Find the 2nd largest element in an array with minimum number of comparisons

Question

For an array of size N, what is the number of comparisons required?

Answer 1

Use Bubble sort or Selection sort algorithm which sorts the array in descending order. Don't sort the array completely. Just two passes. First pass gives the largest element and second pass will give you the second largest element.

No. of comparisons for first pass: n-1

No. of comparisons for first pass: n-2

Total no. of comparison for finding second largest: 2n-3

May be you can generalize this algorithm. If you need the 3rd largest then you make 3 passes.

By above strategy you don't need any temporary variables as Bubble sort and Selection sort are in place sorting algorithms.