BC之Claris and XOR

http://acm.hdu.edu.cn/showproblem.php?pid=5661

Claris and XOR

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 146    Accepted Submission(s): 51

Problem Description

Claris loves bitwise operations very much, especially XOR, because it has many beautiful features. He gets four positive integers a,b,c,d that
satisfies a≤b and c≤d.
He wants to choose two integers x,y that
satisfies a≤x≤b and c≤y≤d,
and maximize the value of x XOR y.
But he doesn't know how to do it, so please tell him the maximum value of x XOR y.

 

Input

The first line contains an integer T(1≤T≤10,000)——The
number of the test cases.

For each test case, the only line contains four integers a,b,c,d(1≤a,b,c,d≤1018).
Between each two adjacent integers there is a white space separated.

 

Output

For each test case, the only line contains a integer that is the maximum value of x XOR y.

 

Sample Input

2
1 2 3 4
5 7 13 15

 

Sample Output

6
11

Hint

In the first test case, when and only when $x=2,y=4$, the value of $x~XOR~y$ is the maximum.
In the second test case, when and only when $x=5,y=14$ or $x=6,y=13$, the value of $x~XOR~y$ is the maximum.

 

Source

BestCoder Round #79 (div.2)

 

Recommend

wange2014   |   We have carefully selected several similar problems for you:  5664 5663 5662 5661 5660 

 

我真也是服了，一个1<<50一样的数据彻底把我打败，从BC的时候，到赛后自己狂敲，然后狂不对，改dfs，超时，依旧不对，我去真也是醉了，看题解思路稍有差别，剪枝，依旧WR

各种测试，我去都不对，然后忽然发现有个1<<num的，应该越界了，改之，不到100毫秒就A掉，直接无语，又被细节打败了。

官方题解：

考虑从高位到低位贪心，对于每一位，如果x，y只有唯一的取法，那么只能这么取；否则贪心地必须使答案的这一位等于1。如果x，y都是0，1都能取，则设这是从右向左数第len位，因为x，y能取的值一定都是连续的一段，因此x，y的后len位都能取0111...1（len-1个1）和1000...0（len-1个0）（否则做不到从右向左数第len位都能取0,1）。也就是说，后len位的贡献一定能达到可能的上界111...1（len个1）。此时不必继续考虑后面的位。

如果x，y在这一位并不是0,1都能取，那么由于要使得答案的这一位等于1，也只有唯一的取法。

至此，这一位考虑完毕，然后根据选取的方案，修正一下x和y的范围，然后对后一位做即可。

细节决定成败。。。

下面是几种思路，既然想了就都粘上吧，都能过。（不多转2进制的函数没用，直接1<<判断就好了。。。）

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<ctime>
#define eps 1e-6
#define MAX 100005
#define INF 0x3f3f3f3f
#define LL long long
#define pii pair<string,int>
#define rd(x) scanf("%d",&x)
#define rd2(x,y) scanf("%d%d",&x,&y)
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
using namespace std;
char ch[100];
string  getbia(LL num){
    int i=0;
    string str="",str1;
    while(num){
        if(num%2) str+="1";
        else str+="0";
        num=num>>1;
       // cout<<"OOOOOOO"<<endl;
    }
    int len = str.length();
    for(int i=len-1;i>=0;i--)
        str1+= str[i];
    return str1;
}
int main()
{
    int T;
    LL a ,b,c,d;
    scanf("%d",&T);
    while(T--)
    {
      scanf("%I64d%I64d",&a,&b);
      scanf("%I64d%I64d",&c,&d);
      if(b>d){
        swap(a,c);
        swap(b,d);
      }
      string str1=getbia(d);
      string str2=getbia(b);
      //cout<<str1<<endl;
      int maxLen = str1.length();
      LL res=0;
      for(int i=0;i<=maxLen;i++){
            //cout<<a<<' ' <<b<<' '<<c<<' '<<d<<endl;
        LL temp=(LL)1<<(maxLen-1-i);
        int mark=0;
        if(temp<=d){ ///可以是1
            if(temp-1>=a){
              res+=temp,mark=1;
              d = d>=temp ? d-temp : d;
              c = c>=temp ? c-temp : 0;
              a = a>=temp ? temp-1 : a;
              b = b>=temp ? temp-1 : b;
            }
        }
        if(temp-1>=c&&!mark) { ///可以是0
            if(temp<=b){
              res+=temp,mark;
              d = d>=temp ? temp-1 : d;
              c = c;
              a = a>=temp ? a-temp : a;
              b = b>=temp ? b-temp : 0;
            }
        }
        if(!mark){
          d = d>=temp ? d-temp : d;
          c = c>=temp ? c-temp : c;
          a = a>=temp ? a-temp : a;
          b = b>=temp ? b-temp : b;
        }
        if(a>b) swap(a,b);
        if(c>d) swap(c,d);
        if(b>d){
         swap(a,c);
         swap(b,d);
        }
      }
      printf("%I64d\n",res);
    }
    return 0;
}

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<ctime>
#define eps 1e-6
#define MAX 100005
#define INF 0x3f3f3f3f
#define LL long long
#define pii pair<string,int>
#define rd(x) scanf("%d",&x)
#define rd2(x,y) scanf("%d%d",&x,&y)
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
using namespace std;
char ch[100];
string  getbia(LL num){
    int i=0;
    string str="",str1;
    while(num){
        if(num%2) str+="1";
        else str+="0";
        num=num>>1;
       // cout<<"OOOOOOO"<<endl;
    }
    int len = str.length();
    for(int i=len-1;i>=0;i--)
        str1+= str[i];
    return str1;
}
//LL tempRes=0;
LL dfs(LL a,LL b,LL c,LL d,int maxLen,LL res){
    LL temp=(LL)1<<(maxLen);
    if(maxLen<0) return res;
    LL a1,b1,c1,d1;
    LL res1=0,res2=0,res3=0,mark=0;

    if((temp<=d&&temp-1>=c) &&(temp-1>=a&&temp<=b)){  ///开始没有这段优化，一直是超时的。。。
        return res+((LL)1<<(maxLen+1))-1;
    }
    if(temp<=d){ ///可以是1
        if(temp-1>=a){
          mark=1;
          d1 = d-temp ;
          c1 = c>=temp ? c-temp : 0;
          a1 = a;
          b1 = b>=temp ? temp-1 : b;
          res1 = dfs(a1,b1,c1,d1,maxLen-1,res+temp);
        }
    }
    if(temp-1>=c&&!mark) { ///可以是0
        if(temp<=b){
          mark=1;
          d1 = d>=temp ? temp-1 : d;
          c1 = c;
          a1 = a>=temp ? a-temp : 0;
          b1 = b-temp;
          res2 = dfs(a1,b1,c1,d1,maxLen-1,res+temp);
        }
    }
    if(!mark){ ///此位异或后不可能为1
       // cout<<"4:";
        a1 = a>=temp ? a-temp : a;
        b1 = b>=temp ? b-temp : b;
        d1 = d>=temp ? d-temp : d;
        c1 = c>=temp ? c-temp : c;
        res3 = dfs(a1,b1,c1,d1,maxLen-1,res);
    }
     LL mmax = max(res1,max(res2,res3)) ;
     return mmax;
}

int main()
{
    int T;
    LL a ,b,c,d;
    scanf("%d",&T);
    while(T--)
    {
      scanf("%I64d%I64d",&a,&b);
      scanf("%I64d%I64d",&c,&d);
      if(b>d){
        swap(a,c);
        swap(b,d);
      }
      string str1=getbia(d);
      string str2=getbia(b);
      int maxLen = str1.length();
      LL res=dfs(a,b,c,d,maxLen-1,0);
      printf("%I64d\n",res);
    }
    return 0;
}

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<ctime>
#define eps 1e-6
#define MAX 100005
#define INF 0x3f3f3f3f
#define LL long long
#define pii pair<string,int>
#define rd(x) scanf("%d",&x)
#define rd2(x,y) scanf("%d%d",&x,&y)
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
using namespace std;
char ch[100];
string  getbia(LL num){
    int i=0;
    string str="",str1;
    while(num){
        if(num%2) str+="1";
        else str+="0";
        num=num>>1;
       // cout<<"OOOOOOO"<<endl;
    }
    int len = str.length();
    for(int i=len-1;i>=0;i--)
        str1+= str[i];
    return str1;
}
int main()
{
    int T;
    LL a ,b,c,d;
    scanf("%d",&T);
    while(T--)
    {
      scanf("%I64d%I64d",&a,&b);
      scanf("%I64d%I64d",&c,&d);
      if(b>d){
        swap(a,c);
        swap(b,d);
      }
      string str1=getbia(d);
      string str2=getbia(b);
      //cout<<str1<<endl;
      int maxLen = str1.length();
      LL res=0;
      for(int i=0;i<=maxLen;i++){
            //cout<<a<<' ' <<b<<' '<<c<<' '<<d<<endl;
        LL temp=(LL)1<<(maxLen-1-i);
        int mark=0;
        if(temp<=d){ ///可以是1
            if(temp-1>=a){
              res+=temp,mark=1;
              d = d>=temp ? d-temp : d;
              c = c>=temp ? c-temp : 0;
              a = a>=temp ? temp-1 : a;
              b = b>=temp ? temp-1 : b;
            }
        }
        if(temp-1>=c&&!mark) { ///可以是0
            if(temp<=b){
              res+=temp,mark;
              d = d>=temp ? temp-1 : d;
              c = c;
              a = a>=temp ? a-temp : a;
              b = b>=temp ? b-temp : 0;
            }
        }
        if(!mark){
          d = d>=temp ? d-temp : d;
          c = c>=temp ? c-temp : c;
          a = a>=temp ? a-temp : a;
          b = b>=temp ? b-temp : b;
        }
        if(a>b) swap(a,b);
        if(c>d) swap(c,d);
        if(b>d){
         swap(a,c);
         swap(b,d);
        }
      }
      printf("%I64d\n",res);
    }
    return 0;
}