回溯-例题实战

1 寻找二叉树所有路径（leetcode 257）

1.1 backtracking设计

从可选取列表选择当前遍历元素，进行递归调用，递归调用后再进行回溯，即把该元素从选取列表中移除，进入下一个回溯递归调用。

if(root.left != null){
            backTracking(root.left, path);
            path.remove(path.size() - 1);
        }
        if(root.right != null){
            backTracking(root.right, path);
            path.remove(path.size() - 1);
        }

终止条件，当遍历到叶子节点就终止遍历

if(root.left == null && root.right == null){
            list.add(new ArrayList<>(path));
            return;
        }

确定参数，再递归过程中，一方面要用path记录已经选取的结果集，另一方面要有一个候选列表可供当前选择。

public void backTracking(TreeNode root, List path){

1.2 算法设计代码

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

/**
 * @author zdh
 * @date 2021/7/10 17:48
 */
public class BinTreePaths {
    List<List<Integer>> list = new ArrayList<>();
    List<String> strings = new ArrayList<>();
    List<Integer> path = new ArrayList<>();

    public List<String> binaryTreePaths(TreeNode root) {
        list.clear();
        path.clear();
        strings.clear();

        backTracking(root, path);
        for (List l:
             list) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < l.size(); i++) {
                sb.append("->"+l.get(i));
            }
            sb.replace(0,2, "");
            strings.add(sb.toString());
        }
        return strings;
    }

    public void backTracking(TreeNode root, List path){
        path.add(root.val);
        if(root.left == null && root.right == null){
            list.add(new ArrayList<>(path));
            return;
        }

        if(root.left != null){
            backTracking(root.left, path);
            path.remove(path.size() - 1);
        }
        if(root.right != null){
            backTracking(root.right, path);
            path.remove(path.size() - 1);
        }
    }

    public static void main(String[] args) {
        TreeNode t4 = new TreeNode(4, null, null);
        TreeNode t3 = new TreeNode(3, null, null);
        TreeNode t2 = new TreeNode(2, t3, t4);
        TreeNode t = new TreeNode(1, null, t2);
        List<String > lists = new BinTreePaths().binaryTreePaths(t);
        for (String l:
             lists) {
            System.out.println(l);
        }
    }
}