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LAZYPROP.H
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LAZYPROP.H
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#ifndef SEGTREE_H
#define SEGTREE_H
#include <vector>
#include <iostream>
#include <string>
#include <cstdint>
template <typename T>
class segtree {
public:
std::vector<T> arr;
std::vector<T> tree;
std::vector<T> addcache;
std::vector<T> setcache;
int64_t n;
int64_t size;
T identity = 0;
T combine(T a, T b) { // This binary operation is what the tree uses for querying. It is unrelated to any existing operations (including overloaded ones).
return a + b;
}
int64_t ceillog(int64_t x) {
int64_t pwr = 1;
int64_t ex = 0;
while (pwr < x) {
pwr = pwr + pwr;
ex++;
}
return ex;
}
void reconcile(int x) {
if (x >= size) {
arr[x - size] = tree[x];
return;
}
tree[x] = combine(tree[x * 2], tree[x * 2 + 1]);
}
segtree(std::vector<T> v) {
n = v.size();
arr = std::vector<T>(n);
for (int64_t i = 0; i < n; i++) arr[i] = v[i];
size = 1<<ceillog(n);
tree = std::vector<T>(2 * size, identity);
addcache = std::vector<T>(2 * size, identity);
setcache = std::vector<T>(2 * size, identity);
for (int64_t i = 0; i < n; i++) tree[size + i] = arr[i];
for (int64_t i = size - 1; i > 0; i--) reconcile(i);
}
T queryutil(int64_t a, int64_t b, int64_t k, int64_t x, int64_t y) {
// std::cout << k << " ";
if (b < x || a > y) return identity; // If [x, y] is completely outside [a, b] then we return 0
if (a <= x && y <= b) return tree[k]; // If [x, y] is completely inside [a, b] we simply use the cached value at the tree index
propagate(k, y - x + 1);
int64_t d = x + (y - x) / 2;
return combine(queryutil(a, b, 2 * k, x, d), queryutil(a, b, 2 * k + 1, d + 1, y)); // Otherwise recur on the child nodes
}
T query(int64_t a, int64_t b) {
return queryutil(a, b, 1, 0, size - 1);
}
T update(int64_t x, T k) {
tree[x + size] = k;
arr[x] = k;
int64_t i = x + size;
while (i > 0) {
i = i / 2;
reconcile(i);
}
return k;
}
void inctree(int64_t x, T v) {
tree[x] += v;
if (x >= size) arr[x - size] += v;
}
void settree(int64_t x, T v) {
tree[x] = v;
if (x >= size) arr[x - size] = v;
}
void propagate(int64_t i, int64_t rangesize) {
if (i >= size) return;
if (setcache[i] != 0) { // Propagate the set. We simply propagate the setted value to the children.
setcache[2 * i] = setcache[i];
setcache[2 * i + 1] = setcache[i]; // propagate to children
settree(2 * i, (rangesize / 2) * setcache[i]);
settree(2 * i + 1, (rangesize / 2) * setcache[i]); // because we're blatantly settingvalues we just do this to the node of the rangesize
addcache[2 * i] = 0;
addcache[2 * i + 1] = 0; // clear the addcaches
setcache[i] = 0; // clear the current node
return;
}
if (addcache[i] != 0) { // Propagate the add
for (int index = 0; index < 2; index++) {
// case 1: if the set cache is zero we simply add
if (setcache[2 * i + index] == 0) addcache[2 * i + index] += addcache[i];
else { // case 2: otherwise we update the set cache and clear the add cache
setcache[2 * i + index] += addcache[i];
addcache[2 * i + index] = 0;
}
}
// update the node values
inctree(2 * i, (rangesize / 2) * addcache[i]);
inctree(2 * i + 1, (rangesize / 2) * addcache[i]);
addcache[i] = 0;
}
}
// [a ... b] is the added range. [x ... y] is the range of the node T[k]
T addrangeutil(int64_t a, int64_t b, int64_t k, int64_t x, int64_t y, T v) {
if (b < x || a > y) return v; // do nothing if [x, y] is completely outside [a, b]
if (a <= x && y <= b) { // If [x, y] is completely inside [a, b] we cache the value so the tree knows that every element in this range needs to be changed
inctree(k, v * (y - x + 1));
// Interaction step: we might also have to change the setcache
if (setcache[k] == 0) addcache[k] += v;
else setcache[k] += v;
return v;
}
// Otherwise [x, y] intersects [a, b] but is not completely inside it.
propagate(k, y - x + 1); // send the values downwards
int64_t d = x + (y - x) / 2;
addrangeutil(a, b, 2 * k, x, d, v);
addrangeutil(a, b, 2 * k + 1, d + 1, y, v);
reconcile(k);
return v;
}
T setrangeutil(int64_t a, int64_t b, int64_t k, int64_t x, int64_t y, T v) {
if (b < x || a > y) return v; // do nothing if [x, y] is completely outside [a, b]
if (a <= x && y <= b) { // If [x, y] is completely inside [a, b] we cache the value so the tree knows that every element in this range needs to be changed
settree(k, v * (y - x + 1));
// Interaction step: we might also have to change the caches
setcache[k] = v;
addcache[k] = 0;
return v;
}
// Otherwise [x, y] intersects [a, b] but is not completely inside it.
propagate(k, y - x + 1); // send the values downwards
int64_t d = x + (y - x) / 2;
setrangeutil(a, b, 2 * k, x, d, v);
setrangeutil(a, b, 2 * k + 1, d + 1, y, v);
reconcile(k);
return v;
}
T addrange(int64_t a, int64_t b, T v) { return addrangeutil(a, b, 1, 0, size - 1, v); }
T setrange(int64_t a, int64_t b, T v) { return setrangeutil(a, b, 1, 0, size - 1, v); }
void flush() { // Clears all caches
while (true) {
int64_t left = size * 2;
int64_t right = -1;
for (auto i : addcache) {
left = std::min(left, i);
right = std::max(right, i);
}
for (auto i : setcache) {
left = std::min(left, i);
right = std::max(right, i);
}
if (right < 0) return;
addrange(left, right, 0);
}
}
std::string toString() {
std::string res = "[";
for (int64_t i = 0; i < tree.size(); i++) {
if (i > 0) res = res + " ";
res = res + std::to_string(tree[i]);
if (i == size - 1) res = res + " |";
}
res = res + "][";
for (int64_t i = 0; i < addcache.size(); i++) {
if (i > 0) res = res + " ";
res = res + std::to_string(addcache[i]);
}
res = res + "][";
for (int64_t i = 0; i < setcache.size(); i++) {
if (i > 0) res = res + " ";
res = res + std::to_string(setcache[i]);
}
res = res + "]";
return res;
}
void disp() {
std::cout << toString() << "\n";
}
};
/*
#include <bits/stdc++.h>
using namespace std;
void csesprob() {
int64_t n, q;
cin >> n >> q;
vector<int64_t> v(n);
for (int64_t i = 0; i < n; i++) cin >> v[i];
segtree<int64_t> tree(v);
tree.identity = (int64_t)(0);
// tree.disp();
int64_t x, a, b, c;
for (int64_t i = 0; i < q; i++) {
cin >> x >> a >> b;
a--;
b--;
// cout << x << " " << a << " " << b << " = ";
if (x == 1) {
cin >> c;
tree.addrange(a, b, c);
}
else if (x == 2) {
cin >> c;
tree.setrange(a, b, c);
}
else cout << tree.query(a, b) << endl;
// tree.disp();
}
return;
}
int main()
{
csesprob();
return 0;
}
*/
#endif