Question

There are two circles A and B with their centres C1(x1,y1) and C2(x2,y2) and radius R1 and R2. The task is to check both circles A and B touch each other or not. Input: C1=(3,4)

C2=(14,18)
R1=5,R2=8
Output: Circles do not touch each other. Input: C1=(2,3)
C2=(15,28)
R1=12,R2=10
Output: Circles intersect with each other. With the implementation below, can you propose 2 optimizations to improve runtime? No executable code is required for justification.

Answer 1

In geometric problems, optimizations such as eliminating square root calculations by comparing squared distances and avoiding repeated calculations can improve runtime.

Step-by-step explanation:

When discussing the touching or intersecting of two circles, we are engaging with a geometric problem where optimization can play a significant role in the runtime of algorithms used to solve such a scenario. Two straightforward optimizations to consider without modifying the code are:

• Distance Calculation Optimization: Instead of computing the actual Euclidean distance between the centers of the two circles, which includes a square root operation, you can compare the squares of the distances and radii. This eliminates the need for the costly square root computation and can reduce the runtime significantly.
• Avoid Repeated Calculations: If your algorithm calculates the distance between the centers of the circles multiple times, you can optimize by storing the result in a variable and reusing it instead of recalculating it, to save on processing time.