如何对数组进行二进制搜索，即偶数索引上的数字是升序的，奇数索引上的数字是降序的

Question

how to do binary search on array which is the numbers on even indexes are ascending and the numbers on odd indexes are descending example the array {-3,10,0,9,5,0,7,-1} and i want to find a number: x=5

i think i should do binary search on even indexes alone, and on odd indexes alone

Answer 1

You can use two binary searches, one for the increasing and decreasing values each. There will be a few simple modifications:

1. The bounds will not be [0, n-1] (where n is the length of array). The opening and closing limit will be different for the descending and ascending values respectively.
2. Instead of adjusting low = mid + 1 or high = mid - 1 , you'll use low = mid + 2 and high = mid - 2 so that the parity of the middle index doesn't change during the search.

Since this is a simple task, I'll leave the formal algorithm for the reader to figure out.

Answer 2

You are right, you can perform two separate binary searches. One on

(-3,0,5,0,7)

and the other on

(-1,0,9,10).

As regards the implementation, you can use a standard algorithm and

• replace all indexes by their double ( i becomes 2i ) for the first search;

• replace all indexes by m-2i where m is n or n-1 , whichever is odd for the second search.

---

You cannot do with a single search, replacing the even indexes by 2i and the odd ones by m-2i because there is no guarantee that this would correspond to a growing sequence (eg (-3,-1,0,0,5,9,7,10) ). A preliminary merge is required, taking linear time.