1.排序算法分类

1.1 比较排序：

交换排序：基础冒泡排序、优化冒泡排序、基础快速排序、递归版优化快速排序、循环版优化快速排序插入排序：基础插入排序、希尔优化插入排序选择排序：选择排序、二叉堆排序、多叉堆排序归并排序：归并排序1.2 非比较排序：计数排序桶排序基数排序

2.基础概念解读

2.1 时间复杂度

随着排序数据总量n的变大，排序总耗时的上升情况。有五个符号来表示不同的意思：O(n^2) 大O 表示该排序算法增量情况 <= n^2o(n^2) 小o 表示该排序算法增量情况 < n^2θ(n^2) 希腊字母theta 表示该排序算法增量情况 == n^2ω(n^2) 希腊字母小欧米伽 表示该排序算法增量情况 > n^2Ω(n^2) 希腊字母大欧米伽 表示该排序算法增量情况 >= n^2

2.2 稳定性

如果a=b，排序前a在b之前，排序后a还在b之前，则稳定如果a=b，排序前a在b之前，排序后a在b之后，则不稳定

2.3 逆序对

比如{2, 4, 3, 1}这样一个数列，就有{2, 1},{4, 3},{4, 1},{3, 1}等逆序对，数量为4

3.排序算法对比

4.代码实现（Java）

5.伪代码实现

5.1 基础冒泡排序

BasicBubbleSort(A)    for i=1 to A.length-1        for j=A.length down to i + 1            if A[j] < A[j-1]                exchange A[j] with A[j-1]

5.2 优化冒泡排序

OptimizeBubbleSort(A)    for i=1 to A.length-1        didSwap = false;        for j=A.length down to i + 1            if A[j] < A[j-1]                exchange A[j] with A[j-1]                didExchange = true        if didExchange == true            return

5.3 基础快速排序

BasicQuickSort(A, p, r)    if p < r        q = BasicPartition(A, p, r)        BasicQuickSort(A, p, q-1)        BasicQuickSort(A, q+1, r)        BasicPartition(A, p, r)    x = A[r]    i = p-1    for j=p to r-1        if A[j] <= x            i = i + 1            exchange A[i] with A[j]    exchange A[i+1] with A[r]    return i + 1

5.4 递归优化快速排序

RecuOptimizeQuickSort(A, sort, end)    if start < end        mid = RecuOptimizePartition(A, start, end)        RecuOptimizeQuickSort(A, start, mid-1)        RecuOptimizeQuickSort(A, start+1, end)RecuOptimizePartition(A, start, end)    生成介于start和end之间的三个不重复的随机数r1,r2,r3    取A[r1],A[r2],A[r3]这三个数的中位数，并将该中位数的下标赋值给r0    x = A[r0]    i = start - 1    for j = start to end - 1        if A[j] <= x            i = i + 1            exchange A[i] with A[j]    exchange A[i+1] with A[end]    return i+1

5.5 循环优化快速排序

LoopOptimizeQuickSort(A)    stack = []    start = 0    end = A.length - 1    stack.push(start)    stack.push(end)    while stack.isNotEmpty()        end = stack.pop()        start = stack.pop()        if start < end            base = LoopOptimizePartition(A, start, end)            // 右半边            stack.push(base+1)            stack.push(end)            // 左半边            stack.push(start)            stack.push(base-1)LoopOptimizePartition(A, start, end)    生成介于start和end之间的三个不重复的随机数r1,r2,r3    取A[r1],A[r2],A[r3]这三个数的中位数，并将该中位数的下标赋值给r0    x = A[r0]    i = start - 1    for j = start to end - 1        if A[j] <= x            i = i + 1            exchange A[i] with A[j]    exchange A[i+1] with A[end]    return i+1

5.6 基础插入排序

InsertionSort(A)    for j=2 to A.length        key = A[j]        i = j - 1        while i > 0 and A[i] > key            A[i+1] = A[i]            i = i - 1        A[i+1] = key

5.7 希尔优化插入排序

ShellInsertionSort(A)    increment = A.length    do {        increment = increment/3 + 1        for j = increment to A.length            key = A[j]            i = j - increment            while 0 <= i and A[i] > key                A[i+increment] = A[i]                i = i - increment            A[i+increment] = key    }while(1 < increment);

5.8 选择排序

SelectionSort(A)    for i=1 to n-1        min = i        for j=i+1 to n            if A[min] > A[j]                min = j        exchange A[min] with A[i]

5.9 二叉堆排序

HeapSort(A)    BuildMaxHeap(A)    for i = A.length downto 2        exchange A[1] with A[i]        A.heap-size = A.heap-size - 1        MaxHeapify(A, 1)BuildMaxHeap(A)    A.heap-size = A.length    for i = A.length/2 downto 1        MaxHeapify(A, i)MaxHeapify(A, i)    l = LEFT(i)    r = RIGHT(i)    if l <= a.heap-size and A[l] > A[i]        largest = l    else largest = i    if r <= A.heap-size and A[r] > A[largest]        largest = r    if largest != i        exchange A[i] with A[largest]        MaxHeapify(A, largest)LEFT(i)    return 2iRIGHT(i)    return 2i+1

5.10 多叉堆排序

5.11 归并排序

MergeSort(A, p, r)    if p < r        q = (p+r)/2 (向下取整)        MergeSort(A, p, q)        MergeSort(A, q+1, r)        Merge(A, p, q, r)Merge(A, p, q, r)    n1 = q - p + 1    n2 = r - q    let L[1..n1+1] and R[1..n2 + 1] be new arrays    for i = 1 to n1        L[i] = A[p + i - 1]    for j = 1 to n2        R[j] = A[q + j]    L[n1+1] = 正无穷大    R[n2+1] = 正无穷大    i = 1    j = 1    for k = p to r        if L[i] <= R[j]            A[k] = L[i]            i = i + 1        else            A[k] = R[j]            j = j + 1

5.12 计数排序

CountingSort(A, B, k)    let C[0...k] be a new array    for i = 0 to k        C[i] = 0    for j = 1 to A.length        C[A[j]] = C[A[j]] + 1    for i = 1 to k        C[i] = C[i] + C[i-1]    for j = A.length downto 1        B[C[A[j]]] = A[j]        C[A[j]] = C[A[j]] - 1

5.13 基数排序

5.14 桶排序

https://www.cnblogs.com/zer0Black/p/6169858.htmlBucketSort(A)    n = A.length    let B[0.. n-1] be a new array    for i = 0 to n-1        make B[i] an empty list    for i = 1 to n        insert A[i] into list B[
    
     ]    for i = 0 to n-1        sort list B[i] with insertion sort    concatenate the lists B[0],B[1],...,B[n-1] together in order