基礎概念

Binary Search 的概念類似 Quick Sort 中的概念。Binary Search 需要仰賴已經排序好的資料，所以雖然搜尋的效率比線性搜尋來得高，但是刪減資料都會需要耗費另外的成本做排序。 而其實做方式有兩種：Iteration 和 Recursion。

Time Complexity：

• Best： O(1)
• Average：O(log n)
• Worst：O(log n)

Space Complexity： O(1)

實作

Python

Iteration

def binarySearch(arr, l, r, x):

    while l <= r:

        mid = l + (r - l) // 2

        # Check if x is present at mid
        if arr[mid] == x:
            return mid

        # If x is greater, ignore left half
        elif arr[mid] < x:
            l = mid + 1

        # If x is smaller, ignore right half
        else:
            r = mid - 1

    # If we reach here, then the element
    # was not present
    return -1

Recursion

def binarySearch(arr, l, r, x):

    # Check base case
    if r >= l:

        mid = l + (r - l) // 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 binarySearch(arr, l, mid-1, x)

        # Else the element can only be present
        # in right subarray
        else:
            return binarySearch(arr, mid + 1, r, x)

    else:
        # Element is not present in the array
        return -1