Get all algebraically unique solutions to the 24 Game in C++. https://repl.it/@lijt931/24-Game-Solver
Run directly here, or compile in C++17 or above and run.
Follow the instructions:
Please enter 4 cards in [1, 13] (e.g. 1 4 5 6) followed by an optional target (default 24):
1 2 3 4
#1: (1+3)*(2+4) = 24
#2: ((1*2)*3)*4 = 24
#3: ((1+2)+3)*4 = 24
Note that other equivalent solutions like 4*3*2*1 are omitted.
The cards and the target can be arbitrary real numbers, for example:
Please enter 4 cards in [1, 13] (e.g. 1 4 5 6) followed by an optional target (default 24):
-1 -2.5 3 4.5 5.5
#1: (-2.5*(-1-3))-4.5 = 5.5
The algorithm consists of two parts. The first part use brute-force to generate all possible solutions and the second part eliminates equivalent ones.
Each permutation of the 4 cards is traversed, then each permutation of the operands (+, -, *, /), then each permutation of precedence.
One way to achieve this is to use a polynomial class and define the equivalence criterion. This algorithm uses a simpler way, which is assigning a transcendental number (e.g. PI, e) to each card value, and compare the arithmetic results.