The path of regaining algorithm--binary search

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Subordinate to--recursion and divide and conquer

Description : Given the ordered n elements a[0;n-1], now to find a specific element x in these n elements.

Naive Method : Of course, this is a good word, understand the most stupid method, that is, sequential search, compare 0 to n-1 elements, until the element x or search all the elements, to determine the X is not in the element, this method is well used n elements in the order of the conditions, so the worst case, Time complexity is O (n) comparison.

Two-point search : This method takes full advantage of the order relationship between elements and uses the divide-and-conquer strategy to complete the search task in the worst case with O (log (n)) time. The basic idea is to divide n elements into the same number of halves, taking A[N/2] and X as a comparison,

If X=A[N/2], then X is found and the algorithm terminates.

If X<A[N/2], the search continues only in the left half of array a (0 to N/2)

If X>A[N/2], the search continues only in the right half of array a (N/2 to n-1)

Code Program :

template< class type >int BinarySearch (type a[], const t& x, int n) {    int l=0,r=n-1;    while (L <= R)    {        int m = (l+r)/2;        if (x = = A[m])    return m;        if (x < a[m])    r = m-1;        else    L = m+1;    }    return-1;    X is not found, returns-1}

Analysis : As can be seen from the above code, the size of the array to be searched is halved by the while loop of the algorithm executed once.

Therefore, in the worst case, the while array executes O (log (n)) times, while the code execution time in the loop body is approximately O (1).

Ultimately, the overall algorithm has an O (log (n) time complexity in the worst case scenario.

Small Knowledge : The idea of binary search algorithm is easy to understand, but it is not a simple matter to write a correct binary search algorithm. Knuth, in his book The Art of computer programming:sorting and searching, mentions that the first binary search algorithm appeared as early as 1946, But the first completely correct binary search algorithm didn't appear until 1962.

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The path of regaining algorithm--binary search