Resolve Package Dependencies with Cycle Detection

Problem Statement

You are tasked with writing a build system component that resolves package dependencies. You are given a dictionary where keys are package names (strings) and values are lists of their direct dependencies (strings).

Implement a function resolve_build_order(package, dependency_map) that returns a list of all packages required to install the target package, ordered such that every dependency appears before the package that requires it. If a cycle is detected, or if a dependency is required but missing from the dependency_map, the function should raise an error or return an empty list/appropriate indicator.

Function Signature

def resolve_build_order(target, dependency_map):
    # Returns a list of strings representing the installation order
    pass

Constraints

• dependency_map contains up to 10,000 packages.
• Cycles must be detected and handled (do not enter an infinite loop).
• A package missing from the keys of dependency_map is considered a leaf node with no dependencies.

Example 1

Input: dependency_map = {'A': ['B', 'C'], 'B': ['C'], 'C': []}, target = 'A' Output: ['C', 'B', 'A'] Explanation: 'C' is a dependency of 'B' and 'A', so it must be installed first. 'B' depends on 'C', and 'A' depends on 'B' and 'C'.

Example 2

Input: dependency_map = {'A': ['B'], 'B': ['A']}, target = 'A' Output: Error (Cycle Detected)

Edge Cases

• Disconnected components that are not required by the target.
• Chains of dependencies of depth > 1000.
• Target package has no dependencies.