Answer:
The minimum distance between two closest number in an array is |$x-$y|
Algorithm: Pseudo code
minimum_distance(arr[0..n-1])
merge_sort(arr[0..n-1])
min_dist←∞
for i=0 to i=n-2 do
if (|arr[i+1]-arr[i])| < min_dist do
min_dist = |arr[i+1]-arr[i])|
return min_dist
Efficiency class:
The running time for worst case of merge sort is O(n logn) and for traversing the array is O(n) so total time will be:
T (n) = O(n logn) + O(n)
the term O(n logn) is dominating in above equation so the total running time will be T (n) = O(n logn)
Explanation:
minimum_distance(arr[0..n-1])
merge_sort(arr[0..n-1]) //merge sort is used to sort the array
min_dist←∞
for i=0 to i=n-2 do
if (|arr[i+1]-arr[i])| < min_dist do
min_dist = |arr[i+1]-arr[i])|
return min_dist
// above loop calculates the least distance between the two elements of pre-sorted array then keeps the track of the all possible least distances at different position where the elements available and then return the least distance
