Select optimal graph algorithm based on problem constraints
Selects optimal graph algorithms based on problem constraints, graph properties, and performance requirements.
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README.mdSelect the optimal graph algorithm based on problem constraints, graph properties, and performance requirements.
| Scenario | Algorithm | Complexity |
|---|---|---|
| Unweighted | BFS | O(V+E) |
| Non-negative weights | Dijkstra | O((V+E)log V) |
| Negative weights | Bellman-Ford | O(VE) |
| All pairs | Floyd-Warshall | O(V^3) |
| DAG | Topological + DP | O(V+E) |
| Scenario | Algorithm | Complexity |
|---|---|---|
| Sparse graph | Kruskal | O(E log E) |
| Dense graph | Prim | O(V^2) or O(E log V) |
{
"type": "object",
"properties": {
"problemType": {
"type": "string",
"enum": ["shortestPath", "mst", "connectivity", "flow", "matching", "traversal"]
},
"graphProperties": { "type": "object" },
"constraints": {
"type": "object",
"properties": {
"V": { "type": "integer" },
"E": { "type": "integer" },
"negativeWeights": { "type": "boolean" },
"negativeCycles": { "type": "boolean" }
}
}
},
"required": ["problemType", "constraints"]
}
{
"type": "object",
"properties": {
"success": { "type": "boolean" },
"recommendedAlgorithm": { "type": "string" },
"complexity": { "type": "string" },
"alternatives": { "type": "array" },
"reasoning": { "type": "string" }
},
"required": ["success", "recommendedAlgorithm"]
}
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