Which algorithm is preferable to find a specific number from unsorted array?

Answer 1

If the array is unsorted then there is no algorithm that can be applied other than a sequential traversal from one end of the array to the other until the number is found or the end of the array is reached. This is an extremely poor algorithm as the worst case would be O(n) for n elements. While this may be fine for small arrays, it is highly inefficient for larger arrays.

To apply a more efficient algorithm with a worst case of O(log n), you must sort the array. You can then use a binary search algorithm by starting at the middle element. If that's your value, you're done. If not and the value you seek is less than this value, then you can eliminate all the elements in the upper half of the array, otherwise you can eliminate all the elements in the lower half of the array. Repeat the process with the remaining subarray, reducing the number of remaining elements by half each time. If you end up with a subarray with no elements then the value does not exist.

Sorted arrays that are perfectly balanced offer the best performance. For instance, an array with 63 elements is perfectly balanced because after the first iteration you are left with another perfectly balanced array of 31 elements (because you eliminated 31 elements plus the middle element). After the next iteration you will be left with 15 elements, then 7, 3, 1 and finally 0. Thus a 63-element array takes no more than 6 iterations to determine that a value does not exist, compared to 63 iterations with a sequential traversal search upon an unsorted array. 6 iterations is also the average because the 6th iteration can locate any one of 32 values, which is more than half the values.