Shortest Distance from Source (BFS)

Given a directed graph represented as an adjacency list graph and a source node src, return an array dist where dist[i] represents the shortest distance (number of edges) from src to node i. If node i is unreachable from src, dist[i] should be Infinity. The distance from src to itself is 0.

Examples

Input: graph = [[1, 2], [3], [4], [5], [3], []], src = 0
Output: [0, 1, 1, 2, 2, 3]
Explanation: 
- Distance from 0 to 0: 0 (same node)
- Distance from 0 to 1: 1 (direct edge)
- Distance from 0 to 2: 1 (direct edge)
- Distance from 0 to 3: 2 (0 -> 1 -> 3 or 0 -> 2 -> 4 -> 3)
- Distance from 0 to 4: 2 (0 -> 2 -> 4)
- Distance from 0 to 5: 3 (0 -> 1 -> 3 -> 5)

Input: graph = [[1], [2], []], src = 0
Output: [0, 1, 2]
Explanation: Linear path 0 -> 1 -> 2

Input: graph = [[1], [2], []], src = 2
Output: [Infinity, Infinity, 0]
Explanation: Node 2 cannot reach nodes 0 or 1

Input: graph = [[1], [2], [0]], src = 0
Output: [0, 1, 2]
Explanation: Graph with cycle, but shortest distances are still valid

Constraints

• Graph is represented as an adjacency list where graph[i] contains all nodes reachable from node i
• Nodes are numbered from 0 to n-1 where n is the number of nodes
• Graph may contain cycles
• Graph may be disconnected
• Distance from src to itself is always 0
• Unreachable nodes have distance Infinity
• Input validation: handle invalid inputs gracefully (non-array graph, invalid node indices)

Function Signature

function shortestDistance(graph, src) {
  // Your code here
}

Test Cases

• Base cases: single node graph [[], 0] -> [0]
• Direct neighbors: [[1, 2], [], []], 0 -> [0, 1, 1]
• Multi-hop paths: [[1], [2], [3], []], 0 -> [0, 1, 2, 3]
• Disconnected nodes: [[1], [], [3], []], 0 -> [0, 1, Infinity, Infinity]
• Graph with cycle: [[1], [2], [0]], 0 -> [0, 1, 2]
• Source with no outgoing edges: [[], [0], []], 1 -> [1, 0, Infinity]
• Large graphs with multiple paths