Efficient Circuit Connection Modeling with a Circular Doubly Linked List

Problem Description : In circuit analysis, graph theory is commonly used to model circuits; each two‑terminal component is represented as an edge and its terminals as vertices. The challenge is how to store the relationships between vertices and perform connect and disconnect operations efficiently.

Method 1 – Adjacency List : Each vertex maintains an array of adjacent vertices. Connecting a vertex takes O(n) time, disconnecting takes O(n²) time (since array element removal is O(n)), and the total space required is O(n²). This approach is similar to a traditional adjacency list and can be complex to implement.

Circular Doubly Linked List : By using a circular doubly linked list, both connecting and disconnecting a vertex can be done in O(1) time, and the overall space consumption is O(n). The structure of a single node and multiple nodes is illustrated in the original figures.

Implementation :

class ListNode{
public next: ListNode;
public prev: ListNode;
constructor() {
this.next = this;
this.prev = this;
}
public destroy() {
this.next = null;
this.prev = null;
}
public connect(node: ListNode): void {
const next1: ListNode = this.next;
const next2: ListNode = node.next;
this.next = next2;
next2.prev = this;
node.next = next1;
next1.prev = node;
}
public disConnect(): void {
this.prev.next = this.next;
this.next.prev = this.prev;
this.next = this;
this.prev = this;
}
}

Summary : Using a circular doubly linked list is superior both in time and space, and its implementation is straightforward and less error‑prone, making it well‑suited for subsequent circuit calculations. The article emphasizes that mastering data structures and algorithms is essential for applying the right technique in appropriate scenarios.