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折半查找法，也称二分查找，是一种高效的查找算法，特别适用于已排序的数组。它通过不断缩小查找范围来快速定位目标元素。以下是关于折半查找法的详细实现和理解。
Fold-halving, or binary search, is an efficient searching algorithm primarily used for sorted arrays. By repeatedly dividing the search interval in half, this method allows for rapid location of a target element. Below is the detailed implementation and explanation of fold-halving in C++.
Before performing fold-halving, the array must be sorted. The given array is sorted to facilitate the fold-halving process:
arr = {1,2,3,4,5,6,7,8,9,10,11} Initialization:
low as the initial smallest index (0).high as the initial largest index (10).mid, the middle index of the array.Loop Until mid is Within Bounds:
low is less than or equal to high.mid as the average of low and high, using integer division for exact mid-point calculation.key with the element at mid.Comparison and Range Adjustment:
key equals arr[mid], return mid as the target's position.key is greater than arr[mid], set low to mid + 1 and adjust the search interval to [mid + 1, high].key is less than arr[mid], set high to mid - 1 and adjust the search interval to [low, mid - 1].Initial Setup:
low = 0, high = 10, mid = 5.First Comparison:
arr[5] is 7. Return mid = 5.key is present multiple times, ensure the loop continues until all possible locations are exhausted.The time complexity of fold-halving is O(log n), making it significantly more efficient than linear search for large arrays. The space complexity is O(1) as no additional data structures are used.
Fold-halving is an essential algorithm for efficient array searching. By leveraging sorted data and dividing the search space, this method quickly pinpoints the target element, demonstrating its efficiency and reliability in various applications.
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