Path Sum Path Sum II

1.Path Sum

Given a binary tree and a sum, determine if the tree has a root-to-leaf path such that adding up all the values along the path equals the given sum.

For example:
Given the below binary tree and sum = 22,

              5
             / \
            4   8
           /   / \
          11  13  4
         /  \      \
        7    2      1

上面的题只需要判断是否有条路径的和为sum，而不需要求出所有的路径。

    public static boolean findPathSum(TreeNode<Integer> root, int sum) {
        if (root == null) {
            return false;
        }

        if (root.left == null && root.right == null) {
            return root.data == sum;
        }

        return (root.left != null && findPathSum(root.left, sum - root.data)) ||
                (root.right != null && findPathSum(root.right, sum - root.data));
    }

上面的代码，会沿着root先递归到最下面一个左子节点。假设此条路径就刚好满足和为sum，此时

        if (root.left == null && root.right == null) {
            return root.data == sum;
        }

会返回true。那么root.left != null && findPathSum(root.left, sum - root.data)会沿着堆栈信息一直回去返回true，后面的root.right != null && findPathSum(root.right, sum - root.data)这行不再被执行！
如果中间任意一条路径的和刚好满足sum，具体的逻辑跟上面是一致的。

2.Path Sum II

Given a binary tree and a sum, find all root-to-leaf paths where each path’s sum equals the given sum.

For example:
Given the below binary tree and sum = 22,

              5
             / \
            4   8
           /   / \
          11  13  4
         /  \    / \
        7    2  5   1

这道题要求将路径和为sum的所有路径都数出来，那么至少需要将树的所有路径都遍历，同时判断每条路径的和，看是否等于sum。如果相等则输出。

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

/**
 * Created by wanglei on 19/4/16.
 */
public class TreePathSum {

    public static List<String> list = new ArrayList<>();
    public static int target = 22;

    public static TreeNode<Integer> init() {
        TreeNode<Integer> root = new TreeNode<>(5);
        TreeNode<Integer> node4 = new TreeNode<>(4);
        TreeNode<Integer> node8 = new TreeNode<>(8);
        TreeNode<Integer> node11 = new TreeNode<>(11);
        TreeNode<Integer> node13 = new TreeNode<>(13);
        TreeNode<Integer> node42 = new TreeNode<>(4);
        TreeNode<Integer> node7 = new TreeNode<>(7);
        TreeNode<Integer> node2 = new TreeNode<>(2);
        TreeNode<Integer> node5 = new TreeNode<>(5);
        TreeNode<Integer> node1 = new TreeNode<>(1);
        root.left = node4;
        root.right = node8;
        node4.left = node11;
        node8.left = node13;
        node8.right = node42;
        node11.left = node7;
        node11.right = node2;
        node42.left = node5;
        node42.right = node1;

        return root;
    }
    
    public static void findPathSum2(TreeNode<Integer> root, int sum, String path, List<String> res) {
        if (root == null) {
            return;
        }

        if (root.left == null && root.right == null) {
            if (sum == target) {
                res.add(path);
            }
            return;
        }

        if (root.left != null) {
            findPathSum2(root.left, sum + root.left.data, path + "->" + root.left.data, res);
        }
        if (root.right != null) {
            findPathSum2(root.right, sum+root.right.data, path +"->" + root.right.data, res);
        }

    }

    public static void printList(List<String> input) {
        for(String ele: input) {
            System.out.println(ele);
        }
    }

    public static void main(String[] args) {
        TreeNode<Integer> root = init();
        findPathSum2(root, root.data, root.data.toString(), list);
        printList(list);
    }
}