## AlphameticsAlphametics are puzzles in which letters are substituted for the digits in an arithmetic calculation, and the words formed by the operands and answer produce a sensible phrase. The goal is to find the digits that can be substituted for the letters to produce a correct addition statement.Consider the program demonstrated to the right. It decomposes each command line argument into its constituent characters, sorts the characters, goes through all permutations of all combinations of 10 digits taken 4 at a time in search of the solution, reports each solution, and the total number of permutations tested.
The following class is available upon request. int* digits = new int[ number_of_letters ]; // Enumerate all combinations of 10 digits taken // "number_of_letters" at a time Combinations combos( 10, number_of_letters ); while (combos.next( digits )) { ... }The standard library of C++ provides the function " ```
bool
next_permutation(array)
``` ". It allows the user to
enumerate all permutations of the supplied array.
Notice the "three three two two one" puzzle below – in addition to the normal puzzle dimension, the numbers named actually add up to "eleven" as well.
A cradle-to-grave discussion of Alphametics
Here is a skeleton you might consider ...
// Find all the letters, and put them in a sorted // list map<char,int> letters; // Create an array of digits that is the same size // as the array of letters int* digits = new int[ letters.size() ]; // Report the array of letters // Iterate through all combinations, and all // permutations of each combination Combinations combos( 10, number_of_letters ); while (combos.next( digits )) do { . . // Test each permutation & report the answer . . } while (next_permutation( digits ));impl | % alphametics i did too d i o t 1 9 0 2 i 9 did 191 --- --- too 200 count is 5040 % alphametics hes the best b e h s t 1 2 4 6 8 hes 426 the 842 ---- ---- best 1268 count is 30240 % alphametics no no too late a e l n o t 0 2 1 7 4 9 no 74 no 74 too 944 ---- ---- late 1092 count is 151200 % alphametics base ball games a b e g l m s 4 7 3 1 5 9 8 base 7483 ball 7455 ----- ----- games 14938 count is 604800 % alphametics usa ussr peace a c e p r s u 2 7 0 1 8 3 9 usa 932 ussr 9338 ----- ----- peace 10270 count is 604800 % alphametics send more money d e m n o r s y 7 5 1 6 0 8 9 2 send 9567 more 1085 ----- ----- money 10652 count is 1814400 % alphametics three three two two one e h l n o r t v w eleven 1 4 7 9 3 6 8 2 0 three 84611 three 84611 two 803 two 803 one 391 ------ ------ eleven 171219 count is 3628800 % alphametics double double toil trouble b d e i l o r t u 0 7 4 3 6 9 5 1 8 double 798064 double 798064 toil 1936 ------- ------- trouble 1598064 count is 3628800 % alphametics world trade center a c d e l n o r t w 0 1 4 2 8 9 3 6 7 5 world 53684 trade 76042 ------ ------ center 129726 count is 3628800 % alphametics this isa great time waster a e g h i m r s t w 0 4 9 6 2 3 7 8 5 1 this 5628 isa 280 great 97405 time 5234 ------ ------ waster 108547 count is 3628800 |