Groupon面经：Find paths in a binary tree summing to a target value

You are given a binary tree (not necessarily BST) in which each node contains a value. Design an algorithm to print all paths which sum up to that value. Note that it can be any path in the tree - it does not have to start at the root.

http://stackoverflow.com/questions/4591763/find-paths-in-a-binary-search-tree-summing-to-a-target-value

Traverse through the tree from the root and do a post-order gathering of all path sums. Use a hashtable at each node to store the possible paths rooted at a node and going down-only. Key is the path sum, value is the actual path. We can construct all paths going through a node from itself and its childrens' paths.

Here is psuedo-code that implements the above, but stores only the sums and not the actual paths. For the paths themselves, you need to store the end node in the hashtable (we know where it starts, and there's only one path between two nodes in a tree).

function findsum(tree, target)

  # Traverse the children

  if tree->left

    findsum(tree.left, target)

  if tree->right

    findsum(tree.right, target)

  # Single node forms a valid path

  tree.sums = {tree.value}

  # Add this node to sums of children

  if tree.left

    for left_sum in tree.left.sums

      tree.sums.add(left_sum + tree.value)

  if tree.right

    for right_sum in tree.right.sums

      tree.sums.add(right_sum + tree.value)

  # Have we formed the sum?

  if target in tree.sums

    we have a path

  # Can we form the sum going through this node and both children?

  if tree.left and tree.right

    for left_sum in tree.left.sums

      if target - left_sum in tree.right.sums

        we have a path

  # We no longer need children sums, free their memory

  if tree.left

    delete tree.left.sums

  if tree.right

    delete tree.right.sums

巴特西

Groupon面经：Find paths in a binary tree summing to a target value

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