eightqueens_concepts - Solve a Problem

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If an 8 Queens algorithm tried every possible square on the board for placing each queen, how many entries are there at the 8th and final level of its full decision tree?
infinity (8 ** 8) = 16,777,216 (648) = 512 (6463626160595857) = 1.78e14 (6464646464646464) = 4.72e21 (order shuffled)*
What does a better algorithm do to avoid having to explore so many possibilities?
Compute all correct answers ahead of time and save them in a cache. Limit to placing only one queen in each column or row of the board. Use a dictionary to increase the efficiency of the algorithm. Raise an error because the problem is too computationally expensive to solve. Randomly skip certain squares based on a heuristic. (order shuffled)
How do we make an 8 Queens exploration function that stops once it finds one solution to the problem?
Raise an error if more than one solution prints out. Use a return statement to exit all recursive calls. Call the exit() function to quit the program after finding a solution. Return a bool value of True when finding a solution, and checking for this in each call. Print all solutions, but then erase the output to hide it. (order shuffled)