Algorithm presentation about bellman fords.

1. Bellman-Ford
Algorithm
Shortest Path with Negative
Weights
Presented By
Sabrina Hasem (59)
Md Abu Bakkar Siddiq (62) 1

2. Presented to
Faria Sultana Bintha Rohman
Lab Technical Officer (LTO)
Department of CSE
Feni University
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3. Introduction
• The Bellman-Ford Algorithm finds the shortest paths
from a single source to all other vertices in a weighted
graph.
• Unlike Dijkstra’s algorithm, it works with negative
weights.
• It also detects negative weight cycles.
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4. How It Works
• Initialization: dist[source] = 0, others = ∞
• Repeat |V|-1 times:
Relax all edges:
if dist[u] + w < dist[v]: dist[v] = dist[u] + w
• Cycle Check: One more pass — if still updates, negative
cycle exists.
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5. Pseudocode
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6. Time and Space
Complexity
• Time Complexity: O(V * E)
• Space Complexity: O(V)
• Suitable for sparse graphs.
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7. Bellman-Ford vs Dijkstra
Feature Bellman-Ford Dijkstra
Negative Weights Yes No
Cycle Detection Yes NO
Time Complexity O(VE) O(V log V + E)
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8. Conclusion
• Bellman-Ford is a powerful algorithm for:
⚬ Handling negative weights
⚬ Detecting negative weight cycles
⚬ Solving single-source shortest path
problems
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9. Q&A
"Thank you! We'd be happy to
answer any questions."
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10. Thank
You
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