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My first instinct was greedy and it was wrong.
Model the problem as a minimum cost bipartite matching between analysts and devices, where edge weights are Manhattan distances. Since n ≤ 10 and m ≤ 15, use dynamic programming with bitmask over devices to compute the minimum cost assignment efficiently.
Pro tip: Mention that the DP state can be optimized by only considering the first n devices or using memoization, and discuss the trade-off between DP and Hungarian algorithm given the small constraints.
Restate the problem: assign each of n analysts to a distinct device to minimize total Manhattan distance. Confirm constraints and that n ≤ m.
Select dynamic programming with bitmask over devices (or Hungarian algorithm) due to small n and m. Explain why DP is suitable: state space 2^m * n is manageable.
Define dp[i][mask] as min cost to assign first i analysts using devices in mask. Transition: dp[i][mask] = min over j not in mask of dp[i-1][mask without j] + dist(i-1, j).
Implement iteratively or recursively with memoization. Optimize by precomputing distances and using bit operations. Discuss time complexity O(n * 2^m * m).
Test with small cases, edge cases (n=0, n=m). Analyze complexity and compare with alternative approaches like Hungarian algorithm O(n^2 m).
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