What counts as a binary search comparison?

问题

I'm writing a program that determines how many comparisons it takes to run a binary search algorithm for a given number and sorted array. What I don't understand is what counts as a comparison.

// returns the number of comparisons it takes to find key in sorted list, array
  public static int binarySearch(int key, int[] array) {
    int left = 0;
    int mid;
    int right = array.length - 1;
    int i = 0;
    while (true) {
      if (left > right) {
        mid = -1;
        break;
      }
      else {
        mid = (left + right)/2;
        if (key < array[mid]) {
          i++;
          right = mid - 1;
        }
        else if (key > array[mid]) {
          i++;
          left = mid + 1;
        }
        else {
          break; // success
        }
      }
    }
    return i;
  }

The function returns i, which is supposed to be the total number of comparisons made in finding the key in array. But what defines a comparison? Is it any time there is a conditional?

Thanks for any help, just trying to understand this concept.

回答1:

Usually, a comparison occurs each time the key is compared to an array element. The code seems to not be counting that, though. It is counting how many times one of the search boundaries (left or right) is changed. It's not exactly the same thing being counted, but it's pretty close to the same thing, since the number of times a boundary is shifted is directly related to the number of times through the loop and hence to the number of times a comparison is made. At most, the two ways of counting will be off by 1 or 2 (I didn't bother to figure that out exactly).

Note also that if one were to use the usual definition, the code could be rewritten to use Integer.compare(int,int) do a single comparison of key with array[mid] to determine whether key was less than, equal to, or greater than array[mid].

public static int binarySearch(int key, int[] array) {
    int left = 0;
    int mid;
    int right = array.length - 1;
    int i = 0;
    while (left <= right) {
        mid = (left + right)/2;
        int comp = Integer.compare(key, array[mid]);
        i++;
        if (comp < 0) {
            right = mid - 1;
        }
        else if (comp > 0) {
            left = mid + 1;
        }
        else {
            break; // success
        }
    }
    return i;
}

来源：https://stackoverflow.com/questions/46913368/what-counts-as-a-binary-search-comparison