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2012-04-17 13:44 106 查看
 
 

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

 
 

import java.util.Arrays;

public class WordMath {

int[] weigh = new int[26];

public int maximumSum(String[] summands) {
for (String s : summands)
for (int j = 0, n = s.length(); j < n; j++)
weigh[s.charAt(j) - 'A'] += Math.pow(10, n - j - 1);
Arrays.sort(weigh);
int ret = 0;
for (int i = 0; i < 10; i++)
ret += weigh[25 - i] * (9 - i);
return ret;
}

}

 
                                            

                                        

                        
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