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.
看得别人的代码,然后写出来的 :http://www.2cto.com/kf/201312/262420.html
public class UniqueBinarySearchTrees { public static void main(String[] args) { int n = (int)(Math.random()*100); // 随机生成数字 System.out.println(n); int num = numTrees(n); System.out.println(num); } private static int numTrees(int n) { if (n == 0 || n == 1) { return n; } else { // 以i为根节点时,其左子树构成为[0,...,i-1],其右子树构成为[i+1,...,n]构成 // 因此,dp[i] = sigma(dp[0...k] * dp[k+1...i]) 0 <= k < i - 1 // dp[3] = dp[0] * dp[2] + dp[1] * dp[1] + dp[2] * dp[0] int[] num = new int[n+1]; num[0] = num[1] = 1; for (int i = 2; i < num.length; i++) { num[i] = 0; for (int j = 0; j < i; j++) { num[i] = num[i] + num[j] * num[i-j-1]; } } return num[n]; } } }
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故不积跬步,无以致千里