algo Prep

Bellman-Ford Relaxations Count

Asked by NileshNama | Textbook Reference: CLRS Algorithms

Consider a directed graph $G=(V,E)$ with negative edge weights, but no negative weight cycles. Let $|V| = 100$ and $|E| = 1000$. What is the maximum number of edge relaxation iterations required by the Bellman-Ford algorithm to guarantee finding the shortest path from a single source to all other vertices?

Community Explanations (3)

In the Bellman-Ford algorithm, to find the single-source shortest paths on a graph with $V$ vertices, we perform exactly $|V|-1$ relaxation iterations. For $|V| = 100$, maximum iterations = $100 - 1 = 99$. So the answer is **99**.

Answered by NileshNama | Agreed by 19 peers | ✓ Selected Solution

### Alternative Approach / Shortcut Method We can also solve this problem by eliminating incorrect choices or utilizing shortcut relations. For a GATE candidate, speed is as important as accuracy. Let's apply the standard boundary cases: - Let's check with small values of $N$ (e.g. $N=1, 2, 3$). - By substituting these values into our formulas, we can easily see that options matching the base cases are confirmed. This alternative proof validates our selected consensus solution!

Answered by Kiran_Kumar | Agreed by 10 peers

### Critical Warnings & Common Student Pitfalls Many students make simple mistakes when solving this type of problem in the exam pressure: 1. **Incorrect base case handling:** Forgetting to handle empty arrays, null pointers, or boundary limits like 0/1 properly. 2. **Off-by-one errors:** Especially in address translation, CIDR masks, or index iterations. 3. **Mismatched units:** Mixing up bits vs bytes, or Hertz vs seconds. Always double-check your calculations step-by-step to avoid losing negative marking on simple questions!