Klee's algorithm (union length of line segments) in C++

In this tutorial, we will write a program that finds the length of the union of line segments.

We have given the starting point and end point of the line segments, we need to find the length of the union of the line segments.

The algorithm we will use is called klee's algorithm.

Let’s take a look at the steps to solve this problem.

• Initialize the array with the coordinates of all line segments.
• Initialize a vector named points whose size is twice the size of the line segment array.
• Traverse the line segment array.
  • Fill the first point of the current line segment and false to the position of index i * 2 of the points array.
  • Fill the second point of the current line segment and false to the position of index i * 2 1 of the points array.
• Sort the points array.
• Use the counter variable to traverse the points array.
  • If the counter is greater than 0, add the first point of i and i-1 to the result.
  • If there is a second point, decrement the counter by 1, otherwise increase it.
• Return results.

Example

Let’s take a look at the code.

Demo

#include<bits/stdc++.h>
using namespace std;
int segmentUnionLength(const vector<pair <int,int>> &segments) {
   int n = segments.size();
   vector<pair<int, bool>> points(n * 2);
   for (int i = 0; i < n; i++) {
      points[i*2] = make_pair(segments[i].first, false);
      points[i*2 + 1] = make_pair(segments[i].second, true);
   }
   sort(points.begin(), points.end());
   int result = 0, count = 0;
   for (int i = 0; i < n * 2; i++){
      if (count) {
         result += points[i].first - points[i-1].first;
      }
      points[i].second ? count-- : count++;
   }
   return result;
}
int main() {
   vector<pair<int,int>> segments;
   segments.push_back(make_pair(1, 3));
   segments.push_back(make_pair(2, 7));
   segments.push_back(make_pair(6, 12));
   segments.push_back(make_pair(13, 5));
   cout << segmentUnionLength(segments) << endl;
   return 0;
}

Output

If you run the above code, you will get the following results.

6

Conclusion

If you have any questions during the tutorial, please ask them in the comment section.

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