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Program to find how many lines intersect in Python

Suppose we are given a list that contains values in pairs of (m, c). These values represent a line, where y = mx + c. We are also given two values, l, and r. We have to find out the number of the lines that intersect with each other between the range x = l to x = h.

So, if the input is like input_list = [[4, 6],[-6, 10],[8, 12]], l = 0, h = 2, then the output will be 2.

Program to find how many lines intersect in Python

If we look at the given photo, the lines 4x + 6 = 0 and -6x + 10 intersect within the given range. So, there are two lines that are intersecting, so the output is 2.

To solve this, we will follow these steps −

  • seg := a list containing pairs [(m * l + c, m * h + c, i) for index i, and values (m, c) in input_list]
  • sort the list seg
  • ans := a new list of the size of input_list containing 0s
  • c := a new map from seg
  • for each (x, y, i) in seg, do
    • if c[x] > 1, then
      • ans[i] := 1
  • max_c := -(10 ^ 10)
  • prv := -(10 ^ 10)
  • for each (x, y, i) in seg, do
    • if x is same as prv, then
      • ans[i] := 1
    • if y <= max_c, then
      • ans[i] := 1
    • max_c := maximum of (max_c, y)
      • prv := x
  • min_c = 10 ^ 10
  • prv = 10 ^ 10
  • for each (x, y, i) in seg reversed, do
    • if x is same as prv, then
      • ans[i] := 1
    • if y >= min_c, then
      • ans[i] := 1
    • min_c := minimum of (min_c, y)
    • prv := x
  • return sum of the elements of list (ans)

Example

Let us see the following implementation to get better understanding −

from collections import Counter

def solve(input_list, l, h):
   seg = [(m * l + c, m * h + c, i) for i, (m, c) in
enumerate(input_list)]
   seg.sort()
   ans = [0 for _ in input_list]
   c = Counter(seg)
   for (x, y, i) in seg:
      if c[x] > 1:
         ans[i] = 1
   max_c = -(10 ** 10)
   prv = -(10 ** 10)
   for (x, y, i) in seg:
      if x == prv:
         ans[i] = 1
      if y <= max_c:
         ans[i] = 1
      max_c = max(max_c, y)
      prv = x
   min_c = 10 ** 10
   prv = 10 ** 10
   for (x, y, i) in seg[::-1]:
      if x == prv:
         ans[i] = 1
      if y >= min_c:
         ans[i] = 1
      min_c = min(min_c, y)
      prv = x
   return sum(ans)

print(solve([[4, 6],[-6, 10],[8, 12]], 0, 2))

Input

[[4, 6],[-6, 10],[8, 12]], 0, 2

Output

2