用于二进制搜索的Python程序（递归和迭代）

简而言之，这种搜索算法利用了已经排序的元素集合，在一次比较后忽略一半的元素。

1. 将 x 与中间元素进行比较。
2. 如果 x 与中间元素匹配，我们返回中间索引。
3. 否则，如果 x 大于中间元素，则 x 只能位于中间元素之后的右（更大）半子数组中。然后我们再次将算法应用于右半部分。
4. 否则，如果 x 更小，则目标 x 必须位于左（下）半部分。所以我们将算法应用于左半部分。

递归：

Python3

# Python 3 program for recursive binary search.
# Modifications needed for the older Python 2 are found in comments.
 
# Returns index of x in arr if present, else -1
def binary_search(arr, low, high, x):
 
    # Check base case
    if high >= low:
 
        mid = (high + low) // 2
 
        # If element is present at the middle itself
        if arr[mid] == x:
            return mid
 
        # If element is smaller than mid, then it can only
        # be present in left subarray
        elif arr[mid] > x:
            return binary_search(arr, low, mid - 1, x)
 
        # Else the element can only be present in right subarray
        else:
            return binary_search(arr, mid + 1, high, x)
 
    else:
        # Element is not present in the array
        return -1
 
# Test array
arr = [ 2, 3, 4, 10, 40 ]
x = 10
 
# Function call
result = binary_search(arr, 0, len(arr)-1, x)
 
if result != -1:
    print("Element is present at index", str(result))
else:
    print("Element is not present in array")

输出：

Element is present at index 3

迭代：

Python3

# Iterative Binary Search Function
# It returns index of x in given array arr if present,
# else returns -1
def binary_search(arr, x):
    low = 0
    high = len(arr) - 1
    mid = 0
 
    while low <= high:
 
        mid = (high + low) // 2
 
        # If x is greater, ignore left half
        if arr[mid] < x:
            low = mid + 1
 
        # If x is smaller, ignore right half
        elif arr[mid] > x:
            high = mid - 1
 
        # means x is present at mid
        else:
            return mid
 
    # If we reach here, then the element was not present
    return -1
 
 
# Test array
arr = [ 2, 3, 4, 10, 40 ]
x = 10
 
# Function call
result = binary_search(arr, x)
 
if result != -1:
    print("Element is present at index", str(result))
else:
    print("Element is not present in array")

输出：

Element is present at index 3

有关详细信息，请参阅文章二进制搜索！