WordMath | Topcoder Archive

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

```
{"TOP", "CODER"}
```
```
Returns: 99437
```
The example given in the problem statement.
```
{"AAA", "AAA"}
```
```
Returns: 1998
```
With only one letter, the maximum sum is obtained by setting A = 9.
```
{"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
```
{"AB", "BA"}
```
```
Returns: 187
```

{"READIEST","OPERATIC","TOPCODER","PREDICTS","RAPIDEST","ASTEROID","AIRSPEED"}

Returns: 563639653

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