可以用迭代和递归两种方法求解,实例代码如下所示:
package com.zhumq.lianxi;
import org.junit.Test;
public class UniqueBinarySearchTree {
//迭代解法
public static int numTrees(int n) {
//有n个元素但是从0开始的所以定义n+1个元素,正好sum[n]就是最后一个元素。
int[] sum = new int[n+1];
sum[0] = 1;
sum[1] = 1;
for(int i=2;i<=n;i++) {
for(int k = 1;k<=i;k++) {
sum[i] += sum[k-1]*sum[i-k];
}
}
return sum[n];
}
//递归解法
public static int numTrees2(int n) {
if(n<=1) return 1;
int sum = 0;
//化成子问题求解
for(int i = 1; i<=n;i++) {
sum += numTrees2(i-1)*numTrees2(n-i);
}
return sum;
}
@Test
public void test() {
System.out.println(numTrees(3));
}
@Test
public void test2() {
System.out.println(numTrees2(3));
}
}