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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
dynamic programming. 最重要的就是找规律！！！
i=0, count[0]=1 //empty tree
i=1, count[1]=1 //one tree
i=2, count[2]=count[0]*count[1] // 0 is root
+ count[1]*count[0] // 1 is root
i=3, count[3]=count[0]*count[2] // 1 is root
+ count[1]*count[1] // 2 is root
+ count[2]*count[0] // 3 is root
i=4, count[4]=count[0]*count[3] // 1 is root
+ count[1]*count[2] // 2 is root
+ count[2]*count[1] // 3 is root
+ count[3]*count[0] // 4 is root
..
..
..
Recurrence formula: i=n, count[n] = sum(count[0..k]*count[k+1...n]) 0 <= k < n-1
base case: count[0] = 1 count[1] = 1
Java code:
public class Solution { public int numTrees(int n) { int[] count = new int[n+1]; count[0] = 1; count[1] = 1; for(int i = 2; i<= n; i++){ for(int j = 0; j < i; j++){ count[i] += count[j] * count[i-1-j]; } } return count[n]; } }
Reference:
1. http://www.programcreek.com/2014/05/leetcode-unique-binary-search-trees-java/
2. http://bangbingsyb.blogspot.com/2014/11/leetcode-unique-binary-search-trees-i-ii.html
Leetcode Unique Binary Search Trees
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原文地址：http://www.cnblogs.com/anne-vista/p/4963929.html
