Program to Find the Shortest Distance Between Two Points in C++

Suppose we have a list of coordinates where each element is of the form [x, y], representing Euclidean coordinates. We have to find the smallest squared distance (x₁ - x₂) ² + (y₁ - y₂) ² between any two provided coordinates.

So, if the input is like coordinates = {{1, 2},{1, 4},{3, 5}}, then the output will be 4.

To solve this, we will follow these steps −

Define one map ytorightmostx
sort the array coordinates
ret := infinity
for each p in cordinates −
- it = return the value where (p[1] - sqrt(ret)) is in ytorightmostx or the smallest value greater than it from ytorightmostx
- while it is not equal to last element of ytorightmostx, do −
  - yd := first - p[1] of it
  - if yd > 0 and yd * yd >= ret, then −
    - Come out from the loop
  - nxt = it
  - increase nxt by 1
  - ret := minimum of (ret, dist(p[0], p[1], first value of it, second value of it)
  - xd := second value of it - p[0]
  - if xd * xd >= ret, then −
    - delete it from ytorightmostx
  - it := nxt
- ytorightmostx[p[1]] := p[0]
return ret
Define a function dist(), this will take xl, yl, xr, yr.
- xd := xl - xr
- yd := yl - yr
- return xd * xd + yd * yd

Example

Let us see the following implementation to get a better understanding −

Live Demo

#include <bits/stdc++.h>
using namespace std;
long long dist(long long xl, long long yl, long long xr, long long yr) {
   long long xd = xl - xr;
   long long yd = yl - yr;
   return xd * xd + yd * yd;
}
int solve(vector<vector<int>>& coordinates) {
   map<long long, long long> ytorightmostx;
   sort(coordinates.begin(), coordinates.end());
   long long ret = 1e18;
   for (auto& p : coordinates) {
      auto it = ytorightmostx.lower_bound(p[1] - sqrt(ret));
      while (it != ytorightmostx.end()) {
         long long yd = it->first - p[1];
         if (yd > 0 && yd * yd >= ret) {
            break;
         }
         auto nxt = it;
         nxt++;
         ret = min(ret, dist(p[0], p[1], it->second, it->first));
         long long xd = (it->second - p[0]);
         if (xd * xd >= ret) {
            ytorightmostx.erase(it);
         }
         it = nxt;
      }
      ytorightmostx[p[1]] = p[0];
   }
   return ret;
}
int main(){
   vector<vector<int>> coord = {{1, 2},{1, 4},{3, 5}};
   cout << solve(coord) << endl;
   return 0;
}