Unique Binary Search Trees -- leetcode
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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
基本思路:
树的构成,则是依次选节点,作为根。
而该节点左边的所有元素,将会组成该根节点的左子树。
而右边所有元素,将会组成该节点的右子树。
则以该元素作为根的所有不同二叉 树个数为,左子树的不同个数 * 右子树的不同个数。
递推式为:
dp[i] = ∑ dp[j] * dp[ i-1-j] 0<=j<i
class Solution {public: int numTrees(int n) { vector<int> dp(n+1); dp[0] = 1; dp[1] = 1; for (int i=2; i<=n; i++) { for (int j=0; j<i; j++) dp[i] += dp[j] * dp[i-1-j]; } return dp[n]; }};
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