Graph Coloring with Pre-assigned Nodes

You are given an undirected graph represented as an adjacency list. Some nodes in the graph have already been assigned a color (either 'red' or 'blue'), while other nodes are uncolored. Implement a function that determines if it is possible to assign colors to all uncolored nodes such that no two adjacent nodes share the same color.

If a valid coloring exists, return a dictionary (or map) that assigns a color ('red' or 'blue') to every node (including those pre-assigned). If no valid coloring exists, return an appropriate indicator (e.g., null or an empty dictionary).

Input:

• An adjacency list for the graph. Example:
  {
  'A': ['B', 'C'],
  'B': ['A', 'D'],
  'C': ['A'],
  'D': ['B']
  }
• A dictionary (or map) for pre-assigned colors. Example:
  {
  'A': 'red',
  'D': 'blue'
  }

Constraints:

• The graph may consist of multiple connected components.
• The total number of nodes is at most 10^4.
• The graph does not contain self-loops or parallel edges.

Implement your solution in the programming language of your choice. Make sure to handle all edge cases and include comments in your code to explain your approach.