详细介绍：【DFS序 异或树状数组】P12385 [蓝桥杯 2023 省 Python B] 异或和|普及+
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P12385 [蓝桥杯 2023 省 Python B] 异或和
题目描述
给一棵含有 n n n 个结点的有根树，根结点为 1 1 1，编号为 i i i 的点有点权 a i a_i ai ( i ∈ [ 1 , n ] ) (i \in [1, n]) (i∈[1,n])。现在有两种操作，格式如下：
- 1 x y 1\ x\ y 1xy 该操作表示将点 x x x 的点权改为 y y y。
- 2 x 2\ x 2x 该操作表示查询以结点 x x x 为根的子树内的所有点的点权的异或和。
现有长度为 m m m 的操作序列，请对于每个第二类操作给出正确的结果。
输入格式
输入的第一行包含两个正整数 n , m n, m n,m，用一个空格分隔。
第二行包含 n n n 个整数 a 1 , a 2 , … , a n a_1, a_2, \dots, a_n a1,a2,…,an，相邻整数之间使用一个空格分隔。
接下来 n − 1 n-1 n−1 行，每行包含两个正整数 u i , v i u_i, v_i ui,vi，表示结点 u i u_i ui 和 v i v_i vi 之间有一条边。
接下来 m m m 行，每行包含一个操作。
输出格式
输出若干行，每行对应一个查询操作的答案。
输入输出样例 #1
输入 #1
4 4
1 2 3 4
1 2
1 3
2 4
2 1
1 1 0
2 1
2 2输出 #1
4
5
6说明/提示
评测用例规模与约定
- 对于 30 % 30\% 30% 的评测用例， n , m ≤ 1000 n, m \leq 1000 n,m≤1000；
- 对于所有评测用例， 1 ≤ n , m ≤ 100000 1 \leq n, m \leq 100000 1≤n,m≤100000， 0 ≤ a i , y ≤ 100000 0 \leq a_i, y \leq 100000 0≤ai,y≤100000， 1 ≤ u i , v i , x ≤ n 1 \leq u_i, v_i, x \leq n 1≤ui,vi,x≤n。
DFS序 异或树状数组 线段树
操作一：单点修改。 操作二：区间查询
vSort[node] 记录node的DFS序，node子树的DFS序为[vSort[node], vEnd[node])
注意：bit[vSort[i]] = a[i]，不是bit[i]=a[i]
代码
核心代码
#include <iostream>
#include <sstream>
#include <vector>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<string>
#include<algorithm>
#include<functional>
#include<queue>
#include <stack>
#include<iomanip>
#include<numeric>
#include <math.h>
#include <climits>
#include<assert.h>
#include<cstring>
#include<list>
#include<array>
#include <bitset>
using namespace std;
template<
class T1
, class T2
>
std::istream&
operator >>
(std::istream& in, pair<T1, T2>
& pr) {
in >> pr.first >> pr.second;
return in;
}
template<
class T1
, class T2
, class T3
>
std::istream&
operator >>
(std::istream& in, tuple<T1, T2, T3>
& t) {
in >> get<
0>
(t) >> get<
1>
(t) >> get<
2>
(t);
return in;
}
template<
class T1
, class T2
, class T3
, class T4
>
std::istream&
operator >>
(std::istream& in, tuple<T1, T2, T3, T4>
& t) {
in >> get<
0>
(t) >> get<
1>
(t) >> get<
2>
(t) >> get<
3>
(t);
return in;
}
template<
class T1
, class T2
, class T3
, class T4
, class T5
, class T6
, class T7
>
std::istream&
operator >>
(std::istream& in, tuple<T1, T2, T3, T4,T5,T6,T7>
& t) {
in >> get<
0>
(t) >> get<
1>
(t) >> get<
2>
(t) >> get<
3>
(t) >> get<
4>
(t) >> get<
5>
(t) >> get<
6>
(t);
return in;
}
template<
class T
= int>
vector<T>
Read() {
int n;
cin >> n;
vector<T>
ret(n);
for (int i = 0; i < n; i++) {
cin >> ret[i];
}
return ret;
}
template<
class T
= int>
vector<T>
ReadNotNum() {
vector<T> ret;
T tmp;
while (cin >> tmp) {
ret.emplace_back(tmp);
if ('\n' == cin.get()) {
break;
}
}
return ret;
}
template<
class T
= int>
vector<T>
Read(int n) {
vector<T>
ret(n);
for (int i = 0; i < n; i++) {
cin >> ret[i];
}
return ret;
}
template<
int N = 1'000'000>
class COutBuff
{
public:
COutBuff() {
m_p = puffer;
}
template<
class T
>
void write(T x) {
int num[28], sp = 0;
if (x <
0)
*m_p++ = '-', x = -x;
if (!x)
*m_p++ = 48;
while (x)
num[++sp] = x % 10, x /= 10;
while (sp)
*m_p++ = num[sp--] + 48;
AuotToFile();
}
void writestr(const char* sz) {
strcpy(m_p, sz);
m_p += strlen(sz);
AuotToFile();
}
inline void write(char ch)
{
*m_p++ = ch;
AuotToFile();
}
inline void ToFile() {
fwrite(puffer, 1, m_p - puffer, stdout);
m_p = puffer;
}
~COutBuff() {
ToFile();
}
private:
inline void AuotToFile() {
if (m_p - puffer > N - 100) {
ToFile();
}
}
char puffer[N], * m_p;
};
template<
int N = 1'000'000>
class CInBuff
{
public:
inline CInBuff() {
}
inline CInBuff<N>
&
operator>>
(char& ch) {
FileToBuf();
while (('\r' == *S) || ('\n' == *S) || (' ' == *S)) { S++;
}//忽略空格和回车
ch = *S++;
return *this;
}
inline CInBuff<N>
&
operator>>
(int& val) {
FileToBuf();
int x(0), f(0);
while (!isdigit(*S))
f |= (*S++ == '-');
while (isdigit(*S))
x = (x <<
1) + (x <<
3) + (*S++ ^ 48);
val = f ? -x : x; S++;
//忽略空格换行
return *this;
}
inline CInBuff&
operator>>
(long long& val) {
FileToBuf();
long long x(0);
int f(0);
while (!isdigit(*S))
f |= (*S++ == '-');
while (isdigit(*S))
x = (x <<
1) + (x <<
3) + (*S++ ^ 48);
val = f ? -x : x; S++;
//忽略空格换行
return *this;
}
template<
class T1
, class T2
>
inline CInBuff&
operator>>
(pair<T1, T2>
& val) {
*this >> val.first >> val.second;
return *this;
}
template<
class T1
, class T2
, class T3
>
inline CInBuff&
operator>>
(tuple<T1, T2, T3>
& val) {
*this >> get<
0>
(val) >> get<
1>
(val) >> get<
2>
(val);
return *this;
}
template<
class T1
, class T2
, class T3
, class T4
>
inline CInBuff&
operator>>
(tuple<T1, T2, T3, T4>
& val) {
*this >> get<
0>
(val) >> get<
1>
(val) >> get<
2>
(val) >> get<
3>
(val);
return *this;
}
template<
class T
= int>
inline CInBuff&
operator>>
(vector<T>
& val) {
int n;
*this >> n;
val.resize(n);
for (int i = 0; i < n; i++) {
*this >> val[i];
}
return *this;
}
template<
class T
= int>
vector<T>
Read(int n) {
vector<T>
ret(n);
for (int i = 0; i < n; i++) {
*this >> ret[i];
}
return ret;
}
template<
class T
= int>
vector<T>
Read() {
vector<T> ret;
*this >> ret;
return ret;
}
private:
inline void FileToBuf() {
const int canRead = m_iWritePos - (S - buffer);
if (canRead >= 100) {
return;
}
if (m_bFinish) {
return;
}
for (int i = 0; i < canRead; i++)
{
buffer[i] = S[i];
//memcpy出错
}
m_iWritePos = canRead;
buffer[m_iWritePos] = 0;
S = buffer;
int readCnt = fread(buffer + m_iWritePos, 1, N - m_iWritePos, stdin);
if (readCnt <= 0) { m_bFinish = true;
return;
}
m_iWritePos += readCnt;
buffer[m_iWritePos] = 0;
S = buffer;
}
int m_iWritePos = 0;
bool m_bFinish = false;
char buffer[N + 10], * S = buffer;
};
class CNeiBo
{
public:
static vector<vector<
int>>
Two(int n, const vector<pair<
int, int>>
& edges, bool bDirect, int iBase = 0)
{
vector<vector<
int>>
vNeiBo(n);
for (const auto&
[i1, i2] : edges)
{
vNeiBo[i1 - iBase].emplace_back(i2 - iBase);
if (!bDirect)
{
vNeiBo[i2 - iBase].emplace_back(i1 - iBase);
}
}
return vNeiBo;
}
static vector<vector<
int>>
Two(int n, const vector<vector<
int>>
& edges, bool bDirect, int iBase = 0)
{
vector<vector<
int>>
vNeiBo(n);
for (const auto& v : edges)
{
vNeiBo[v[0] - iBase].emplace_back(v[1] - iBase);
if (!bDirect)
{
vNeiBo[v[1] - iBase].emplace_back(v[0] - iBase);
}
}
return vNeiBo;
}
static vector<vector<std::pair<
int, int>>
>
Three(int n, vector<vector<
int>>
& edges, bool bDirect, int iBase = 0)
{
vector<vector<std::pair<
int, int>>
>
vNeiBo(n);
for (const auto& v : edges)
{
vNeiBo[v[0] - iBase].emplace_back(v[1] - iBase, v[2]);
if (!bDirect)
{
vNeiBo[v[1] - iBase].emplace_back(v[0] - iBase, v[2]);
}
}
return vNeiBo;
}
static vector<vector<std::pair<
int, int>>
>
Three(int n, const vector<tuple<
int, int, int>>
& edges, bool bDirect, int iBase = 0)
{
vector<vector<std::pair<
int, int>>
>
vNeiBo(n);
for (const auto&
[u, v, w] : edges)
{
vNeiBo[u - iBase].emplace_back(v - iBase, w);
if (!bDirect)
{
vNeiBo[v - iBase].emplace_back(u - iBase, w);
}
}
return vNeiBo;
}
static vector<vector<
int>>
Mat(vector<vector<
int>>
& neiBoMat)
{
vector<vector<
int>>
neiBo(neiBoMat.size());
for (int i = 0; i < neiBoMat.size(); i++)
{
for (int j = i + 1; j < neiBoMat.size(); j++)
{
if (neiBoMat[i][j])
{
neiBo[i].emplace_back(j);
neiBo[j].emplace_back(i);
}
}
}
return neiBo;
}
};
template<
class ELE
= int >
class ITreeArrSumOpe
{
public:
virtual void Assign(ELE& dest, const ELE& src) = 0;
virtual ELE Back(const ELE& n1, const ELE& n2) = 0;
};
template<
class ELE
= int >
class CTreeArrAddOpe
:public ITreeArrSumOpe<
ELE>
{
public:
virtual void Assign(ELE& dest, const ELE& src) {
dest += src;
}
virtual ELE Back(const ELE& n1, const ELE& n2) {
return n1 - n2;
}
};
template<
class ELE
= int, class ELEOpe
= CTreeArrAddOpe<ELE>
>
class CTreeArr
{
public:
CTreeArr(int iSize) :m_vData(iSize + 1)
{
}
void Add(int index, ELE value)
{
if ((index <
0) || (index >= m_vData.size() - 1)) {
return;
}
index++;
while (index < m_vData.size())
{
m_ope.Assign(m_vData[index], value);
index += index &
(-index);
}
}
ELE Sum(int index)//[0...index]之和
{
index++;
ELE ret = 0;
while (index)
{
m_ope.Assign(ret, m_vData[index]);
index -= index &
(-index);
}
return ret;
}
ELE Sum() {
return Sum(m_vData.size() - 2);
}
ELE Get(int index)
{
return m_ope.Back(Sum(index), Sum(index - 1));
}
private:
ELEOpe m_ope;
vector<ELE> m_vData;
};
template<
class ELE
= int >
class CTreeArrXorOpe
: public ITreeArrSumOpe <
ELE> {
public:
virtual void Assign(ELE& dest, const ELE& src) {
dest ^= src;
}
virtual ELE Back(const ELE& n1, const ELE& n2) {
return n1 ^ n2;
}
};
template<
class ELE
= int >
class CTreeArrXor
: public CTreeArr<
ELE, CTreeArrXorOpe<
ELE>> {
public:
using CTreeArr<ELE, CTreeArrXorOpe<ELE>>
::CTreeArr;
};
class Solution
{
public:
vector<
int>
Ans(const int N, vector<
int>
& a, vector<pair<
int, int>> edge, vector<tuple<
int, int, int>>
& ope) {
auto neiBo = CNeiBo::Two(N, edge, false, 1);
int m_iSort = 0;
vector<
int>
vSort(N), vSortEnd(N);
function<
void(int, int)> DFS = [&
](int cur, int par) {
vSort[cur] = m_iSort++;
for (const auto& next : neiBo[cur]) {
if (next == par) {
continue;
}
DFS(next, cur);
}
vSortEnd[cur] = m_iSort;
};
DFS(0, -1);
CTreeArrXor<
int>
bit(N);
vector<
int>
tmp1(N);
for (int i = 0; i < N; i++) {
bit.Add(vSort[i], a[i]);
tmp1[vSort[i]] = bit.Get(vSort[i]);
}
vector<
int> ans;
for (auto [kind, x, y] : ope) {
x--;
if (1 == kind) {
const int inx = vSort[x];
bit.Add(inx, y ^ bit.Get(inx));
tmp1[inx] = bit.Get(inx);
}
else {
const int cur = bit.Sum(vSortEnd[x] - 1) ^ bit.Sum(vSort[x] - 1);
ans.emplace_back(cur);
}
}
return ans;
}
};
int main() {
#ifdef _DEBUG
freopen("a.in", "r", stdin);
#endif // DEBUG
ios::sync_with_stdio(0); cin.tie(nullptr);
//CInBuff<> in; COutBuff<10'000'000> ob;
int N,Q;
cin >> N >> Q;
auto a = Read<
int>
(N );
auto edge = Read<pair<
int,int>>
(N-1);
vector<tuple<
int, int, int>>
ope(Q);
for (int i = 0; i < Q; i++) {
cin >> get<
0>
(ope[i]) >> get<
1>
(ope[i]);
if (1 == get<
0>
(ope[i])) {
cin >> get<
2>
(ope[i]);
}
}
#ifdef _DEBUG
//printf("N=%d",N);
Out(a, ",a=");
Out(ope, ",ope=");
Out(edge, ",edge=");
/*Out(que, ",que=");*/
//Out(ab, ",ab=");
//Out(par, "par=");
//Out(que, "que=");
//Out(B, "B=");
#endif // DEBUG
auto res = Solution().Ans(N,a,edge,ope);
for (const auto& i : res)
{
cout << i <<
"\n";
}
return 0;
};单元测试
vector<
int> a;
vector<pair<
int, int>> edge;
vector<tuple<
int, int, int>> ope;
TEST_METHOD(TestMethod11)
{
a = {
1,2,3,4
}, ope = {
{
2,1,0
},{
1,1,0
},{
2,1,0
},{
2,2,0
}
}, edge = {
{
1,2
},{
1,3
},{
2,4
}
};
auto res = Solution().Ans(a.size(), a, edge, ope);
AssertEx({
4,5,6
}, res);
}
# 扩展阅读
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视频课程
先学简单的课程，请移步CSDN学院，听白银讲师（也就是鄙人）的讲解。
https://edu.csdn.net/course/detail/38771
如何你想快速形成战斗了，为老板分忧，请学习C#入职培训、C++入职培训等课程
https://edu.csdn.net/lecturer/6176
测试环境
操作系统：win7 开发环境： VS2019 C++17
或者 操作系统：win10 开发环境： VS2022 C++17
如无特殊说明，本算法用**C++**实现。
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