排序算法之 - 归并排序

归并排序也有类似于快速排序的 切割 的过程，但是快速排序会选择基准值，而归并排序则直接将列表 尽可能两等分（若长度为奇数，那么有一侧会少一个元素，左侧还是右侧是无妨的）。当分割到左右两侧都只剩下一个元素的时候，分割完成，开始往上层拼接结果。拼接的大致流程是：取左右两侧队首的元素，比较两者大小，较小的先进入已排序列表。重复执行此流程，直至有一侧为空，将另一侧剩余元素直接合并到已排序列表的右侧。归并排序也是一种“分治法”，将问题分割到不可再分割的最小单元，然后开始往回执行，最终得到结果，它同样要使用递归。。以下是归并排序的执行流程示意图：

• 归并排序执行流程及结果：
  

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附PHP实现代码：

<?php

function merge($arrayNeedsSort)
{
    if (empty($arrayNeedsSort) || count($arrayNeedsSort) <= 1) {
        // 基准条件，退出
        return $arrayNeedsSort;
    } else {
        $res = [];
        $left = [];
        $right = [];

        $length = count($arrayNeedsSort);

        if ($length % 2 == 0) {
            // 长度为偶数，对半分
            list($left, $right) = array_chunk($arrayNeedsSort, ($length / 2));
        } else {
            // 长度为奇数，左侧比右侧少一
            list($left, $right, $last) = array_chunk($arrayNeedsSort, (($length - 1) / 2));
            // 切割后将剩余的一个元素补到右侧的列表末尾
            $right[] = $last[0];
        }

        // 先对左侧进行排序
        $left = merge($left);

        // 再对右侧进行排序
        $right = merge($right);

        $flag = count($left) + count($right);
        while ($flag > 0) {
            if (empty($left)) {
                // 当左侧为空，直接合并右侧的剩余元素，并退出循环
                $res = array_merge($res, $right);
                // 为了完整输出中间打印流程，此处将 break; 替换为 $flag = 0;
                $flag = 0;
                // break;
            } elseif (empty($right)) {
                // 当右侧为空，直接合并左侧的剩余元素，并退出循环
                $res = array_merge($res, $left);
                // 为了完整输出中间打印流程，此处将 break; 替换为$flag = 0;
                $flag = 0;
                // break;
            } elseif ($left[0] <= $right[0]) {
                $res[] = array_shift($left);
            } else {
                $res[] = array_shift($right);
            }
            $flag--;

            // 可以打印中间过程进行观察
            echo '<pre>';
            print_r($res);
        }

        return $res;
    }
}

$array = [5, 9, 3, 1, 2, 8, 4, 7, 6];
$res = merge($array);
echo '<pre>';
print_r($res);

--snip--打印中间值的结果如下--
Array
(
    [0] => 5
)
Array
(
    [0] => 5
    [1] => 9
)
Array
(
    [0] => 1
)
Array
(
    [0] => 1
    [1] => 3
)
Array
(
    [0] => 1
)
Array
(
    [0] => 1
    [1] => 3
)
Array
(
    [0] => 1
    [1] => 3
    [2] => 5
    [3] => 9
)
Array
(
    [0] => 2
)
Array
(
    [0] => 2
    [1] => 8
)
Array
(
    [0] => 6
)
Array
(
    [0] => 6
    [1] => 7
)
Array
(
    [0] => 4
)
Array
(
    [0] => 4
    [1] => 6
    [2] => 7
)
Array
(
    [0] => 2
)
Array
(
    [0] => 2
    [1] => 4
)
Array
(
    [0] => 2
    [1] => 4
    [2] => 6
)
Array
(
    [0] => 2
    [1] => 4
    [2] => 6
    [3] => 7
)
Array
(
    [0] => 2
    [1] => 4
    [2] => 6
    [3] => 7
    [4] => 8
)
Array
(
    [0] => 1
)
Array
(
    [0] => 1
    [1] => 2
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
    [5] => 6
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
    [5] => 6
    [6] => 7
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
    [5] => 6
    [6] => 7
    [7] => 8
)
Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
    [5] => 6
    [6] => 7
    [7] => 8
    [8] => 9
)