Mastermind is a game where the code maker selects a series of P pegs from C colors, and the code breaker tries to guess the code, with the help of hints after each guess. After a guess, the code maker gives a response made up of some number of black pegs and some number of white pegs. A black peg is awarded for every peg in the guess which is the right color in the right position. A white peg is awarded for every peg in the guess which is the right color in the wrong position. Only one response peg can be awarded for any peg in the code or guess, which black responses taking precedence over white responses. For example, if the code is AABBC And the guess is ABCDC The code maker would give a black peg for the match of A in the first position, and a second black peg for the match of C in the last position. He would give one white peg for the B in the wrong position. The C in the third position would not get a peg because the C in the code was already given a black peg. So the response would be 2 black pegs and one white peg. The order of the black and white pegs in the response has no significance. Define an algorithm with O(P) runtime complexity to determine the correct response to a guess. The algorithm should require a feasible amount of memory for P<1000 and C<1000 (meaning you can't have a table of size C^P). Don
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