Sort

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import random

# selections sort

# Time o(n^2)
# Space o(n)
# n^2 遍历，只要有更小的，就换元素
def selection_sort(nums):
    if len(nums) == 0:
        return []
    n = len(nums)
    for i in range(n):
        for j in range(i+1,n):
            if nums[j] < nums[i]:
                nums[i], nums[j] = nums[j], nums[i]
    return nums

# Time o(n^2)
# Space o(n)
# n^2 遍历, 每一遍从 index0 开始遍历，比较当前是否比下一个大，bubble 向上，
def bubble_sort(nums):
    n = len(nums)
    if n <= 1:
        return nums
    for i in range(n):
        for j in range(0, n-i-1):
            if nums[j] > nums[j+1]:
                nums[j], nums[j+1] = nums[j+1], nums[j]
    return nums

# Time o(n^2)
# Space o(n)
# 对 0...i-1 的部分进行遍历，将所有大于等于 nums[i] 的部分向后移动一个，将 nums[i] 放在空位上
def insersion_sort(nums):
    n = len(nums)
    if n <= 1:
        return nums
    for i in range(1,n):
        key = nums[i]
        j = i-1
        while j >= 0 and key <= nums[j]:
            nums[j+1] = nums[j]
            j -= 1
        nums[j+1] = key 
    return nums

# heap sort !

# Binary Heap: both of the left child and right child are smaller than the parent.
# bottom up recursion 构建 MaxHeap， heapify 的条件是左右子树都是已经 heapify 好的
def heapify(arr, n ,i):
    l = 2*i + 1
    r = 2*i + 2

    largest = i
    if l < n and nums[largest] < nums[l]:
        largest = l
        
    if r < n and nums[largest] < nums[r]:
        largest = r
    
    if largest != i:
        nums[largest], nums[i] = nums[i], nums[largest]
        heapify(arr, n, largest)
        
# swap 头尾，heapify [0, i-1], 不断前进
# Time o(nlogn)
# Space o(n)
def heap_sort(arr):
    n = len(arr)
    
    for i in range(n//2, -1, -1):
        heapify(arr, n, i)
    
    for i in range(n-1, 0, -1):
        arr[0], arr[i] = arr[i], arr[0]
        heapify(arr, i, 0)
        
    return nums

# --- merge sort ---
# Time o(nlogn) worst, average, best
# Space o(n)
def merge_sort(arr):
    n = len(arr)
    if n > 1:
        mid = n//2
        left = arr[:mid]
        right = arr[mid:]
        left = merge_sort(left)
        right = merge_sort(right)
        
        i = j = k = 0
        
        while i < len(left) and j < len(right) :
            if left[i] < right[j]:
                arr[k] = left[i]
                i += 1
            else:
                arr[k] = right[j]
                j += 1
            k += 1
        
        if i < len(left):
            arr[k] = left[i]
            k += 1
        
        if j < len(right):
            arr[k] = right[j]
            j += 1
    return arr

# time o(nlogn) average, o(n^2) worst
# space o(n)
def partition(nums, l, r):
    pivot = nums[r]
    i = l
    for j in range(l, r):
        if nums[j] <= pivot:
            nums[i], nums[j] = nums[j], nums[i]
            i += 1
    nums[i], nums[r] = nums[r], nums[i]
    return i

def random_parition(nums, l, r):
    if l >= r:
        return
    pivot = random.randint(l, r)
    nums[pivot], nums[r] = nums[r], nums[pivot]
    return partition(nums, l, r)
    
def quick_sort(nums, l, r):
    if l >= r:
        return 
    pivot = random_parition(nums, l, r)
    quick_sort(nums,l, pivot-1)
    quick_sort(nums,pivot+1, r)
    
        
nums_list = [
    [],
    [2,1,3,4,5,6],
    [1,2,3,4,5,6],
    [6,5,4,3,2,1],
    [6,3,4,7,8,1]]


# selection sort
for nums in nums_list:
    print(selection_sort(nums))

# bubble sort
for nums in nums_list:
    print(bubble_sort(nums))
 
# heap sort 
print("heap_sort")
for nums in nums_list:
    print(heap_sort(nums))

# merge sort
print("merge sort")
for nums in nums_list:
    print(merge_sort(nums))


# quick sort
print("quick sort")
for nums in nums_list:
    quick_sort(nums, 0, len(nums)-1)
    print(nums)