Cryptarithm - Trilogy

Problem Preview

"A cryptarithm is a mathematical puzzle where the goal is to find the correspondence between letters and digits such that the given arithmetic equation consisting of letters holds true. Given a cryptarithm as an array of strings crypt, count the number of its valid solutions. The solution is valid if each letter represents a different digit, and the leading digit of any multi-digit number is not zero. ### Example * For crypt = ["SEND", "MORE", "MONEY"] the output should be 1 , because there is only one solution to this cryptarithm: 0 = 0 , M = 1 , Y = 2 , E = 5 , N = 6 , D = 7 , R = 8 and S = 9 ( 9567 + 1085 = 10652 ) * For crypt = ["GREEN", "BLUE", "BLACK"] the output should be 12 , because there are 12 possible solutions. * For crypt = ["ONE", "TWO", "THREE"] the output should be 0 , because there are no valid solutions. ### Input/Output * [execution time limit] 0.5 seconds (cpp) * [memory limit] 1 GB * [input] array.string crypt Array of three non-empty strings containing only uppercase English letters. Guaranteed constraints: - 1 ≤ crypt[i].length ≤ 35 . * [output] integer The number of valid solutions."