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
求二叉排序树的数量。
记忆化搜索,相比于discuss的做法还做了一个对半的优化,可惜数据量太小,不能体现我的优势。
在搜索的过程中,将搜索过的数量记下来。
class Solution {
public:
int dp[50];
int numTrees(int n) {
if(n<=1) return 1;
int res=0;
for(int mid=1;mid<=n/2;mid++)
{
if(dp[mid-1]==0) dp[mid-1]=numTrees(mid-1);
if(dp[n-mid]==0) dp[n-mid]=numTrees(n-mid);
res+=dp[mid-1]*dp[n-mid];
}
res*=2;
if(n%2)
{
if(dp[n/2]==0) dp[n/2]=numTrees(n/2);
res+=dp[n/2]*dp[n/2];
}
return res;
}
};