有没有更有效的方法来做这个算法？

Question

To the best of my knowledge, this algorithm will search correctly and turn out true when it needs too. In class we are talking about Big O analysis so this assignment is to show how the recursive search is faster than an iterative search. The point is to search for a number such that A[i] = i (find an index that is the same as the number stored at the index). This algorithm versus an iterative one only varies by about 100 nanoseconds, but sometimes the iterative one is faster. I set up the vector in main using the rand() function. I run the two algorithms a million times and record the times. The question I am asking is, is this algorithm as efficient as possible or is there a better way to do it?

bool recursiveSearch(vector<int> &myList, int beginning, int end)
{
    int mid = (beginning + end) / 2;

    if (myList[beginning] == beginning) //check if the vector at "beginning" is
    {                                      //equal to the value of "beginning"
        return true;
    }

    else if (beginning == end) //when this is true, the recursive loop ends.
    {                          //when passed into the method: end = size - 1
        return false;
    }

    else
    {
        return (recursiveSearch(myList, beginning, mid) || recursiveSearch(myList, mid + 1, end));
    }

}

Edit: The list is pre-ordered before being passed in and a check is done in main to make sure that beginning and the end both exist

Answer 1

一种可能的“改进”是不通过传递引用来复制每次递归中的向量：

bool recursiveSearch(const vector<int>& myList, int beginning, int end)

Answer 2

Unless you know something special about the ordering of the data, there is absolutely no advantage to performing a partitioned search like this.

Indeed, your code is actually [trying] to do a linear search, so it is actually implementing a simple for loop with the cost of a lot of stack and overhead.

Note that there is a weirdness in your code: If the first element doesn't match, you will call recursiveSearch(myList, beginning /*=0*/, mid) . Since we already know that element 0 doesn't match, you're going to subdivide again, but only after re-testing the element.

So given a vector of 6 elements that has no matches, you're going to call:

recursiveSearch(myList, 0, 6); -> < recursiveSearch(myList, 0, 3) || recursiveSearch(myList, 4, 6); > -> < recursiveSearch(myList, 0, 1) || recursiveSearch(2, 3) > < recursiveSearch(myList, 4, 5); || recursiveSearch(myList, 5, 6); > -> < recursiveSearch(myList, 0, 0) || recursiveSearch(myList, 1, 1) > < recursiveSearch(myList, 2, 2) || recursiveSearch(myList, 3, 3) > ...

In the end, you're failing on a given index because you reached the condition where begin and end were both that value, that seems an expensive way of eliminating each node, and the end-result is not a partitioned search, it a simple linear search, you just use a lot of stack-depth to get there.

So, a simpler and faster way to do this would be:

for (size_t i = beginning; i < end; ++i) {
    if (myList[i] != i)
        continue;
    return i;
}

Since we're trying to optimize here, it's worth pointing out that MSVC, GCC and Clang all assume that if expresses the likely case, so I'm optimizing here for the degenerate case where we have a large vector with no or late matches. In the case where we get lucky and we find a result early, then we're willing to pay the cost of a potential branch miss because we're leaving. I realize that the branch cache will soon figure this out for us, but again - optimizing ;-P

As others have pointed out, you could also benefit from not passing the vector by value (forcing a copy)

const std::vector<int>& myList

Answer 3

An obvious "improvement" would be to run threads on all the remaining cores. Simply divvy up the vector into number of cores - 1 pieces and use a condition variable to signal the main thread when found.

Answer 4

If you need to find an element in an unsorted array such that A[i] == i , then the only way to do it is to go through every element until you find one.

The simplest way to do this is like so:

bool find_index_matching_value(const std::vector<int>& v)
{
    for (int i=0; i < v.size(); i++) {
        if (v[i] == i)
            return true;
    }
    return false; // no such element
}

This is O(n) , and you're not going to be able to do any better than that algorithmically. So we have to turn our attention to micro-optimisations.

In general, I would be quite astonished if on modern machines, your recursive solution is faster in general than the simple solution above. While the compiler will (possibly) be able to remove the extra function call overhead (effectively turning your recursive solution into an iterative one), running through the array in order (as above) allows for optimal use of the cache, whereas, for large arrays, your partitioned search will not.