# TopCoder SRM 144 DIV2 (550-point)

Source: Internet
Author: User

Problem Statement

Let's say you have a binary string such as the following:

011100011

One way to encrypt this string is to add to each digit the sum of its adjacent digits. For example, the above string wocould become:

123210122

In particle, ifPIs the original string, andQIs the encrypted string, thenQ [I] = P [I-1] + P [I] + P [I + 1]For all digit positionsI. Characters off the left and right edges of the string are treated as zeroes.

An encrypted string given to you in this format can be decoded as follows (using123210122As an example ):

Now we repeat the process, assuming the opposite aboutP [0]:

Note that this algorithm produces at most two decodings for any given encrypted string. There can never be more than one possible way to decode a string once the first binary digit is set.

Given a stringMessage, Containing the encrypted string, return a vector <string> with exactly two elements. the first element shoshould contain the decrypted string assuming the first character is '0'; the second element shoshould assume the first character is '1 '. if one of the tests fails, return the string "NONE" in its place. for the above example, you shoshould return{"011100011", "NONE "}.

Definition

 Class: BinaryCode Method: Decode Parameters: String Returns: Vector Method signature: Vector decode (string message) (Be sure your method is public)
Limits

 Time limit (s ): 2 Memory limit (MB ): 64
Constraints
- MessageWill contain between 1 and 50 characters, inclusive.
- Each character inMessageWill be either '0', '1', '2', or '3 '.
Examples
0)

 `"123210122"`
`Returns: { "011100011",  "NONE" }`
 The example from above.
1)

 `"11"`
`Returns: { "01",  "10" }`
 We know that one of the digits must be '1', and the other must be '0'. We return both cases.
2)

 `"22111"`
`Returns: { "NONE",  "11001" }`
 Since the first digit of the encrypted string is '2', the first two digits of the original string must be '1'. Our test fails when we try to assume thatP [0] = 0.
3)

 `"123210120"`
`Returns: { "NONE",  "NONE" }`
 This is the same as the first example, but the rightmost digit has been changed to something inconsistent with the rest of the original string. No solutions are possible.
4)

 `"3"`
`Returns: { "NONE",  "NONE" }`

5)

 `"12221112222221112221111111112221111"`
`Returns: { "01101001101101001101001001001101001",  "10110010110110010110010010010110010" }`

This problem statement is the exclusive and proprietary property of TopCoder, Inc. any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c) 2003, TopCoder, Inc. all rights reserved.

Analysis:

Including the string class and vector container, it took some time to understand these things, but it was still modeled on a blog method.

I found that there are still many things I don't understand, so I just want to figure them out ~~

Code:

`#include <cstdio>#include <cstdlib>#include <iostream>#include <string>#include <cstring>#include <vector>using namespace std;class BinaryCode{    public:    vector <string> decode(string message){        vector <string> ret;        string str1(message.size(), 0), str2(message.size(), 0);        str1[0]='0';        str2[0]='1';        if(1==message.size()){            if(message[0]<'0'||message[0]>'1'){                str1="NONE";                str2="NONE";            }            else if(message[0] == '0')                str2 = "NONE";            else if(message[0] == '1')                str1 = "NONE";        }        else{            int i;            for(i=0; i<message.size(); ++i){                if(0 == i){                    if(str1!="NONE"){                        str1[i+1] = message[i]-str1[i]+'0';                        if(str1[i+1]<'0'||str1[i+1]>'1')                            str1 = "NONE";                    }                    if(str2!="NONE"){                        str2[i+1] = message[i]-str2[i]+'0';                        if(str2[i+1]<'0'||str2[i+1]>'1')                            str2 = "NONE";                    }                }                else{                    if(str1!="NONE"){                        str1[i+1] = message[i]-str1[i]+'0'-str1[i-1]+'0';                        if(str1[i+1]<'0'||str1[i+1]>'1')                            str1 = "NONE";                    }                    if(str2!="NONE"){                        str2[i+1] = message[i]-str2[i]+'0'-str2[i-1]+'0';                        if(str2[i+1]<'0'||str2[i+1]>'1')                            str2 = "NONE";                    }                }            }            if(str1!="NONE"&&message[i-1]!=str1[i-1]-'0'+str1[i-2])                str1 = "NONE";            if(str2!="NONE"&&message[i-1]!=str2[i-1]-'0'+str2[i-2])                str2 = "NONE";        }        ret.push_back(str1);        ret.push_back(str2);        return ret;    }};`

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