计数排序

描述

计数排序（Counting sort）是一种稳定的线性时间排序算法。它的复杂度为 Ο(n+k)（其中 k 是整数的范围大小）

基本思想

对于给定的输入序列中的每一个元素x，确定该序列中值小于x的元素的个数（此处并非比较各元素的大小，而是通过对元素值的计数和计数值的累加来确定）。然后顺序输出

实现

var CountingSort = (arr) => {
  // 判空及防止数组越界
  if (arr == null || arr.length <= 1) return arr;
  // 找最大最小
  let min = Math.min(...arr)
  let range = Math.max(...arr) - min + 1
  // 建立长度为 range 的数组，下标 0~8 对应数字 1~9
  let counting = new Array(range).fill(0)
  // 遍历 arr 中的每个元素
  for (const x of arr) {
    // 将每个整数出现的次数统计到计数数组中对应下标的位置
    counting[x - min] += 1
  }
  // 记录前面比自己小的数字的总数
  let preCounts = 0
  for (let i = 0; i < counting.length; i++) {
    // 将 counting 计算成当前数字在结果中的起始下标位置。位置 = 前面比自己小的数字的总数。
    preCounts += counting[i]
    // 当前的数字比下一个数字小，累计到 preCounts 中
    counting[i] = preCounts - counting[i]
  }
  let result = new Array(arr.length)
  for (const x of arr) {
    // counting[x - 1] 表示此元素在结果数组中的下标
    let index = counting[x - min]
    result[index] = x
    // 更新 counting[x - 1]，指向此元素的下一个下标
    counting[x-min]+=1
  }
  for (let i = 0; i < arr.length; i++) {
    arr[i] = result[i]
  }
  return arr
}

过程分析

假如当前输入 [0,2,3,4,1,5,3,1,6,3,6,7,1,2]

1. 找出 max = 7 和 min = 0，生成一个数组 counting = [0, 0, 0, 0, 0, 0, 0, 0] 用于计数
2. 遍历 arr 对每个数进行收集， [1, 3, 2, 3, 1, 1, 2, 1]
3. 记录比自己小的数字的总数 counting = [0, 1, 4, 6, 9, 10, 11, 13]
4. 初始化新数组 [empty × 14]，再遍历 arr
   1. x = 0, counting[0] = 0 counting[0]++
      1. result = [0, empty × 13]
      2. counting = [1, 1, 4, 6, 9, 10, 11, 13]
   2. x = 2, counting[2] = 4 counting[2]++
      1. result = [0, empty × 3, 2, empty × 9]
      2. counting = [1, 1, 5, 6, 9, 10, 11, 13]
   3. x = 3, counting[3] = 6 counting[3]++
      1. result = [0, empty × 3, 2, empty × 1, 3, empty × 7]
      2. counting = [1, 1, 5, 7, 9, 10, 11, 13]
   4. x = 4, counting[4] = 9 counting[4]++
      1. result = [0, empty × 3, 2, empty × 1, 3, empty × 2, 4, empty × 4]
      2. counting = [1, 1, 5, 7, 10, 10, 11, 13]
   5. x = 1, counting[1] = 1 counting[1]++
      1. result = [0, 1, empty × 2, 2, empty × 1, 3, empty × 2, 4, empty × 4]
      2. counting = [1, 2, 5, 7, 10, 10, 11, 13]
   6. x = 5, counting[5] = 10 counting[5]++
      1. result = [0, 1, empty × 2, 2, empty × 1, 3, empty × 2, 4, 5, empty × 3]
      2. counting = [1, 2, 5, 7, 10, 11, 11, 13]
   7. x = 3, counting[3] = 7 counting[3]++
      1. result = [0, 1, empty × 2, 2, empty × 1, 3, 3, empty × 1, 4, 5, empty × 3]
      2. counting = [1, 2, 5, 8, 10, 11, 11, 13]
   8. x = 1, counting[1] = 2 counting[1]++
      1. result = [0, 1, 1, empty × 1, 2, empty × 1, 3, 3, empty × 1, 4, 5, empty × 3]
      2. counting = [1, 3, 5, 8, 10, 11, 11, 13]
   9. x = 6, counting[6] = 11 counting[6]++
      1. result = [0, 1, 1, empty × 1, 2, empty × 1, 3, 3, empty × 1, 4, 5, 6, empty × 2]
      2. counting = [1, 3, 5, 8, 10, 11, 12, 13]
   10. x = 3, counting[3] = 8 counting[3]++
       1. result = [0, 1, 1, empty × 1, 2, empty × 1, 3, 3, 3, 4, 5, 6, empty × 2]
       2. counting = [1, 3, 5, 9, 10, 11, 13, 13]
   11. x = 6, counting[6] = 12 counting[6]++
       1. result = [0, 1, 1, empty × 1, 2, empty × 1, 3, 3, 3, 4, 5, 6, 6, empty × 1]
       2. counting = [1, 3, 5, 9, 10, 11, 13, 13]
   12. x = 7, counting[6] = 13 counting[7]++
       1. result = [0, 1, 1, empty × 1, 2, empty × 1, 3, 3, 3, 4, 5, 6, 6, 7]
       2. counting = [1, 3, 5, 9, 10, 11, 13, 14]
   13. x = 1, counting[1] = 3 counting[1]++
       1. result = [0, 1, 1, 1, 2, empty × 1, 3, 3, 3, 4, 5, 6, 6, 7]
       2. counting = [1, 4, 5, 9, 10, 11, 13, 14]
   14. x = 2, counting[2] = 5 counting[2]++
       1. result = [0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7]
       2. counting = [1, 4, 6, 9, 10, 11, 13, 14]
5. 最后输出数组 [0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7]

算法复杂度

平均时间复杂度	最好情况	最坏情况	空间复杂度	排序方式	稳定性
O(n+k)	O(n+k)	O(n+k)	O(n+k)	out-place	稳定

源码地址