Open in App
Not now

# Ternary representation of Cantor set

• Last Updated : 06 Sep, 2022

Given three integers A, B and L, the task is to print the ternary cantor set from range [A, B] upto L levels.
Ternary Cantor Set: A ternary Cantor set is a set built by removing the middle part of a line segment when divided into 3 parts and repeating this process with the remaining shorter segments. Below is an illustration of a cantor set.

An illustration of a Ternary Cantor Set

Examples:

Input: A = 0, B = 1, L = 2
Output:
Level 0: [0.000000] — [1.000000]
Level 1: [0.000000] — [0.333333] [0.666667] — [1.000000]
Level 2: [0.000000] — [0.111111] [0.222222] — [0.333333] [0.666667] — [0.777778] [0.888889] — [1.000000]
Explanation: For the given range [0, 1], in level 1, it is divided into three parts ([0, 0.33], [0.33, 0.67], [0.67, 1]). From the three parts, the middle part is ignored. This process is continued for every part in the subsequent executions.
Input: A = 0, B = 9, L = 3
Output:
Level_0: [0.000000] — [9.000000]
Level_1: [0.000000] — [3.000000] [6.000000] — [9.000000]
Level_2: [0.000000] — [1.000000] [2.000000] — [3.000000] [6.000000] — [7.000000] [8.000000] — [9.000000]
Level_3: [0.000000] — [0.333333] [0.666667] — [1.000000] [2.000000] — [2.333333] [2.666667] — [3.000000] [6.000000] — [6.333333] [6.666667] — [7.000000] [8.000000] — [8.333333] [8.666667] — [9.000000]

Approach:

1. Create a linked list data structure for each node of the Set, having the start value, end value and a pointer to the next node.
2. Initialize the list with the start and end value given as the input.
3. For the next level:
• Create a new node where the difference between the start and end values is of the initial, i.e. start value is less than the initial end value.
• Further, modify the original node, such that the end value is more of the initial start value.
• Place the pointer to the new node after the original one accordingly

Below is the implementation of the above approach:

## Javascript



Output:
Level_0 : [0.000000] — [9.000000]
Level_1 : [0.000000] — [3.000000] [6.000000] — [9.000000]
Level_2 : [0.000000] — [1.000000] [2.000000] — [3.000000] [6.000000] — [7.000000] [8.000000] — [9.000000]

References: Cantor Set Wikipedia
Related Article: N-th term of George Cantor set of rational numbers

My Personal Notes arrow_drop_up
Related Articles