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المحاضرة 9 من 10

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From Graphs to Trees to a Binary Search Tree

Separate connections, parent-child structure and key order, then build the original BST example.

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Step 1 of 7 · Understand

First describe the connections

Goal: Identify vertices and edges before adding tree rules.

A graph describes objects and connections. An object is a vertex or node; a connection is an edge. Two nodes joined by one undirected edge form a graph. One isolated node with no edges also forms a graph.

An edge must have endpoints in the vertex set. A drawn line with no specified endpoints does not describe a valid edge by itself. Some mathematical conventions also allow an empty graph; we will use nonempty examples here.

A self-loop is an edge from a node to itself. This is a graph term, not a program loop. It is allowed in some graph models and excluded in a simple graph. Before classifying a drawing, state the graph model.

BST means Binary Search Tree. We will add the requirements behind those words one at a time.

Remember: A graph says what is connected; it need not be a tree.

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مصادر الدرس وملاحظات المراجعة

يعتمد ترتيب الموضوعات والأمثلة على صفحات 76–84 من الدفتر. نسبة الدفتر إلى الدكتور غير مؤكدة. الشرح والتفاعلات التعليمية صياغة مساعدة، وليست نقلًا حرفيًا.

شرح تكميلي بالإنجليزية والعربية يتبع أمثلة وترتيب محاضرة الدفتر9 في صفحات PDF76–84. المصدر محفوظ وغير مؤكد النسبة لدكتور الطالب. الكود التكميلي وتصحيحات الادعاءات مفحوصة بصورة منفصلة؛ ليست اقتباسات من الأستاذ.

PDF76–84 inspected visually. The arrowhead between1 and2 on PDF79 is difficult to distinguish in both the full PDF and overlapping part2 page34; the written label is weakly connected. With1→2,1→3,3→2 that label is valid. With2→1,1→3,3→2 the graph is strongly connected. The lesson explicitly teaches both conditional interpretations; no uncertain arrow is silently approved. A rooted tree requires connectivity and no cycles, not merely naming a root or one parent. Binary does not mean exactly two children; the first array value is a root only for an explicitly chosen insertion convention. “One BST from a dataset” is only deterministic for a fixed insertion order/duplicate policy, not an unordered set. Duplicate keys are handled by the stated policy, not forbidden by every possible BST. Self-loops are cycles of length1 when permitted; a cycle graph is not the same as any graph containing a cycle. Finite labeled node sets do not produce infinitely many simple graphs.

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