5.3.1 Unique Binary Sear Trees

class Solution {
public:
int numTrees(int n) {
return numTrees_2(n);
}
int numTrees_1(int n) {
int dp[n+1];
memset(dp, 0, sizeof(dp));
dp[0] = 1;
for (int i = 1; i <= n; ++i)
for (int j = 0; j < i; j++)
dp[i] += dp[j] * dp[i-j-1];
return dp
;
}
int numTrees_2(int n) {
if (n < 0) return 0;
vector<int> dp(n+1, 0);
dp[0] = 1; dp[1] = 1;
for(int i = 2;i <= n; ++i){
dp[i] = dp[i-1] * (4 * i - 2)/(i + 1);
}
return dp
;
}
};