Algorithm

95.unique-binary-search-trees-ii

Description:

Given an integer n, generate all structurally unique BST’s (binary search trees) that store values 1 … n.

Example:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Input: 3
Output:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

Similar Question: 96.unique-binary-search-trees

Binary Search Tree(BST):

  • Key(L)<Key(Current)<Key(R)
  • Both subtrees of each node are also BSTs

Appropriate Answer (Divide-and-conquer):

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
<?php

namespace LeetCode\UniqueBinarySearchTreesII;

/**
 * Definition for a binary tree node.
 */
// class TreeNode
// {
//     public $val = null;
//     public $left = null;
//     public $right = null;
//     function __construct($val = 0, $left = null, $right = null)
//     {
//         $this->val = $val;
//         $this->left = $left;
//         $this->right = $right;
//     }
// }

class Solution
{
    /**
     * @param int $n
     * @return TreeNode[]
     */
    public function generateTrees($n)
    {
        $numbers = range(1, $n);
        return $this->generateTreesByNumbers($numbers);
    }

    /**
     * @param int[] $originalNumbers
     * @return array
     */
    private function generateTreesByNumbers($originalNumbers)
    {
        if (count($originalNumbers) == 0) {
            return [null];
        }

        if (count($originalNumbers) == 1) {
            return [new TreeNode(array_pop($originalNumbers))];
        }

        $result = [];
        //[1,2,3] => (1, [2,3]) (2, [1,3]) (3, [1,2])
        foreach ($originalNumbers as $key => $val) {
            $currentNumbers = $originalNumbers;
            unset($currentNumbers[$key]);
            $otherNumbers = $currentNumbers;

            $result = array_merge($result, $this->binarySearch($val, $otherNumbers));
        }

        return $result;
    }

    /**
     * @param int $val
     * @param int[] $otherNumbers
     * @return TreeNode[]
     */
    private function binarySearch($val, $otherNumbers)
    {
        $smallerNumbers = array_filter($otherNumbers, function ($otherNumber) use ($val) {
            return $otherNumber < $val;
        });

        $biggerNumbers = array_filter($otherNumbers, function ($otherNumber) use ($val) {
            return $otherNumber > $val;
        });

        $smallerTrees = $this->generateTreesByNumbers($smallerNumbers);
        $biggerTrees = $this->generateTreesByNumbers($biggerNumbers);

        $trees = [];
        foreach ($smallerTrees as $aSmallerTree) {
            foreach ($biggerTrees as $aBiggerTree) {
                $tree = new TreeNode($val, $aSmallerTree, $aBiggerTree);
                $trees[] = $tree;
            }
        }

        return $trees;
    }
}

ʕ •ᴥ•ʔ：由 linsheng 提供的解法。