The document describes the closest pair problem in computational geometry. It involves finding the shortest distance between any two points in a set of points in a two-dimensional space. The problem is solved by first sorting the points by their x-coordinates, then recursively dividing the set into halves using a vertical dividing line and solving for the minimum distances in the left and right subsets until single points remain. The minimum distances of the subsets are then used to find the overall closest pair of points between the original sets.

1. ACM PROBLEM
TITLE:
THE CLOSEST PAIR
Presented to:
Dr. Abdul Qadir
Dean of Faculty Computing
Department of Computer Science
Mohammad Ali Jinnah University, Islamabad
Presented By:
Mohammad Imran Mukhtar
BC-113004
Department of Computer Science
Mohammad Ali Jinnah University, Islamabad

2. PROBLEM DESCRIPTION
 Given a set of points in a two dimensional space
 Each set starts with an integer N (0<=N<=10000),
which denotes the number of points in this set.
 Q : We have to find the closest distance between
the two points

3. HOW TO SOLVE IT?
There are following steps according to which we can solve
this problem :
1. Sort points according to their x-coordinates.

4. 2. SPLIT THE SET OF POINTS INTO TWO EQUAL-SIZED SUBSETS BY A
VERTICAL LINE X=XMID.

5. 3. SOLVE THE PROBLEM RECURSIVELY IN THE LEFT AND RIGHT
SUBSETS. THIS YIELDS THE LEFT-SIDE AND RIGHT-SIDE MINIMUM
DISTANCES DLMIN AND DRMIN, RESPECTIVELY.
Dividing the left side
Now dividing the left side
into sub categories

6. Continuously dividing Continuously dividing

7. After that solving the left most side to find the minimum
distance between the two points.

9.  By putting the values in this formula :
 Distance = sqrt{(1 – 1)2 + (2 – 11)2}
= sqrt{ (0)2 + (-9)2 }
= sqrt{81}
= 9
 Distance = sqrt{(4 – 10)2 + (5 – 6)2}
= sqrt{ (-6)2 + (-1)2 }
= sqrt{36 + 1}
= sqrt{37}
= 6.08
So the minimum distance between the two subsets is 6.08