基本算法介绍以及代码实现（python）

常见算法介绍

1.线性搜索

def linear_search(arr, target):
    for i, element in enumerate(arr):
        if element == target:
            return i
    return -1

2.二分搜索

# 闭区间写法
def binary_search1(nums, target):
    left, right = 0, len(nums) - 1  # 闭区间 [left, right]
    while left <= right:  # 区间不为空
        # 循环不变量：
        # nums[left-1] < target
        # nums[right+1] >= target
        mid = (left + right) // 2
        if nums[mid] < target:
            left = mid + 1  # 范围缩小到 [mid+1, right]
        else:
            right = mid - 1  # 范围缩小到 [left, mid-1]
    return left

3.冒泡排序

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        for j in range(0, n-i-1):
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]
    return arr
 
# 示例使用
array = [64, 34, 25, 12, 22, 11, 90]
sorted_array = bubble_sort(array)
print("Sorted array is:", sorted_array)

4.快速排序

def quicksort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quicksort(left) + middle + quicksort(right)
 
# 示例使用
example_list = [3,6,8,10,1,2,1,4,7,5]
sorted_list = quicksort(example_list)
print(sorted_list)  # 输出: [1, 1, 2, 3, 4, 5, 6, 7, 8, 10]

5.归并排序

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = arr[:mid]
    right = arr[mid:]
    left = merge_sort(left)
    right = merge_sort(right)
    return merge(left, right)
 
def merge(left, right):
    result = []
    i, j = 0, 0
    while i < len(left) and j < len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    result += left[i:]
    result += right[j:]
    return result
 
# 使用示例
arr = [5, 3, 4, 1, 2]
sorted_arr = merge_sort(arr)
print(sorted_arr)  # 输出: [1, 2, 3, 4, 5]

6.插入排序

def insertion_sort(arr):
    for i in range(len(arr)):
        pre_index = i - 1
        current = arr[i]
        while pre_index >= 0 and arr[pre_index] > current:
            arr[pre_index + 1] = arr[pre_index]
            pre_index -= 1
        arr[pre_index + 1] = current
    return arr
 
# 示例使用
example_list = [10, 5, 3, 8, 2, 6]
sorted_list = insertion_sort(example_list)
print(sorted_list)  # 输出: [2, 3, 5, 6, 8, 10]

7.选择排序

def selection_sort(arr):
    for i in range(len(arr)):
        # 寻找最小元素的索