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Range Linear Add Range Min
(DataStructure/rangelinearaddrangemin.hpp)
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- Last update: 2024-04-26 03:18:17+09:00
- Include:
#include "DataStructure/rangelinearaddrangemin.hpp"
Code
#pragma once
struct RangeLinearAddRangeMin {
RangeLinearAddRangeMin() {}
template <typename T> RangeLinearAddRangeMin(vector<T> &a) {
n = 1, height = 0;
while (n < SZ(a))
n <<= 1, height++;
base.resize(n * 2);
lazy.resize(n * 2);
bridges.resize(n * 2);
rep(i, n, n * 2) base[i] = P(i - n, 1000000000000LL);
rep(i, 0, SZ(a)) base[i + n] = P(i, a[i]);
rep(i, 0, n * 2) lazy[i] = Linear{0, 0};
rep(i, n, n * 2) bridges[i] = {base[i], base[i]};
for (int i = n - 1; i >= 1; i--)
find(i);
}
void update(int L, int R, ll a, ll b) {
int lb = L + n, rb = R + n;
while (lb < rb) {
if (lb & 1) {
lazy[lb] = merge(lazy[lb], Linear{a, b});
lb++;
}
lb >>= 1;
if (rb & 1) {
rb--;
lazy[rb] = merge(lazy[rb], Linear{a, b});
}
rb >>= 1;
}
lb = L + n, rb = R + n;
for (int i = 1; i <= height; i++) {
if (((lb >> i) << i) != lb)
find(lb >> i);
if (((rb >> i) << i) != rb)
find((rb - 1) >> i);
}
}
ll query(int L, int R) {
int lb = L + n, rb = R + n;
ll ret = INF;
while (lb < rb) {
if (lb & 1) {
chmin(ret, subtree(lb));
lb++;
}
lb >>= 1;
if (rb & 1) {
rb--;
chmin(ret, subtree(rb));
}
rb >>= 1;
}
return ret;
}
private:
struct P {
ll x, y;
P(ll _x = 0, ll _y = 0) : x(_x), y(_y) {}
P operator+(const P &p) const {
return P(x + p.x, y + p.y);
}
P operator-(const P &p) const {
return P(x - p.x, y - p.y);
}
bool operator<(const P &p) const {
return (y != p.y ? y < p.y : x < p.x);
}
bool operator==(const P &p) const {
return (x == p.x and y == p.y);
}
bool operator!=(const P &p) const {
return (x != p.x or y != p.y);
}
};
i128 cross(const P &a, const P &b) {
return i128(a.x) * b.y - i128(a.y) * b.x;
}
int n, height;
using Linear = pair<ll, ll>;
using B = pair<P, P>;
vector<P> base;
vector<Linear> lazy;
vector<B> bridges;
void find(int i) {
if (i >= n)
return;
Linear offset = {0, 0};
for (int x = i; x; x >>= 1)
offset = merge(offset, lazy[x]);
int lb = i * 2, rb = i * 2 + 1;
int border = rb;
while (border < n)
border <<= 1;
border -= n;
Linear Ladd = lazy[lb], Radd = lazy[rb];
for (;;) {
// cerr<<i<<' '<<lb<<' '<<rb<<'\n';
if (lb >= n and rb >= n)
break;
P a = bridges[lb].first, b = bridges[lb].second;
P c = bridges[rb].first, d = bridges[rb].second;
a = apply(a, offset);
b = apply(b, offset);
c = apply(c, offset);
d = apply(d, offset);
a = apply(a, Ladd);
b = apply(b, Ladd);
c = apply(c, Radd);
d = apply(d, Radd);
if (a != b and cross(b - a, c - a) < 0) {
lb = lb * 2;
Ladd = merge(Ladd, lazy[lb]);
} else if (c != d and cross(c - b, d - b) < 0) {
rb = rb * 2 + 1;
Radd = merge(Radd, lazy[rb]);
} else if (a == b) {
rb = rb * 2;
Radd = merge(Radd, lazy[rb]);
} else if (c == d) {
lb = lb * 2 + 1;
Ladd = merge(Ladd, lazy[lb]);
} else {
i128 c1 = cross(b - a, d - c);
i128 c2 = cross(b - a, b - c);
bool side;
if (c1 == 0 and c2 == 0)
side = (c.x < border);
else
side = (c.x * c1 + (d.x - c.x) * c2 < c1 * border);
if (side) {
lb = lb * 2 + 1;
Ladd = merge(Ladd, lazy[lb]);
} else {
rb = rb * 2;
Radd = merge(Radd, lazy[rb]);
}
}
}
bridges[i] = {apply(base[lb], Ladd), apply(base[rb], Radd)};
}
ll subtree(int i) {
Linear add = {0, 0};
for (int x = i; x; x >>= 1)
add = merge(add, lazy[x]);
while (i < n) {
if (apply(bridges[i].first, add).y <
apply(bridges[i].second, add).y)
i = i * 2;
else
i = i * 2 + 1;
add = merge(add, lazy[i]);
}
P ret = apply(base[i], add);
return ret.y;
}
Linear merge(Linear a, Linear b) {
a.first += b.first;
a.second += b.second;
return a;
}
P apply(P a, Linear b) {
a.y += a.x * b.first + b.second;
return a;
}
};
/**
* @brief Range Linear Add Range Min
*/#line 2 "DataStructure/rangelinearaddrangemin.hpp"
struct RangeLinearAddRangeMin {
RangeLinearAddRangeMin() {}
template <typename T> RangeLinearAddRangeMin(vector<T> &a) {
n = 1, height = 0;
while (n < SZ(a))
n <<= 1, height++;
base.resize(n * 2);
lazy.resize(n * 2);
bridges.resize(n * 2);
rep(i, n, n * 2) base[i] = P(i - n, 1000000000000LL);
rep(i, 0, SZ(a)) base[i + n] = P(i, a[i]);
rep(i, 0, n * 2) lazy[i] = Linear{0, 0};
rep(i, n, n * 2) bridges[i] = {base[i], base[i]};
for (int i = n - 1; i >= 1; i--)
find(i);
}
void update(int L, int R, ll a, ll b) {
int lb = L + n, rb = R + n;
while (lb < rb) {
if (lb & 1) {
lazy[lb] = merge(lazy[lb], Linear{a, b});
lb++;
}
lb >>= 1;
if (rb & 1) {
rb--;
lazy[rb] = merge(lazy[rb], Linear{a, b});
}
rb >>= 1;
}
lb = L + n, rb = R + n;
for (int i = 1; i <= height; i++) {
if (((lb >> i) << i) != lb)
find(lb >> i);
if (((rb >> i) << i) != rb)
find((rb - 1) >> i);
}
}
ll query(int L, int R) {
int lb = L + n, rb = R + n;
ll ret = INF;
while (lb < rb) {
if (lb & 1) {
chmin(ret, subtree(lb));
lb++;
}
lb >>= 1;
if (rb & 1) {
rb--;
chmin(ret, subtree(rb));
}
rb >>= 1;
}
return ret;
}
private:
struct P {
ll x, y;
P(ll _x = 0, ll _y = 0) : x(_x), y(_y) {}
P operator+(const P &p) const {
return P(x + p.x, y + p.y);
}
P operator-(const P &p) const {
return P(x - p.x, y - p.y);
}
bool operator<(const P &p) const {
return (y != p.y ? y < p.y : x < p.x);
}
bool operator==(const P &p) const {
return (x == p.x and y == p.y);
}
bool operator!=(const P &p) const {
return (x != p.x or y != p.y);
}
};
i128 cross(const P &a, const P &b) {
return i128(a.x) * b.y - i128(a.y) * b.x;
}
int n, height;
using Linear = pair<ll, ll>;
using B = pair<P, P>;
vector<P> base;
vector<Linear> lazy;
vector<B> bridges;
void find(int i) {
if (i >= n)
return;
Linear offset = {0, 0};
for (int x = i; x; x >>= 1)
offset = merge(offset, lazy[x]);
int lb = i * 2, rb = i * 2 + 1;
int border = rb;
while (border < n)
border <<= 1;
border -= n;
Linear Ladd = lazy[lb], Radd = lazy[rb];
for (;;) {
// cerr<<i<<' '<<lb<<' '<<rb<<'\n';
if (lb >= n and rb >= n)
break;
P a = bridges[lb].first, b = bridges[lb].second;
P c = bridges[rb].first, d = bridges[rb].second;
a = apply(a, offset);
b = apply(b, offset);
c = apply(c, offset);
d = apply(d, offset);
a = apply(a, Ladd);
b = apply(b, Ladd);
c = apply(c, Radd);
d = apply(d, Radd);
if (a != b and cross(b - a, c - a) < 0) {
lb = lb * 2;
Ladd = merge(Ladd, lazy[lb]);
} else if (c != d and cross(c - b, d - b) < 0) {
rb = rb * 2 + 1;
Radd = merge(Radd, lazy[rb]);
} else if (a == b) {
rb = rb * 2;
Radd = merge(Radd, lazy[rb]);
} else if (c == d) {
lb = lb * 2 + 1;
Ladd = merge(Ladd, lazy[lb]);
} else {
i128 c1 = cross(b - a, d - c);
i128 c2 = cross(b - a, b - c);
bool side;
if (c1 == 0 and c2 == 0)
side = (c.x < border);
else
side = (c.x * c1 + (d.x - c.x) * c2 < c1 * border);
if (side) {
lb = lb * 2 + 1;
Ladd = merge(Ladd, lazy[lb]);
} else {
rb = rb * 2;
Radd = merge(Radd, lazy[rb]);
}
}
}
bridges[i] = {apply(base[lb], Ladd), apply(base[rb], Radd)};
}
ll subtree(int i) {
Linear add = {0, 0};
for (int x = i; x; x >>= 1)
add = merge(add, lazy[x]);
while (i < n) {
if (apply(bridges[i].first, add).y <
apply(bridges[i].second, add).y)
i = i * 2;
else
i = i * 2 + 1;
add = merge(add, lazy[i]);
}
P ret = apply(base[i], add);
return ret.y;
}
Linear merge(Linear a, Linear b) {
a.first += b.first;
a.second += b.second;
return a;
}
P apply(P a, Linear b) {
a.y += a.x * b.first + b.second;
return a;
}
};
/**
* @brief Range Linear Add Range Min
*/