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完成 95，重新完成96
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‎README.adoc

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|Medium
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//|95
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//|{leetcode_base_url}/unique-binary-search-trees-ii/[Unique Binary Search Trees II]
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//|{source_base_url}/_0095_UniqueBinarySearchTreesII.java[Java]
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//|{doc_base_url}/0095-unique-binary-search-trees-ii.adoc[Note]
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//|Medium
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//|
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|95
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|{leetcode_base_url}/unique-binary-search-trees-ii/[Unique Binary Search Trees II]
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|{source_base_url}/_0095_UniqueBinarySearchTreesII.java[Java]
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|{doc_base_url}/0095-unique-binary-search-trees-ii.adoc[Note]
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|Medium
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|{leetcode_base_url}/unique-binary-search-trees/[Unique Binary Search Trees]

‎docs/0095-unique-binary-search-trees-ii.adoc

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[#0095-unique-binary-search-trees-ii]
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= 95. Unique Binary Search Trees II
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https://leetcode.com/problems/unique-binary-search-trees-ii/[LeetCode - Unique Binary Search Trees II]
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include::{sourcedir}/_0095_UniqueBinarySearchTreesII.java[]
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----
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这道题用到了回溯思想！昨天突击，又重新看了一遍回溯。有个模糊影响，但是还是要加强练习。
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‎docs/0096-unique-binary-search-trees.adoc

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[#0096-unique-binary-search-trees]
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= 96. Unique Binary Search Trees
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:stem: latexmath
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给定序列 `1 ... n`，我们选出数字 `i` 作为根，则对于根 `i` 的不同二叉搜索树数量 latexmath:[F(i, n)]，是左右子树个数的笛卡尔积，如下图所示:
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image::images/0096-1.png[]
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image::images/0096-01.png[]
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image::images/0096-02.png[]
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== 公式推到过程
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[asciimath]
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++++
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G_{(n)} \text { 长度为 n 的序列能构成的不同二叉搜索树的个数 }
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F_{(i, n)} \text { 以 i 为根、序列长度为 n 的不同二叉搜索树个数 (1≤i≤n)。 }
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G_{n}=\sum_{i=1}^{n} F_{(i, n)} = F_{(1, n)} + F_{(2, n)} + ... + F_{(n-1, n)} + F_{(n, n)}
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F_{(i, n)} = G_{(i-1)} \cdot G_{(n-i)}
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G_{(n)} = \sum_{i=1}^n G_{(i-1)} \cdot G_{(n-i)} = G_{0} \cdot G_{(n-1)} + ... + G_{(n-1)} \cdot G_{0}
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C_{n+1}=\frac{2(2 n+1)}{n+2} C_{n} \text { 明安图数 或 卡特兰数}
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++++
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TIP: 注意：题目要是二叉搜索树！
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没想到这里还埋了一个数学知识：Catalan number：
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[asciimath]
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++++
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C_{0}=1 \quad \text { and } \quad C_{n+1}=\sum_{i=0}^{n} C_{i} C_{n-i} \quad \text { for } n \geq 0
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C_{0}=1 \text { and } C_{1}=1
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C_{n}=\sum_{i=1}^{n} C_{i-1} C_{n-i} \quad
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C_{0}=1, \quad C_{n+1}=\frac{2(2 n+1)}{n+2} C_{n}
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++++
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include::{sourcedir}/_0096_UniqueBinarySearchTrees.java[]
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----
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[{java_src_attr}]
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----
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include::{sourcedir}/_0096_UniqueBinarySearchTrees_2.java[]
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----
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‎docs/images/0096-1.png renamed to ‎docs/images/0096-01.png

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‎docs/images/0096-02.png

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‎pom.xml

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<asciidoctor-comment-links.version>0.0.2</asciidoctor-comment-links.version>
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<asciidoclet.version>2.0.0</asciidoclet.version>
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<asciidoctor-maven-plugin.version>3.0.0</asciidoctor-maven-plugin.version>
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<mavengem-wagon.version>2.0.2</mavengem-wagon.version>
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<gem-maven-plugin.version>3.0.3</gem-maven-plugin.version>
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<download-maven-plugin.version>1.9.0</download-maven-plugin.version>
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<exec-maven-plugin.version>3.3.0</exec-maven-plugin.version>
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<version>${maven-javadoc-plugin.version}</version>
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<configuration>
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<source>${java.version}</source>
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<doclet>org.asciidoctor.Asciidoclet</doclet>
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<!-- https://github.com/asciidoctor/asciidoclet -->
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<doclet>org.asciidoctor.asciidoclet.Asciidoclet</doclet>
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<docletArtifact>
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<groupId>org.asciidoctor</groupId>
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<artifactId>asciidoclet</artifactId>
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<version>${asciidoclet.version}</version>
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</docletArtifact>
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<additionalJOptions>
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<additionalJOption>-J--add-exports=jdk.javadoc/jdk.javadoc.internal.tool=ALL-UNNAMED</additionalJOption>
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<additionalJOption>-J--add-opens=jdk.compiler/com.sun.tools.javac.api=ALL-UNNAMED</additionalJOption>
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<additionalJOption>-J--add-opens=jdk.compiler/com.sun.tools.javac.tree=ALL-UNNAMED</additionalJOption>
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<additionalJOption>-J--add-opens=jdk.compiler/com.sun.tools.javac.parser=ALL-UNNAMED</additionalJOption>
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<additionalJOption>-Xdoclint:all,-html,-accessibility</additionalJOption>
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</additionalJOptions>
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<!--<overview>src/main/java/overview.adoc</overview>-->
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<additionalparam>
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<additionalOptions>
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--base-dir ${project.basedir}
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-r asciidoctor-diagram
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<!--TODO: How to use asciidoctor-diagram?-->
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--gem-path ${gem.path}
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--require asciidoctor-diagram
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--attribute "stem=latexmath"
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--attribute "icons=font"
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--attribute "name=${project.name}"
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--attribute "version=${project.version}"
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--attribute "title-link=https://www.diguage.com/[${project.name} ${project.version}|地瓜哥]"
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</additionalparam>
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</additionalOptions>
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<additionalDependencies>
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<additionalDependency>
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<groupId>org.jruby</groupId>
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<artifactId>jruby</artifactId>
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<version>${jruby.version}</version>
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</additionalDependency>
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<additionalDependency>
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<groupId>org.asciidoctor</groupId>
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<artifactId>asciidoctorj</artifactId>
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<version>${asciidoctorj.version}</version>
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</additionalDependency>
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<additionalDependency>
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<groupId>org.asciidoctor</groupId>
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<artifactId>asciidoctorj-diagram</artifactId>
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<version>${asciidoctorj-diagram.version}</version>
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</additionalDependency>
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</additionalDependencies>
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</configuration>
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</plugin>
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<plugin>

‎src/main/java/com/diguage/algorithm/leetcode/_0095_UniqueBinarySearchTreesII.java

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package com.diguage.algorithm.leetcode;
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import com.diguage.algorithm.util.TreeNode;
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import java.util.ArrayList;
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import java.util.Collections;
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import java.util.List;
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/**
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* @author D瓜哥 · https://www.diguage.com
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* @since 2024-06-20 11:03:26
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*/
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public class _0095_UniqueBinarySearchTreesII {
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/**
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* 参考 https://leetcode.cn/problems/unique-binary-search-trees-ii/solutions/339143/bu-tong-de-er-cha-sou-suo-shu-ii-by-leetcode-solut/[95. 不同的二叉搜索树 II - 官方题解^]
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*/
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public List<TreeNode> generateTrees(int n) {
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if (n == 0) {
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return Collections.emptyList();
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}
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return generateTrees(1, n);
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}
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private List<TreeNode> generateTrees(int start, int end) {
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List<TreeNode> result = new ArrayList<>();
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if (start > end) {
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result.add(null);
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return result;
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}
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for (int i = start; i <= end; i++) {
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List<TreeNode> leftTrees = generateTrees(start, i - 1);
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List<TreeNode> rightTrees = generateTrees(i + 1, end);
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for (TreeNode left : leftTrees) {
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for (TreeNode right : rightTrees) {
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TreeNode curr = new TreeNode(i);
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curr.left = left;
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curr.right = right;
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result.add(curr);
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}
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}
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}
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return result;
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}
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}

‎src/main/java/com/diguage/algorithm/leetcode/_0096_UniqueBinarySearchTrees_2.java

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package com.diguage.algorithm.leetcode;
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/**
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* = 96. Unique Binary Search Trees
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*
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* https://leetcode.com/problems/unique-binary-search-trees/[Unique Binary Search Trees - LeetCode]
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*
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* @author D瓜哥, https://www.diguage.com/
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* @since 2020-01-27 22:14
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*/
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public class _0096_UniqueBinarySearchTrees_2 {
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public int numTrees(int num) {
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int[] r = new int[num + 1];
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r[0] = 1;
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r[1] = 1;
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for (int n = 2; n <= num; n++) {
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for (int i = 1; i <= n; i++) {
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r[n] += r[i - 1] * r[n - i];
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}
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}
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return r[num];
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}
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public static void main(String[] args) {
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_0096_UniqueBinarySearchTrees_2 solution = new _0096_UniqueBinarySearchTrees_2();
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int r1 = solution.numTrees(3);
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System.out.println((r1 == 5) + " : " + r1);
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}
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}

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