算法：回溯二 生成有效括号对Generate Parentheses

说明

地址： https://leetcode.com/problems/generate-parentheses/

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

解法

解析：
生成有效括号，满足如下条件

1. 左括号个数left要大于等于右括号数right, 也就是必须 right>left才能添加右括号。
2. 左右括号剩余数要大于0.
3. 回溯退出条件为if (left == 0 && right == 0)

package backtracking;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

// https://leetcode.com/problems/generate-parentheses/
public class GenerateParentheses {

  public static void main(String[] args) {
    GenerateParentheses obj = new GenerateParentheses();
    List<String> result = obj.generateParenthesis(3);
    System.out.println("result > " + Arrays.toString(result.toArray()));
  }

  public List<String> generateParenthesis(int n) {
    List<String> result = new ArrayList<>();
    if (n <= 0) {
      return result;
    }

    helper(result, "", n, n);

    return result;
  }

  public void helper(List<String> result, String combine, int left, int right) {
    //exit
    if (left == 0 && right == 0) {
      result.add(combine);
      return;
    }

    if (left > 0) {
      helper(result, combine + '(', left - 1, right);
    }
    if (right > left) {
      helper(result, combine + ')', left, right - 1);
    }
  }
}

代码下载

https://github.com/zgpeace/awesome-java-leetcode/blob/master/code/LeetCode/src/backtracking/GenerateParentheses.java