TopCoder problem "WordMath" used in TCHS SRM 8 (Division I Level Two)



Problem Statement

    A common task for math students is to solve 'word math' questions, where each distinct letter represents a distinct digit.

Given a list of word math numbers to add, your task is to calculate the greatest possible sum of those numbers.



For example, given the expression:
    TOP
+ CODER
the maximum sum possible by substituting numbers is:
    783
+ 98654
-------
  99437
with C = 9, D = 6, E = 5, O = 8, P = 3, R = 4 and T = 7.

Please note that, for this question, word math numbers are allowed to start with a zero.
 

Definition

    
Class:WordMath
Method:maximumSum
Parameters:String[]
Returns:int
Method signature:int maximumSum(String[] summands)
(be sure your method is public)
    
 

Notes

-Different letters must represent different digits, identical letters must represent identical digits.
-Not all digits in the result must appear in the summands.
 

Constraints

-summands will contain between 1 and 10 elements, inclusive.
-Each element of summands will contain between 1 and 8 characters, inclusive.
-Each element of summands will contain only uppercase letters ('A'-'Z').
-summands will contain at most 10 distinct letters.
 

Examples

0)
    
{"TOP", "CODER"}
Returns: 99437
The example given in the problem statement.
1)
    
{"AAA", "AAA"}
Returns: 1998
With only one letter, the maximum sum is obtained by setting A = 9.
2)
    
{"A", "B", "C", "D", "E", "F", "G", "H", "I", "J"}
Returns: 45
Each letter is used once, and there are 10 different letters, so however the digits are distributed this must add up to 0 + 1 + ... + 8 + 9 = 45
3)
    
{"AB", "BA"}
Returns: 187
4)
    
{"READIEST","OPERATIC","TOPCODER","PREDICTS","RAPIDEST","ASTEROID","AIRSPEED"}
Returns: 563639653

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6572

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10060&pm=6572

Writer:

sql_lall

Testers:

PabloGilberto , brett1479 , Olexiy

Problem categories:

Simple Math