The Manhattan distance and Euclidean distance heuristics are commonly used in A* algorithm, but there are other heuristics that can be used depending on the nature of the problem. Here are a few examples of alternative heuristics and their associated time complexities:

1. Diagonal distance heuristic: This heuristic calculates the distance between two nodes by considering both horizontal and vertical movements as well as diagonal movements. The time complexity is also O(n log n), similar to a good heuristic.

2. Octile distance heuristic: This heuristic takes into account both horizontal and vertical movements as well as diagonal movements but assumes that diagonal movements have a cost of √2. The time complexity is also O(n log n), similar to a good heuristic.

3. Zero heuristic: In some cases, you may encounter situations where no heuristic information is available. In such cases, the A* algorithm effectively becomes Dijkstra's algorithm, which has a time complexity of O(n log n), again similar to a good heuristic.

4. Abstraction heuristics: For complex problems, it is sometimes useful to create abstractions or simplifications of the original problem. These abstractions can be used as heuristics to guide the search. The time complexity of such heuristics can vary depending on the complexity of the abstraction.

I hope this helps you explore alternative heuristics for the A* algorithm. If you have any more questions, feel free to ask!
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