compro-library
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test/binary-search-tree/RandomizedBinarySearchTreeSet-med.test.cpp
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- Last update: 2023-06-03 15:52:40+09:00
- Problem: https://yukicoder.me/problems/no/919
Depends on
- RandomizedBinarySearchTree - ランダム平衡二分探索木set
(lib/12-binary-search-tree/RandomizedBinarySearchTreeSet.cpp)
- MonoidRangeSumPointAdd - [区間和, 一点加算]
(lib/99-operator/monoid/MonoidRangeSumPointAdd.cpp)
Code
#define PROBLEM "https://yukicoder.me/problems/no/919"
#include <vector>
#include <iostream>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
using namespace std;
#include "../../lib/12-binary-search-tree/RandomizedBinarySearchTreeSet.cpp"
#include "../../lib/99-operator/monoid/MonoidRangeSumPointAdd.cpp"
template<class T> class Mo{
unordered_map<long long,int> mp;
long long N;
int bucket;
vector<pair<int,int>> range;
vector<int> idx;
public:
Mo(int N, const vector<pair<int,int>>& range) : N(N),range(range),idx(range.size()),bucket(sqrt(N)) {
iota(idx.begin(),idx.end(),0);
sort(idx.begin(),idx.end(),[&](int a, int b){
auto al = range[a].first/bucket;
auto ar = range[a].second;
auto bl = range[b].first/bucket;
auto br = range[b].second;
return (al != bl) ? (al < bl) : ((al%2)?(ar > br):(ar < br));
});
}
//参照でvectorを渡したりすると良い
void solve(const vector<int>& A, RandomizedBinarySearchTreeSet<MonoidRangeSumPointAdd<long long>>& med){
int l = 0, r = 0;
for(int& i:idx){
auto& xl = range[i].first;
auto& xr = range[i].second;
//左端を広げる
while(xl < l){
l--;
med.insert(A[l]);
}
//右端を広げる
while(r < xr){
r++;
med.insert(A[r]);
}
//左端を狭める
while(l < xl){
med.erase(A[l]);
l++;
}
//右端を狭める
while(xr < r){
med.erase(A[r]);
r--;
}
mp[xl*N+xr] = med.get((xr-xl)/2);
}
}
T& operator [] (pair<int,int> p) {
return mp[p.first*N+p.second];
}
};
template <class T> void chmax(T& a, const T b){a=max(a,b);}
int main() {
cin.tie(0);ios::sync_with_stdio(false);
int N; cin >> N;
vector<int> A(N);
for(int i = 0; i < N; ++i) cin >> A[i];
//クエリ区間を列挙、調和級数なのでO(N*logN)
vector<pair<int,int>> range;
for(int n = 1; n <= N; ++n) {
int M = N/n;
for(int i = 0; i+n <= N; i+=n) range.push_back({i,i+n-1});
for(int i = N-M*n; i+n <= N; i+=n) range.push_back({i,i+n-1});
}
//Moで中央値列挙 O(N*sqrt(N)*(logN)^2)
Mo<int> mo(N,range);
RandomizedBinarySearchTreeSet<MonoidRangeSumPointAdd<long long>> med;
med.insert(A[0]);
mo.solve(A,med);
long long ans = 0;
int cnt = 0;
//区間長決め打ち全探索O(N*logN)
for(long long n = 1; n <= N; ++n) {
int M = N/n;
vector<long long> lSum(M,0),rSum(M,0);
vector<pair<int, int>> lRange(M),rRange(M);
//区間取得 O(M)
for(int i = 0; i < M; ++i) {
lRange[i] = range[cnt + i];
lSum[i] = n*mo[lRange[i]];
rRange[i] = range[cnt + i + M];
rSum[i] = n*mo[rRange[i]];
}
//累積和 O(M)
for(int i = 1; i < M; ++i) lSum[i] += lSum[i-1];
for(int i = M-2; 0 <= i; --i) rSum[i] += rSum[i+1];
//累積max O(M)
for(int i = 1; i < M; ++i) chmax(lSum[i],lSum[i-1]);
for(int i = M-2; 0 <= i; --i) chmax(rSum[i],rSum[i+1]);
chmax(ans,lSum[M-1]);
chmax(ans,rSum[0]);
//尺取りしながら左右決め打ち全探索 O(M)
int j = 0;
for(int i = 0; i < M; ++i) {
while(j < M && lRange[i].second >= rRange[j].first) j++;
if(j<M && lRange[i].second < rRange[j].first) {
chmax(ans,lSum[i]+rSum[j]);
}
}
cnt += 2*M;
}
cout << ans << endl;
return 0;
}#line 1 "test/binary-search-tree/RandomizedBinarySearchTreeSet-med.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/919"
#include <vector>
#include <iostream>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
using namespace std;
#line 1 "lib/12-binary-search-tree/RandomizedBinarySearchTreeSet.cpp"
/*
* @title RandomizedBinarySearchTree - ランダム平衡二分探索木set
* @docs md/binary-search-tree/RandomizedBinarySearchTree.md
*/
template<class Monoid> class RandomizedBinarySearchTreeSet {
using TypeNode = typename Monoid::TypeNode;
unsigned int x = 123456789, y = 362436069, z = 521288629, w = 88675123;
unsigned int xor_shift() {
unsigned int t = (x ^ (x << 11)); x = y; y = z; z = w;
return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}
struct Node {
private:
void build() {left = right = nullptr;size = 1;}
public:
Node *left, *right;
TypeNode value, range_value;
int size;
Node() : value(Monoid::unit_node), range_value(Monoid::unit_node) {build();}
Node(TypeNode v) : value(v), range_value(v) {build();}
friend ostream &operator<<(ostream &os, const Node* node) {return os << "{" << node->value << ", " << node->range_value << ", " << node->size << "}";}
};
Node* root;
inline int size(Node *node) {return node==nullptr ? 0 : node->size;}
inline TypeNode range_value(Node *node) {return node==nullptr ? Monoid::unit_node : node->range_value;}
inline TypeNode get(Node *node, size_t k) {
if (node==nullptr) return Monoid::unit_node;
if (k == size(node->left)) return node->value;
if (k < size(node->left)) return get(node->left, k);
else return get(node->right, k-1 - size(node->left));
}
inline Node* update(Node *node) {
node->size = size(node->left) + size(node->right) + 1;
node->range_value = Monoid::func_fold(Monoid::func_fold(range_value(node->left),node->value),range_value(node->right));
return node;
}
inline Node* merge_impl(Node *left, Node *right) {
if (left==nullptr) return right;
if (right==nullptr) return left;
if (xor_shift() % (left->size + right->size) < left->size) {
left->right = merge_impl(left->right, right);
return update(left);
}
else {
right->left = merge_impl(left, right->left);
return update(right);
}
}
inline pair<Node*, Node*> split_impl(Node* node, int k) {
if (node==nullptr) return make_pair(nullptr, nullptr);
if (k <= size(node->left)) {
pair<Node*, Node*> sub = split_impl(node->left, k);
node->left = sub.second;
return make_pair(sub.first, update(node));
}
else {
pair<Node*, Node*> sub = split_impl(node->right, k - 1 - size(node->left));
node->right = sub.first;
return make_pair(update(node), sub.second);
}
}
inline TypeNode fold_impl(Node *node, int l, int r) {
if (l < 0 || size(node) <= l || r<=0 || r-l <= 0) return Monoid::unit_node;
if (l == 0 && r == size(node)) return range_value(node);
TypeNode value = Monoid::unit_node;
int sl = size(node->left);
if(sl > l) value = Monoid::func_fold(value,fold_impl(node->left,l,min(sl,r)));
l = max(l-sl,0), r -= sl;
if(l == 0 && r > 0) value = Monoid::func_fold(value,node->value);
l = max(l-1,0), r -= 1;
if(l >= 0 && r > l) value = Monoid::func_fold(value,fold_impl(node->right,l,r));
return value;
}
inline int lower_bound(Node *node, TypeNode value) {
if (node==nullptr) return 0;
if (value <= node->value) return lower_bound(node->left, value);
else return size(node->left) + lower_bound(node->right, value) + 1;
}
inline int upper_bound(Node *node, TypeNode value) {
if (node==nullptr) return 0;
if (value < node->value) return upper_bound(node->left, value);
else return size(node->left) + upper_bound(node->right, value) + 1;
}
inline void insert_impl(const TypeNode value) {
pair<Node*, Node*> sub = split_impl(this->root, lower_bound(this->root,value));
this->root = this->merge_impl(this->merge_impl(sub.first, new Node(value)), sub.second);
}
inline void erase_impl(const TypeNode value) {
int k1 = lower_bound(value), k2 = upper_bound(value);
if(k1==k2) return;
auto sub = split_impl(this->root,k1);
this->root = merge_impl(sub.first, split_impl(sub.second, 1).second);
}
public:
RandomizedBinarySearchTreeSet() : root(nullptr) {}
inline int size() {return size(this->root);}
inline int empty(void) {return bool(size()==0);}
inline Node* merge(Node *left, Node *right) {return merge_impl(left,right);}
inline pair<Node*, Node*> split(int k) {return split_impl(this->root,k);}
inline void insert(const TypeNode value) {insert_impl(value);}
inline void erase(const TypeNode value) {erase_impl(value);}
inline TypeNode get(size_t k) {return get(this->root, k);}
inline TypeNode fold(int l, int r) {return fold_impl(this->root,l,r);}
inline int lower_bound(TypeNode value) {return lower_bound(this->root,value);}
inline int upper_bound(TypeNode value) {return upper_bound(this->root,value);}
inline int count(TypeNode value) {return upper_bound(value) - lower_bound(value);}
void print() {int m = size(this->root); for(int i=0;i<m;++i) cout << get(i) << " \n"[i==m-1];}
};
#line 1 "lib/99-operator/monoid/MonoidRangeSumPointAdd.cpp"
/*
* @title MonoidRangeSumPointAdd - [区間和, 一点加算]
* @docs md/operator/monoid/MonoidRangeSumPointAdd.md
*/
template<class T> struct MonoidRangeSumPointAdd {
using TypeNode = T;
inline static constexpr TypeNode unit_node = 0;
inline static constexpr TypeNode func_fold(TypeNode l,TypeNode r){return l+r;}
inline static constexpr TypeNode func_operate(TypeNode l,TypeNode r){return l+r;}
inline static constexpr bool func_check(TypeNode nodeVal,TypeNode var){return var == nodeVal;}
};
#line 12 "test/binary-search-tree/RandomizedBinarySearchTreeSet-med.test.cpp"
template<class T> class Mo{
unordered_map<long long,int> mp;
long long N;
int bucket;
vector<pair<int,int>> range;
vector<int> idx;
public:
Mo(int N, const vector<pair<int,int>>& range) : N(N),range(range),idx(range.size()),bucket(sqrt(N)) {
iota(idx.begin(),idx.end(),0);
sort(idx.begin(),idx.end(),[&](int a, int b){
auto al = range[a].first/bucket;
auto ar = range[a].second;
auto bl = range[b].first/bucket;
auto br = range[b].second;
return (al != bl) ? (al < bl) : ((al%2)?(ar > br):(ar < br));
});
}
//参照でvectorを渡したりすると良い
void solve(const vector<int>& A, RandomizedBinarySearchTreeSet<MonoidRangeSumPointAdd<long long>>& med){
int l = 0, r = 0;
for(int& i:idx){
auto& xl = range[i].first;
auto& xr = range[i].second;
//左端を広げる
while(xl < l){
l--;
med.insert(A[l]);
}
//右端を広げる
while(r < xr){
r++;
med.insert(A[r]);
}
//左端を狭める
while(l < xl){
med.erase(A[l]);
l++;
}
//右端を狭める
while(xr < r){
med.erase(A[r]);
r--;
}
mp[xl*N+xr] = med.get((xr-xl)/2);
}
}
T& operator [] (pair<int,int> p) {
return mp[p.first*N+p.second];
}
};
template <class T> void chmax(T& a, const T b){a=max(a,b);}
int main() {
cin.tie(0);ios::sync_with_stdio(false);
int N; cin >> N;
vector<int> A(N);
for(int i = 0; i < N; ++i) cin >> A[i];
//クエリ区間を列挙、調和級数なのでO(N*logN)
vector<pair<int,int>> range;
for(int n = 1; n <= N; ++n) {
int M = N/n;
for(int i = 0; i+n <= N; i+=n) range.push_back({i,i+n-1});
for(int i = N-M*n; i+n <= N; i+=n) range.push_back({i,i+n-1});
}
//Moで中央値列挙 O(N*sqrt(N)*(logN)^2)
Mo<int> mo(N,range);
RandomizedBinarySearchTreeSet<MonoidRangeSumPointAdd<long long>> med;
med.insert(A[0]);
mo.solve(A,med);
long long ans = 0;
int cnt = 0;
//区間長決め打ち全探索O(N*logN)
for(long long n = 1; n <= N; ++n) {
int M = N/n;
vector<long long> lSum(M,0),rSum(M,0);
vector<pair<int, int>> lRange(M),rRange(M);
//区間取得 O(M)
for(int i = 0; i < M; ++i) {
lRange[i] = range[cnt + i];
lSum[i] = n*mo[lRange[i]];
rRange[i] = range[cnt + i + M];
rSum[i] = n*mo[rRange[i]];
}
//累積和 O(M)
for(int i = 1; i < M; ++i) lSum[i] += lSum[i-1];
for(int i = M-2; 0 <= i; --i) rSum[i] += rSum[i+1];
//累積max O(M)
for(int i = 1; i < M; ++i) chmax(lSum[i],lSum[i-1]);
for(int i = M-2; 0 <= i; --i) chmax(rSum[i],rSum[i+1]);
chmax(ans,lSum[M-1]);
chmax(ans,rSum[0]);
//尺取りしながら左右決め打ち全探索 O(M)
int j = 0;
for(int i = 0; i < M; ++i) {
while(j < M && lRange[i].second >= rRange[j].first) j++;
if(j<M && lRange[i].second < rRange[j].first) {
chmax(ans,lSum[i]+rSum[j]);
}
}
cnt += 2*M;
}
cout << ans << endl;
return 0;
}