Making use of binary search algorithm

Question

I'm more interested in the thought process than in the code itself. I'm supposed to find the number of v[i] components in a sorted array such that x < v[i] < y , where x and y are sent as input from the keyboard. I'm supposed to solve this efficiently using a modified binary search instead of a regular search through the vector.

My problem is that I can't visualize how to implement a binary search in this case, the method just doesn't seem fit to me.

Any thoughts ?

Answer 1

You could do a binary search in the array for x and y . Then you could subtract the index of x from the index of y to get how many items are between them.

You'd actually have to subtract 1 from that result since you are using strictly less-than.

For example, say you have an array:

[3, 6, 8, 10, 14, 39, 41, 100]

Let x=8 and y = 39.

The index of x is 2 and the index of y is 5.

5-2 = 3

3-1 = 2

If x and y are allowed to be values that are not contained in your array, you can still follow the same approach. Search for x and if it is not found, use the index of the element that is just larger than x. Likewise for the index of the element that is just smaller than y .

Answer 2

Supposing the original array v is sorted, just follow those steps:

1. Use binary search to locate value x in the array - if it's not there (the lower and upper bounds in binary search meet), get the index of closest higher value
2. Do the same for the y value, get the index of closest lower value if it's not this time
3. Find out how many items are in between (by subtracting indices and adding 1)

Answer 3

Here's a great article if you're interested: Binary Search

Depending on the values of x and y , if they're the lower and upper limits respectively of numbers within the array, it's as simple as applying a general BS algorithm with those limits in place rather than the general first and last element of the array.

Drawing it up on paper will help.