary Search Trees

[Problem]
Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,

Given n = 3, there are a total of 5 unique BST's.

1 3 3 2 1
\ / / / \ \
3 2 1 1 3 2
/ / \ \
2 1 2 3

[Solution]
方法一

class Solution {
public:
int numTrees(int n) {
// Note: The Solution object is instantiated only once and is reused by each test case.

// invalid
if(n <= 0)return 0;

// initial
int dp[n+1];
memset(dp, 0, sizeof(dp));
dp[0] = 1;
for(int i = 1; i <= n; ++i){
for(int j = 1; j <= i; ++j){
dp[i] += dp[j-1]*dp[i-j];
}
}
return dp
;
}
};

方法二：Catalan数 C_n+1= C_n * 2(2n+1)/(n+2)

class Solution {
public:
int numTrees(int n) {
// Note: The Solution object is instantiated only once and is reused by each test case.

// invalid
if(n <= 0)return 0;

// initial
int dp[n+1];
memset(dp, 0, sizeof(dp));
dp[1] = 1;
for(int i = 2; i <= n; ++i){
dp[i] = 2*(2*(i-1)+1)*dp[i-1]/(i-1+2);
}
return dp
;
}
};

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