牛客 子数组最大异或和

题目链接：https://www.nowcoder.com/practice/43f62c52fbac47feaeabe40ac1ab9091?tpId=101&tqId=33209&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking

题目大意：

　　略。

分析：

　　求出前缀异或和后这道题就是"LeetCode 数组中两个数的最大异或值"的升级版,由于有正有负,所以第一位符号位要单独讨论.

　　PS:当只有一个数的时候也要单独讨论

代码如下：

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
#define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
#define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
#define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
#define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
#define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
#define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,0x3f,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}

template<typename T>
ostream &operator<<(ostream &out, vector<T> &v) {
    Rep(i, v.size()) out << v[i] << " \n"[i == v.size() - 1];
    return out;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "\n";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}

template<class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}

inline int toInt(string s) {
    int v;
    istringstream sin(s);
    sin >> v;
    return v;
}

//min <= aim <= max
template<typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
    return min <= aim && aim <= max;
}

typedef unsigned int uI;
typedef long long LL;
typedef unsigned long long uLL;
typedef vector< int > VI;
typedef vector< bool > VB;
typedef vector< char > VC;
typedef vector< double > VD;
typedef vector< string > VS;
typedef vector< LL > VL;
typedef vector< VI > VVI;
typedef vector< VB > VVB;
typedef vector< VS > VVS;
typedef vector< VL > VVL;
typedef vector< VVI > VVVI;
typedef vector< VVL > VVVL;
typedef pair< int, int > PII;
typedef pair< LL, LL > PLL;
typedef pair< int, string > PIS;
typedef pair< string, int > PSI;
typedef pair< string, string > PSS;
typedef pair< double, double > PDD;
typedef vector< PII > VPII;
typedef vector< PLL > VPLL;
typedef vector< VPII > VVPII;
typedef vector< VPLL > VVPLL;
typedef vector< VS > VVS;
typedef map< int, int > MII;
typedef unordered_map< int, int > uMII;
typedef map< LL, LL > MLL;
typedef map< string, int > MSI;
typedef map< int, string > MIS;
typedef multiset< int > mSI;
typedef multiset< char > mSC;
typedef set< int > SI;
typedef stack< int > SKI;
typedef stack< char > SKC;
typedef deque< int > DQI;
typedef queue< int > QI;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-8;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e5 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

class Trie {
public:
    Trie* nxt[2];
    
    Trie() {
        nxt[0] = nxt[1] = NULL;
    }
    
    void insert(string word) {
        Trie* p = this;
        Rep(i, word.size()) {
            int key = word[i] - '0';
            
            if(p->nxt[key] == NULL) {
                p->nxt[key] = new Trie();
            }
            p = p->nxt[key];
        }
    }
    
    int solve(string word) {
        int ret = 0;
        LL mask = (ONE << 31);
        
        Trie* p = this;
        int key = word[0] - '0';
        if(p->nxt[key] == NULL) { // 符号位要单独讨论 
            ret |= mask;
            key = !key;
        }
        mask >>= 1;
        p = p->nxt[key];
        
        For(i, 1, word.size() - 1) {
            key = word[i] - '0';
            
            if(p->nxt[!key] != NULL) {
                ret |= mask;
                key = !key;
            }
            mask >>= 1;
            p = p->nxt[key];
        }
        return ret;
    }
};

int N, ans, arr[maxN];

void findMaximumXOR() {
    Trie trie = Trie();
    vector< string > bits;
    
    Rep(i, N + 1) {
        bits.push_back(bitset< 32 >(arr[i]).to_string());
        trie.insert(bits.back());
        ans = max(ans, trie.solve(bits[i]));
    }
}

int main() {
    //freopen("MyOutput.txt","w",stdout);
    //freopen("input.txt","r",stdin);
    //INIT();
    scanf("%d", &N);
    ans = -inf;
    For(i, 1, N) {
        scanf("%d", &arr[i]);
        arr[i] ^= arr[i - 1]; // 计算前缀异或和 
    }
    
    if(N == 1) ans = arr[1];
    else findMaximumXOR(); // 问题转化为从一个数组中选两个数,使得这两个数的异或和最大 
    
    printf("%d", ans);
    return 0;
}

/*
4
-2 -3 -5 -1
7
1
-5
-5
*/