Getting all nodes at a level in full binary tree, array format

问题

I need to get all the nodes at a certain level in a full binary tree from either the left or right subtree. I currently retrieve the binary tree from the DB as an array, for example: [1,2,3,4,5,6,7] represents a tree like this:

                                     1
                                    / \
                                   /   \
                                  2     3
                                 / \   / \
                                /   \ /   \
                               4    5 6    7

So what I need to do is basically grab a level of the tree and return it as an array. Something like level(3,"left") -> [4,5] or level(2, "right") -> [3]. I was thinking about creating a BinaryTree object doing it recursively, but I can't think of a way to keep track of the level within the call without having to tag every node with a level or something like that as I'd like to keep the DB as clean as possible. Any ideas?

Edit: I really need all the nodes at a level for the left or right subtree, not the whole tree. I'm displaying a tournament, so I need to split it half and half. If I didn't have to split it, I could probably do this:

function level($array, $level_num) {
    return array_slice($array, pow(2, $level_num)-1, pow(2, $level_num));
}

I don't really know how to extend this for getting only the left or right subtree's level array.

回答1:

I upvoted BeetleJuice's answer for using the "Shift Left" bitwise operator << -- it is the perfect building block for this task.

This is as clean as I can make my coding attempt:

Code: (Demo)

function getForkinValues($array,$level,$side='left'){ // left side fork is default
    if($level==1) return current($array);
    $length=$level>2?1<<($level-2):1;  // number of elements to return
    $index=(1<<$level-1)-1;            // first index to return
    if($side=='right') $index+=$length;  // shift to correct index for 'right'
    if(!isset($array[$index+$length-1])) return 'Error: Insufficient Array Length';
    return array_slice($array,$index,$length);

}
$array=['A','B','C','D','E','F','G'];
var_export(getForkinValues($array,3,'right'));

回答2:

// Adjust depth as needed
$depth = 3;

// using bit arithmetic. '<< 3' means multiply by 2 three times.
$start = 1 << $depth-1; // 1 * (2 * 2) because depth is 3
$end = (1 << $depth) -1; // 1 * (2 * 2 * 2) - 1

// if depth=3, this is [4,5,6,7]
$fullLevel = range($start, $end);

print_r($fullLevel);

if($depth > 1):
    $leftBranch = array_slice($fullLevel,0,count($fullLevel)/2);
    $rightBranch = array_slice($fullLevel,count($fullLevel) / 2);

    print_r($leftBranch); // [4,5]
    print_r($rightBranch); // [6, 7]
endif;

来源：https://stackoverflow.com/questions/45291652/getting-all-nodes-at-a-level-in-full-binary-tree-array-format

标签

php

arrays

binary-tree