Oh, no! You have just completed  a lengthy  document when you have an  unfortu- nate Find/Replace mishap.  You have accidentally  removed all spaces, punctuation, and  capitalization  in  the document. A sentence like  "I reset  the  computer.  It  still didn't boot!" would become "iresetthecomputeritstilldidntboot".  You figure that you can add back in the punctation and capitalization later, once you get the individual words properly separated. Most of the words will be in a dictionary,  but some strings, like proper names, will  not. Given a dictionary  (a list of words), design an algorithm  to find the optimal way of "unconcatenating" a sequence of words. In this case, "optimal" is defined  to be the parsing  which  minimizes  the number  of unrecognized sequences of characters. For example, the string "jesslookedjustliketimherbrother"  would be optimally parsed as  "JESS looked just like TIM her brother". This parsing  has seven unrecognized  char- acters, which  we have capitalized  for  clarity.


这是CareerCup Chapter 17的第14题，我没怎么看CareerCup上的解法，但感觉这道题跟​​​​很像，都是有一个dictionary, 可以用一维DP来做，用一个int[] res = new int[len+1]; res[i] refers to minimized # of unrecognized chars in first i chars, res[0]=0, res[len]即为所求。

有了维护量，现在需要考虑转移方程，如下：

int unrecogNum = dict.contains(s.substring(j, i))? 0 : i-j; //看index从j到i-1的substring在不在dictionary里，如果不在，unrecogNum=j到i-1的char数

res[i] = Math.min(res[i], res[j]+unrecogNum);


亲测，我使用的case都过了，只是不知道有没有不过的Corner Case:


1 package fib;  2   3 import java.util.Arrays;  4 import java.util.HashSet;  5 import java.util.Set;  6   7 public class unconcatenating {  8     public int optway(String s, Set<String> dict) {  9         if (s==null || s.length()==0) return 0; 10         int len = s.length(); 11         if (dict.isEmpty()) return len; 12         int[] res = new int[len+1]; // res[i] refers to minimized # of unrecognized chars in first i chars 13         Arrays.fill(res, Integer.MAX_VALUE); 14         res[0] = 0; 15         for (int i=1; i<=len; i++) { 16             for (int j=0; j<i; j++) { 17                 String str = s.substring(j, i); 18                 int unrecogNum = dict.contains(str)? 0 : i-j; 19                 res[i] = Math.min(res[i], res[j]+unrecogNum); 20             } 21         } 22         return res[len]; 23     } 24  25  26     public static void main(String[] args) { 27         unconcatenating example = new unconcatenating(); 28         Set<String> dict = new HashSet<String>(); 29         dict.add("reset"); 30         dict.add("the"); 31         dict.add("computer"); 32         dict.add("it"); 33         dict.add("still"); 34         dict.add("didnt"); 35         dict.add("boot"); 36         int result = example.optway("johnresetthecomputeritdamnstilldidntboot", dict); 37         System.out.print("opt # of unrecognized chars is "); 38         System.out.println(result); 39     } 40  41 }


output是：opt # of unrecognized chars is 8