Algorithm to find shortest distance from a point in set A to points in set B

Question

There a set A with n 3d points (x,y,z) and set B with m 3d points (x,y,z). For each point (Xi,Yi,Zi) in set A we have to find a point in set B that has minimum distance from (Xi,Yi,Zi).

My code is running out of given time limit. Please help.

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
long long np[50000][3],qp[50000][3];
int main()
{
long long n,q,i,j,d,ans,min;
scanf("%lld",&n);
for(i=0;i<n;i++)
    scanf("%lld%lld%lld",&np[i][0],&np[i][0],&np[i][2]);
scanf("%lld",&q);
for(i=0;i<q;i++)
scanf("%lld%lld%lld",&qp[i][0],&qp[i][1],&qp[i][2]);
for(i=0;i<q;i++)
{
    ans=0;
    min=((qp[i][0]-np[0][0])*(qp[i][0]-np[0][0]))+((qp[i][1]-np[0][1])*(qp[i][1]-qp[0][1]))+((qp[i][2]-np[0][2])*(qp[i][2]-np[0][2]));
    for(j=0;j<n;j++)
    {
        d=((qp[i][0]-np[j][0])*(qp[i][0]-np[j][0]))+((qp[i][1]-np[j][1])*(qp[i][1]-qp[j][1]))+((qp[i][2]-np[j][2])*(qp[i][2]-np[j][2]));
        if(d<min)
        {
            ans=j;
            min=d;
        }
    }
    printf("%lld\n",ans);
}
return 0;
}

Take a look at [Shortest distance between points algorithm](http://stackoverflow.com/questions/1602164/shortest-distance-between-points-algorithm). — JAB, Jun 05 '12 at 14:59
Please provide more details. Is your code faulty and infinitely looping, or does it work for smaller datasets and just takes too much time for larger datasets? — mbeckish, Jun 05 '12 at 15:00
It's a pet peeve, but could you please properly indent your code when posting? — Bart, Jun 05 '12 at 15:01
@mbeckish my code is correct. its just algorithm i think is not fast enough, and hence my code is not feasible for large data set. — hell coder, Jun 05 '12 at 15:01

dcp · Answer 1 · 2012-06-05T15:06:38.683

You're using an O(n^2) algo. I doubt that is fast enough. For some ways to do it faster, check out this article.

Or more specifically, you can use the divide an conquer approach described in that article, which is relatively straightforward if you're comfortable with recursion. Since you are dealing with z axis, you'll have to extend the algo described there to use 2 dividing lines (one for x axis, then one for y), so it's going to be a bit more complicated.

score 0 · Answer 2 · answered Jun 05 '12 at 15:28

One approach would be to create a nearest neighbour triangulation from either set which is O(n log n), then use something like a proximity search to drape each point in turn from the other set onto the triangulation to find it's nearest neighbour. For doing this type of thing in C, Joseph O'Rourkes book is going to be well worth reading.

Algorithm to find shortest distance from a point in set A to points in set B

2 Answers2