[leetcode-96-Unique Binary Search Trees]
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
思路:
/**
* Taking 1~n as root respectively:
* 1 as root: # of trees = F(0) * F(n-1) // F(0) == 1
* 2 as root: # of trees = F(1) * F(n-2)
* 3 as root: # of trees = F(2) * F(n-3)
* ...
* n-1 as root: # of trees = F(n-2) * F(1)
* n as root: # of trees = F(n-1) * F(0)
*
* So, the formulation is:
* F(n) = F(0) * F(n-1) + F(1) * F(n-2) + F(2) * F(n-3) + ... + F(n-2) * F(1) + F(n-1) * F(0)
*/
int numTrees(int n) { vector<int>dp(n+1,0); dp[0] = dp[1] = 1; for(int i=2;i<=n;i++) { dp[i] =0; for(int j = 1;j<=i;j++) { dp[i]+= dp[j-1] * dp[i-j]; } } return dp[n]; }
参考:
https://discuss.leetcode.com/topic/5673/dp-problem-10-lines-with-comments
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