test/aoj/0402.test.cpp

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• Last update: 2021-09-23 20:26:31+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0402

Depends on

• convolution/bitwise/fwht.cpp
• convolution/bitwise/xor.cpp

Code

// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0402

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../../convolution/bitwise/fwht.cpp"
#include "../../convolution/bitwise/xor.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  using ll = long long;

  ll n,k;
  cin>>n>>k;
  vector<int> as(n);
  for(int i=0;i<n;i++) cin>>as[i];

  const int LOG = 20;
  const int sz = 1<<LOG;
  vector<ll> cnt(sz,0);
  cnt[0]++;
  for(int i=0,s=0;i<n;i++){
    s^=as[i];
    cnt[s]++;
  }

  fwht(cnt,bitwise_xor::zeta);
  for(ll &v:cnt) v=v*v;
  fwht(cnt,bitwise_xor::moebius);

  k--;
  for(int v=sz-1;v>=0;v--){
    cnt[v]/=2;
    if(cnt[v]<=k){
      k-=cnt[v];
      continue;
    }
    cout<<v<<endl;
    break;
  }
  return 0;
}

#line 1 "test/aoj/0402.test.cpp"
// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0402

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#line 1 "convolution/bitwise/fwht.cpp"

#line 3 "convolution/bitwise/fwht.cpp"
using namespace std;
#endif
// https://kazuma8128.hatenablog.com/entry/2018/05/31/144519
//BEGIN CUT HERE
// O(n \log n)
template<typename T, typename F>
void fwht(vector<T> &as,F f){
  int n=as.size();
  for(int d=1;d<n;d<<=1)
    for(int m=d<<1,i=0;i<n;i+=m)
      for(int j=0;j<d;j++)
        f(as[i+j],as[i+j+d]);
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 1 "convolution/bitwise/xor.cpp"

#line 3 "convolution/bitwise/xor.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
namespace bitwise_xor{
  auto zeta=[](auto& lo,auto& hi){
    auto x=lo+hi,y=lo-hi;
    lo=x;
    hi=y;
  };
  auto moebius=[](auto& lo,auto& hi){
    auto x=lo+hi,y=lo-hi;
    lo=x/decltype(x)(2);
    hi=y/decltype(y)(2);
  };
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 9 "test/aoj/0402.test.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  using ll = long long;

  ll n,k;
  cin>>n>>k;
  vector<int> as(n);
  for(int i=0;i<n;i++) cin>>as[i];

  const int LOG = 20;
  const int sz = 1<<LOG;
  vector<ll> cnt(sz,0);
  cnt[0]++;
  for(int i=0,s=0;i<n;i++){
    s^=as[i];
    cnt[s]++;
  }

  fwht(cnt,bitwise_xor::zeta);
  for(ll &v:cnt) v=v*v;
  fwht(cnt,bitwise_xor::moebius);

  k--;
  for(int v=sz-1;v>=0;v--){
    cnt[v]/=2;
    if(cnt[v]<=k){
      k-=cnt[v];
      continue;
    }
    cout<<v<<endl;
    break;
  }
  return 0;
}

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