[General idea of the title] ____________

Give you n 128-bit binary IP addresses, output the shortest compressed IP address, if the length is the same, output the least dictionary order.

Compression rule: Every 16-bit binary number is a field, such as 0000000110001111, and then four-bit binary number is converted to a 16-bit number, such as 0000000110001111 to 01af, where the leading 0 of each field is removed, and if the leading value of this field is 0, it is denoted by zero. Then, if the values of two or more fields are zero in succession, they are denoted by two colons ":" which means that ":" can only be used once at most in an ip address.

(Dazzling!!!!!!!!!!!!!!!!)

[Sample input]

8
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000010010001101000101011001111000100110101011000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000010010001100000000000000000000000000000000000000000000000001000101011001111000100110101011
11111111111111111111111111110000000000000000000000000000000000000000000000001111000000000000000000000000000000000000000000000000
00010001000100010001000100010000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000
00010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
00000001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
00010001000100010001000100010001000100000001000100010001000100010001000100010001000100010001000100010001000100010001000100010001

[Sample output]

Case #1: ::
Case #2: 0:0:123:4567:89ab::
Case #3: 0:0:123::4567:89ab
Case #4: ffff:fff0:0:0:f::
Case #5: 1111:1110:0:0:1::
Case #6: 1111:1111:1111:1111:1111:1111:1111:1111
Case #7: 111:1111:1111:1111:1111:1111:1111:1111
Case #8: 1111:1111:1011:1111:1111:1111:1111:1111

[Code]

  1 #include <bits/stdc++.h>
  2 #define ll long long
  3 #define pai pair<int,int>
  4 using namespace std;
  5 int bit[4]= {8,4,2,1};//8421 Code table
  6 map<int,string>MAP;
  7 bool comp(string &a,string &b)
  8 {
  9     int len1=a.length(),len2=b.length();
 10     if(len1==len2)return a<b;
 11     return len1<len2;
 12 }
 13 void init()
 14 {
 15     MAP[0]="0";
 16     MAP[1]="1";
 17     MAP[2]="2";
 18     MAP[3]="3";
 19     MAP[4]="4";
 20     MAP[5]="5";
 21     MAP[6]="6";
 22     MAP[7]="7";
 23     MAP[8]="8";
 24     MAP[9]="9";
 25     MAP[10]="a";
 26     MAP[11]="b";
 27     MAP[12]="c";
 28     MAP[13]="d";
 29     MAP[14]="e";
 30     MAP[15]="f";
 31 }
 32 int main()
 33 {
 34 //    cout<<int(':')<<" "<<int('a')<<" "<<int('0')<<endl;
 35 //    string a="::ffff:ffff:0:0:0";
 36 //    string b="0:0:0:ffff:ffff::";
 37 //    string c="0:0:0:1111:1111::";
 38 //    string d="::1111:1111:0:0:0";
 39 //    if(a>b)cout<<"a>b"<<endl;
 40 //    else if(a==b)cout<<"a=b"<<endl;
 41 //    else cout<<"b>a"<<endl;
 42 //    if(c>d)cout<<"c>d"<<endl;
 43 //    else if(c==d)cout<<"c=d"<<endl;
 44 //    else cout<<"d>c"<<endl;
 45     init();
 46     int t;
 47     scanf("%d",&t);
 48     int k=1;
 49     while(k<=t)
 50     {
 51         queue<pai>que;
 52         string ans[10];
 53         int l=0,r=0;
 54         int maxx=0;
 55         getchar();
 56         for(int i=1; i<=8; i++)
 57         {
 58             char add[20];
 59             scanf("%16s",add);
 60             int now=0;
 61             int num=0;
 62             bool flag=false;
 63             for(int j=0; j<16; j++)
 64             {
 65                 now=now+bit[j%4]*(add[j]-'0');
 66                 // cout<<j<<"  "<<now<<endl;
 67                 if(now>0)flag=true;
 68                 if(j%4==3)
 69                 {
 70                     num=num*10+now;
 71                     if(flag)
 72                         ans[i]+=MAP[now];
 73                     now=0;
 74                 }
 75             }
 76             if(num==0)
 77             {
 78                 ans[i]="0";
 79             }
 80         }
 81         int bitnum=0;
 82         for(int i=1; i<=8; i++)
 83         {
 84             if(ans[i].compare("0")==0)
 85             {
 86                 bitnum++;
 87             }
 88             else bitnum=0;
 89             if(bitnum>=2)
 90             {
 91                 if(maxx<=bitnum)
 92                 {
 93                     l=i-bitnum+1;
 94                     r=i;
 95                     que.push(pai(l,r));
 96                     maxx=bitnum;
 97                 }
 98             }
 99         }
100         printf("Case #%d: ",k);
101         if(que.size()==0)
102         {
103             for(int i=1; i<=8; i++)
104             {
105                 cout<<ans[i];
106                 if(i<8)printf(":");
107             }
108             printf("\n");
109         }
110         else
111         {
112             string out[1000];
113             int ans_num=0;
114             while(!que.empty())
115             {
116                 pai p=que.front();
117                 que.pop();
118                 int _l=p.first,_r=p.second;
119                 for(int i=1; i<=8;)
120                 {
121                     if(i==_l)
122                     {
123                         out[ans_num]+="::";
124                         i=_r+1;
125                     }
126                     else
127                     {
128                         out[ans_num]+=ans[i];
129                         if(i<8&&i+1!=_l)
130                             out[ans_num]+=":";
131                         i++;
132                     }
133                 }
134                 ans_num++;
135             }
136             sort(out,out+ans_num,comp);
137             cout<<out[0]<<endl;
138 //            cout<<out[1]<<endl;
139 //            cout<<out[2]<<endl;
140         }
141         k++;
142     }
143     return 0;
144 }
145 /*
146 */
147 /*
148 8
149 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
150 00000000000000000000000000000000000000010010001101000101011001111000100110101011000000000000000000000000000000000000000000000000
151 00000000000000000000000000000000000000010010001100000000000000000000000000000000000000000000000001000101011001111000100110101011
152 11111111111111111111111111110000000000000000000000000000000000000000000000001111000000000000000000000000000000000000000000000000
153 00010001000100010001000100010000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000
154 00010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
155 00000001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
156 00010001000100010001000100010001000100000001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
157 */