牛客子数组最大异或和

系统管理员 2023-06-04 14:56 10阅读 0赞

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][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： ###

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1 #include <bits/stdc++.h>
      2 using namespace std;
      3  
      4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
      5 #define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
      6 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
      7 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
      8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
      9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
     10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
     11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
     12  
     13 #define pr(x) cout << #x << " = " << x << "  "
     14 #define prln(x) cout << #x << " = " << x << endl
     15  
     16 #define LOWBIT(x) ((x)&(-x))
     17  
     18 #define ALL(x) x.begin(),x.end()
     19 #define INS(x) inserter(x,x.begin())
     20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
     21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
     22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
     23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
     24  
     25 #define ms0(a) memset(a,0,sizeof(a))
     26 #define msI(a) memset(a,0x3f,sizeof(a))
     27 #define msM(a) memset(a,-1,sizeof(a))
     28 
     29 #define MP make_pair
     30 #define PB push_back
     31 #define ft first
     32 #define sd second
     33  
     34 template<typename T1, typename T2>
     35 istream &operator>>(istream &in, pair<T1, T2> &p) {
     36     in >> p.first >> p.second;
     37     return in;
     38 }
     39  
     40 template<typename T>
     41 istream &operator>>(istream &in, vector<T> &v) {
     42     for (auto &x: v)
     43         in >> x;
     44     return in;
     45 }
     46 
     47 template<typename T>
     48 ostream &operator<<(ostream &out, vector<T> &v) {
     49     Rep(i, v.size()) out << v[i] << " \n"[i == v.size() - 1];
     50     return out;
     51 }
     52  
     53 template<typename T1, typename T2>
     54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     55     out << "[" << p.first << ", " << p.second << "]" << "\n";
     56     return out;
     57 }
     58 
     59 inline int gc(){
     60     static const int BUF = 1e7;
     61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
     62     
     63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
     64     return *bg++;
     65 } 
     66 
     67 inline int ri(){
     68     int x = 0, f = 1, c = gc();
     69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
     70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
     71     return x*f;
     72 }
     73 
     74 template<class T>
     75 inline string toString(T x) {
     76     ostringstream sout;
     77     sout << x;
     78     return sout.str();
     79 }
     80 
     81 inline int toInt(string s) {
     82     int v;
     83     istringstream sin(s);
     84     sin >> v;
     85     return v;
     86 }
     87 
     88 //min <= aim <= max
     89 template<typename T>
     90 inline bool BETWEEN(const T aim, const T min, const T max) {
     91     return min <= aim && aim <= max;
     92 }
     93 
     94 typedef unsigned int uI;
     95 typedef long long LL;
     96 typedef unsigned long long uLL;
     97 typedef vector< int > VI;
     98 typedef vector< bool > VB;
     99 typedef vector< char > VC;
    100 typedef vector< double > VD;
    101 typedef vector< string > VS;
    102 typedef vector< LL > VL;
    103 typedef vector< VI > VVI;
    104 typedef vector< VB > VVB;
    105 typedef vector< VS > VVS;
    106 typedef vector< VL > VVL;
    107 typedef vector< VVI > VVVI;
    108 typedef vector< VVL > VVVL;
    109 typedef pair< int, int > PII;
    110 typedef pair< LL, LL > PLL;
    111 typedef pair< int, string > PIS;
    112 typedef pair< string, int > PSI;
    113 typedef pair< string, string > PSS;
    114 typedef pair< double, double > PDD;
    115 typedef vector< PII > VPII;
    116 typedef vector< PLL > VPLL;
    117 typedef vector< VPII > VVPII;
    118 typedef vector< VPLL > VVPLL;
    119 typedef vector< VS > VVS;
    120 typedef map< int, int > MII;
    121 typedef unordered_map< int, int > uMII;
    122 typedef map< LL, LL > MLL;
    123 typedef map< string, int > MSI;
    124 typedef map< int, string > MIS;
    125 typedef multiset< int > mSI;
    126 typedef multiset< char > mSC;
    127 typedef set< int > SI;
    128 typedef stack< int > SKI;
    129 typedef stack< char > SKC;
    130 typedef deque< int > DQI;
    131 typedef queue< int > QI;
    132 typedef priority_queue< int > PQIMax;
    133 typedef priority_queue< int, VI, greater< int > > PQIMin;
    134 const double EPS = 1e-8;
    135 const LL inf = 0x7fffffff;
    136 const LL infLL = 0x7fffffffffffffffLL;
    137 const LL mod = 1e9 + 7;
    138 const int maxN = 1e5 + 7;
    139 const LL ONE = 1;
    140 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
    141 const LL oddBits = 0x5555555555555555;
    142 
    143 class Trie {
    144 public:
    145     Trie* nxt[2];
    146     
    147     Trie() {
    148         nxt[0] = nxt[1] = NULL;
    149     }
    150     
    151     void insert(string word) {
    152         Trie* p = this;
    153         Rep(i, word.size()) {
    154             int key = word[i] - '0';
    155             
    156             if(p->nxt[key] == NULL) {
    157                 p->nxt[key] = new Trie();
    158             }
    159             p = p->nxt[key];
    160         }
    161     }
    162     
    163     int solve(string word) {
    164         int ret = 0;
    165         LL mask = (ONE << 31);
    166         
    167         Trie* p = this;
    168         int key = word[0] - '0';
    169         if(p->nxt[key] == NULL) { // 符号位要单独讨论 
    170             ret |= mask;
    171             key = !key;
    172         }
    173         mask >>= 1;
    174         p = p->nxt[key];
    175         
    176         For(i, 1, word.size() - 1) {
    177             key = word[i] - '0';
    178             
    179             if(p->nxt[!key] != NULL) {
    180                 ret |= mask;
    181                 key = !key;
    182             }
    183             mask >>= 1;
    184             p = p->nxt[key];
    185         }
    186         return ret;
    187     }
    188 };
    189 
    190 int N, ans, arr[maxN];
    191 
    192 void findMaximumXOR() {
    193     Trie trie = Trie();
    194     vector< string > bits;
    195     
    196     Rep(i, N + 1) {
    197         bits.push_back(bitset< 32 >(arr[i]).to_string());
    198         trie.insert(bits.back());
    199         ans = max(ans, trie.solve(bits[i]));
    200     }
    201 }
    202 
    203 int main() {
    204     //freopen("MyOutput.txt","w",stdout);
    205     //freopen("input.txt","r",stdin);
    206     //INIT();
    207     scanf("%d", &N);
    208     ans = -inf;
    209     For(i, 1, N) {
    210         scanf("%d", &arr[i]);
    211         arr[i] ^= arr[i - 1]; // 计算前缀异或和 
    212     }
    213     
    214     if(N == 1) ans = arr[1];
    215     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 
    216     
    217     printf("%d", ans);
    218     return 0;
    219 }
    220 
    221 /*
    222 4
    223 -2 -3 -5 -1
    224 7
    225 1
    226 -5
    227 -5
    228 */

转载于:https://www.cnblogs.com/zaq19970105/p/11459669.html

[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]: 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
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