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C++折半查找的实现
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发布时间:2019-03-22

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C++折半查找法的实现与理解

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 Search in C++: Implementation and Explanation

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++.

Sorting: The Initial Step

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}

Key Steps in Fold-Halving

  • Initialization:

    • Define low as the initial smallest index (0).
    • Define high as the initial largest index (10).
    • Calculate mid, the middle index of the array.
  • Loop Until mid is Within Bounds:

    • While low is less than or equal to high.
    • Compute mid as the average of low and high, using integer division for exact mid-point calculation.
    • Compare the target key with the element at mid.
  • Comparison and Range Adjustment:

    • If key equals arr[mid], return mid as the target's position.
    • If key is greater than arr[mid], set low to mid + 1 and adjust the search interval to [mid + 1, high].
    • If key is less than arr[mid], set high to mid - 1 and adjust the search interval to [low, mid - 1].
  • Example: Finding Target Element 7

  • Initial Setup:

    • low = 0, high = 10, mid = 5.
    • Target key = 7.
  • First Comparison:

    • arr[5] is 7. Return mid = 5.
  • Handling Edge Cases

    • Empty Array: Handle array size checks to avoid invalid operations.
    • Single Element Array: Directly compare the single element with the key.
    • Multiple Occurrences of Key: If the key is present multiple times, ensure the loop continues until all possible locations are exhausted.

    Cost of Fold-Halving

    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.

    Conclusion

    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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