The Title requires two subsections in a sequence to maximize the XOR sum of each subsection.
Speaking of XOR, I think of blooming TrieTrieTrie dictionary tree.
First consider how to find the XOR sum of a lll to rrr subsegment ((XOR sum: all XOR values)):
al⊕al+1⊕...⊕ar−1⊕ar=(a1⊕a2⊕...⊕ar−1⊕ar)⊕(a1⊕a2⊕...⊕al−2⊕al−1)a_l\oplus a_{l+1}\oplus...\oplus a_{r-1} \oplus a_{r}=(a_1\oplus a_2\oplus...\oplus a_{r-1} \oplus a_{r})\oplus(a_1\oplus a_2\oplus...\oplus a_{l-2} \oplus a_{l-1})al⊕al+1⊕...⊕ar−1⊕ar=(a1⊕a2⊕...⊕ar−1⊕ar)⊕(a1⊕a2⊕...⊕al−2⊕al−1)
So we can deal with XOR prefix sum and add 01Trie01Trie01Trie tree to solve it.
Considering the requirement of two subsegments, ls[i],rs[i]ls[i],rs[i]ls[i],rs[i] respectively represent the largest XOR subsegment of 1_i1-i1_i and the largest XOR subsegment of i_n I-N i_n. Finally, sweep through maxmaxmax.
The code is not long:
#include<bits/stdc++.h> #define ts cout<<"ok"<<endl #define lowbit(x) (x)&(-x) #define oo (1e18) #define ll long long #define LL unsigned long long using namespace std; int n,a[400005],s[400005],ls[400005],rs[400005],ch[12500000][2],cnt; inline int read(){ int ret=0,ff=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-') ff=-1;ch=getchar();} while(isdigit(ch)){ret=(ret<<3)+(ret<<1)+(ch^48);ch=getchar();} return ret*ff; } inline void insert(int x){ int now=0; for(int i=30;i>=0;i--){ int t=(x&(1<<i))?1:0; if(!ch[now][t]) ch[now][t]=++cnt; now=ch[now][t]; } } inline int find(int x){ int now=0,res=0; for(int i=30;i>=0;i--){ int t=(x&(1<<i))?0:1; if(ch[now][t]){ now=ch[now][t]; res+=(1<<i); } else now=ch[now][!t]; } return res; } signed main(){ n=read(); for(int i=1;i<=n;i++) a[i]=read(); ls[1]=a[1]; insert(a[1]); for(int i=2;i<=n;i++){ ls[i]=max(ls[i-1],find(a[i])); insert(a[i]); } memset(ch,0,sizeof(ch)); cnt=0; rs[n]=a[n]; insert(a[n]); for(int i=n-1;i>=2;i--){ rs[i]=max(rs[i+1],find(a[i])); insert(a[i]); } int ans=0; for(int i=1;i<=n-1;i++) ans=max(ans,ls[i]+rs[i+1]); printf("%d",ans); return 0; }