cpplib
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Segment Tree Beats
(datastructure/segmenttree/segmenttreebeats.hpp)
- View this file on GitHub
- Last update: 2020-08-25 17:20:34+09:00
- Include:
#include "datastructure/segmenttree/segmenttreebeats.hpp"
概要
区間chmin, 区間chmaxなどができるデータ構造.
- https://codeforces.com/blog/entry/57319
- https://smijake3.hatenablog.com/entry/2019/04/28/021457
- https://gist.github.com/tjkendev/20e7f96b9262f7a5d739bdc978c075bd
計算量
- 構築 : $O(n)$
- クエリ : $O(\log n)$
使用例
-
SegmentTreeBeats seg(n, e): $n$要素の$e$で初期化. -
SegmentTreeBeats seg(v): $v$で初期化. -
seg.update_min(l, r, x): 半開区間$[l, r)$を$x$にchmin. -
seg.update_max(l, r, x): 半開区間$[l, r)$を$x$にchmax. -
seg.add_val(l, r, x): 半開区間$[l, r)$に$x$を加算. -
seg.update_val(l, r, x): 半開区間$[l, r)$を$x$に変更. -
seg.query_max(l, r): 半開区間$[l, r)$の最大値クエリ. -
seg.query_min(l, r): 半開区間$[l, r)$の最小値クエリ. -
seg.query_sum(l, r): 半開区間$[l, r)$の総和クエリ.
Verified with
Code
/**
* @brief Segment Tree Beats
* @docs docs/datastructure/segmenttree/segmenttreebeats.md
*/
// clang-format off
struct SegmentTreeBeats {
static const long long INF = 1LL << 60;
struct Node {
Node *left, *right;
long long max_v, smax_v, max_c;
long long min_v, smin_v, min_c;
long long sum;
long long len, ladd, lval;
Node() : left(0), right(0), ladd(0), lval(INF) {}
void init(long long x) {
max_v = min_v = sum = x;
smax_v = -INF; smin_v = INF;
max_c = min_c = 1;
}
void init_empty() {
max_v = smax_v = -INF;
min_v = smin_v = INF;
max_c = min_c = 0;
}
void update_max(long long x) {
sum += (x - max_v) * max_c;
/* */if (max_v == min_v) max_v = min_v = x;
else if (max_v == smin_v) max_v = smin_v = x;
else max_v = x;
if (lval != INF and x < lval) lval = x;
}
void update_min(long long x) {
sum += (x - min_v) * min_c;
/* */if (max_v == min_v) max_v = min_v = x;
else if (max_v == smin_v) min_v = smax_v = x;
else min_v = x;
if (lval != INF and lval < x) lval = x;
}
void addall(long long x) {
max_v += x;
if (smax_v != -INF) smax_v += x;
min_v += x;
if (smin_v != INF) smin_v += x;
sum += len * x;
if (lval != INF) lval += x;
else ladd += x;
}
void updateall(long long x) {
max_v = min_v = x;
smax_v = -INF; smin_v = INF;
max_c = min_c = len;
sum = len * x;
lval = x; ladd = 0;
}
void push() {
if (lval != INF) {
left -> updateall(lval);
right -> updateall(lval);
lval = INF;
return;
}
if (ladd != 0) {
left -> addall(ladd);
right -> addall(ladd);
ladd = 0;
}
if (max_v < left -> max_v) left -> update_max(max_v);
if (left -> min_v < min_v) left -> update_min(min_v);
if (max_v < right -> max_v) right -> update_max(max_v);
if (right -> min_v < min_v) right -> update_min(min_v);
}
void update() {
sum = left -> sum + right -> sum;
if (left -> max_v < right -> max_v) {
max_v = right -> max_v;
max_c = right -> max_c;
smax_v = max(left -> max_v, right -> smax_v);
} else if (left -> max_v > right -> max_v) {
max_v = left -> max_v;
max_c = left -> max_c;
smax_v = max(left -> smax_v, right -> max_v);
} else {
max_v = left -> max_v;
max_c = left -> max_c + right -> max_c;
smax_v = max(left -> smax_v, right -> smax_v);
}
if (left -> min_v < right -> min_v) {
min_v = left -> min_v;
min_c = left -> min_c;
smin_v = min(left -> smin_v, right -> min_v);
} else if (left -> min_v > right -> min_v) {
min_v = right -> min_v;
min_c = right -> min_c;
smin_v = min(left -> min_v, right -> smin_v);
} else {
min_v = left -> min_v;
min_c = left -> min_c + right -> min_c;
smin_v = min(left -> smin_v, right -> smin_v);
}
}
};
int n, n0;
Node *root;
void _update_min(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a || nd -> max_v <= x) return;
if (a <= l && r <= b && nd -> smax_v < x) {
nd -> update_max(x);
return;
}
nd -> push();
_update_min(x, a, b, nd -> left, l, (l + r) >> 1);
_update_min(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _update_max(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a || x <= nd -> min_v) return;
if (a <= l && r <= b && x < nd -> smin_v) {
nd -> update_min(x);
return;
}
nd -> push();
_update_max(x, a, b, nd -> left, l, (l + r) >> 1);
_update_max(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _add_val(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
nd -> addall(x);
return;
}
nd -> push();
_add_val(x, a, b, nd -> left, l, (l + r) >> 1);
_add_val(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _update_val(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
nd -> updateall(x);
return;
}
nd -> push();
_update_val(x, a, b, nd -> left, l, (l + r) >> 1);
_update_val(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
long long _query_max(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return -INF;
if (a <= l && r <= b) return nd -> max_v;
nd -> push();
long long lv = _query_max(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_max(a, b, nd -> right, (l + r) >> 1, r);
return max(lv, rv);
}
long long _query_min(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return INF;
if (a <= l && r <= b) return nd -> min_v;
nd -> push();
long long lv = _query_min(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_min(a, b, nd -> right, (l + r) >> 1, r);
return min(lv, rv);
}
long long _query_sum(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return 0;
if (a <= l && r <= b) return nd -> sum;
nd -> push();
long long lv = _query_sum(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_sum(a, b, nd -> right, (l + r) >> 1, r);
return lv + rv;
}
SegmentTreeBeats(int n, long long val = 0) : n(n) {
n0 = 1; while (n0 < n) n0 <<= 1;
Node *nds = new Node[2 * n0];
root = nds;
nds[0].len = n0;
for (int i = 0; i < n0 - 1; ++i) {
nds[i].left = &nds[2 * i + 1];
nds[i].right = &nds[2 * i + 2];
nds[2 * i + 1].len = nds[2 * i + 2].len = nds[i].len >> 1;
}
for (int i = 0; i < n; ++i) nds[n0 - 1 + i].init(val);
for (int i = n; i < n0; ++i) nds[n0 - 1 + i].init_empty();
for (int i = n0 - 2; i >= 0; i--) nds[i].update();
}
SegmentTreeBeats(const vector<long long> &v) : n((int)v.size()) {
n0 = 1; while (n0 < n) n0 <<= 1;
Node *nds = new Node[2 * n0];
root = nds;
nds[0].len = n0;
for (int i = 0; i < n0 - 1; ++i) {
nds[i].left = &nds[2 * i + 1];
nds[i].right = &nds[2 * i + 2];
nds[2 * i + 1].len = nds[2 * i + 2].len = nds[i].len >> 1;
}
for (int i = 0; i < n; ++i) nds[n0 - 1 + i].init(v[i]);
for (int i = n; i < n0; ++i) nds[n0 - 1 + i].init_empty();
for (int i = n0 - 2; i >= 0; i--) nds[i].update();
}
void update_min(int a, int b, long long x) { _update_min(x, a, b, root, 0, n0); }
void update_max(int a, int b, long long x) { _update_max(x, a, b, root, 0, n0); }
void add_val(int a, int b, long long x) { _add_val(x, a, b, root, 0, n0); }
void update_val(int a, int b, long long x) { _update_val(x, a, b, root, 0, n0); }
long long query_max(int a, int b) { return _query_max(a, b, root, 0, n0); }
long long query_min(int a, int b) { return _query_min(a, b, root, 0, n0); }
long long query_sum(int a, int b) { return _query_sum(a, b, root, 0, n0); }
};
// clang-format on#line 1 "datastructure/segmenttree/segmenttreebeats.hpp"
/**
* @brief Segment Tree Beats
* @docs docs/datastructure/segmenttree/segmenttreebeats.md
*/
// clang-format off
struct SegmentTreeBeats {
static const long long INF = 1LL << 60;
struct Node {
Node *left, *right;
long long max_v, smax_v, max_c;
long long min_v, smin_v, min_c;
long long sum;
long long len, ladd, lval;
Node() : left(0), right(0), ladd(0), lval(INF) {}
void init(long long x) {
max_v = min_v = sum = x;
smax_v = -INF; smin_v = INF;
max_c = min_c = 1;
}
void init_empty() {
max_v = smax_v = -INF;
min_v = smin_v = INF;
max_c = min_c = 0;
}
void update_max(long long x) {
sum += (x - max_v) * max_c;
/* */if (max_v == min_v) max_v = min_v = x;
else if (max_v == smin_v) max_v = smin_v = x;
else max_v = x;
if (lval != INF and x < lval) lval = x;
}
void update_min(long long x) {
sum += (x - min_v) * min_c;
/* */if (max_v == min_v) max_v = min_v = x;
else if (max_v == smin_v) min_v = smax_v = x;
else min_v = x;
if (lval != INF and lval < x) lval = x;
}
void addall(long long x) {
max_v += x;
if (smax_v != -INF) smax_v += x;
min_v += x;
if (smin_v != INF) smin_v += x;
sum += len * x;
if (lval != INF) lval += x;
else ladd += x;
}
void updateall(long long x) {
max_v = min_v = x;
smax_v = -INF; smin_v = INF;
max_c = min_c = len;
sum = len * x;
lval = x; ladd = 0;
}
void push() {
if (lval != INF) {
left -> updateall(lval);
right -> updateall(lval);
lval = INF;
return;
}
if (ladd != 0) {
left -> addall(ladd);
right -> addall(ladd);
ladd = 0;
}
if (max_v < left -> max_v) left -> update_max(max_v);
if (left -> min_v < min_v) left -> update_min(min_v);
if (max_v < right -> max_v) right -> update_max(max_v);
if (right -> min_v < min_v) right -> update_min(min_v);
}
void update() {
sum = left -> sum + right -> sum;
if (left -> max_v < right -> max_v) {
max_v = right -> max_v;
max_c = right -> max_c;
smax_v = max(left -> max_v, right -> smax_v);
} else if (left -> max_v > right -> max_v) {
max_v = left -> max_v;
max_c = left -> max_c;
smax_v = max(left -> smax_v, right -> max_v);
} else {
max_v = left -> max_v;
max_c = left -> max_c + right -> max_c;
smax_v = max(left -> smax_v, right -> smax_v);
}
if (left -> min_v < right -> min_v) {
min_v = left -> min_v;
min_c = left -> min_c;
smin_v = min(left -> smin_v, right -> min_v);
} else if (left -> min_v > right -> min_v) {
min_v = right -> min_v;
min_c = right -> min_c;
smin_v = min(left -> min_v, right -> smin_v);
} else {
min_v = left -> min_v;
min_c = left -> min_c + right -> min_c;
smin_v = min(left -> smin_v, right -> smin_v);
}
}
};
int n, n0;
Node *root;
void _update_min(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a || nd -> max_v <= x) return;
if (a <= l && r <= b && nd -> smax_v < x) {
nd -> update_max(x);
return;
}
nd -> push();
_update_min(x, a, b, nd -> left, l, (l + r) >> 1);
_update_min(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _update_max(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a || x <= nd -> min_v) return;
if (a <= l && r <= b && x < nd -> smin_v) {
nd -> update_min(x);
return;
}
nd -> push();
_update_max(x, a, b, nd -> left, l, (l + r) >> 1);
_update_max(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _add_val(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
nd -> addall(x);
return;
}
nd -> push();
_add_val(x, a, b, nd -> left, l, (l + r) >> 1);
_add_val(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
void _update_val(long long x, int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
nd -> updateall(x);
return;
}
nd -> push();
_update_val(x, a, b, nd -> left, l, (l + r) >> 1);
_update_val(x, a, b, nd -> right, (l + r) >> 1, r);
nd -> update();
}
long long _query_max(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return -INF;
if (a <= l && r <= b) return nd -> max_v;
nd -> push();
long long lv = _query_max(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_max(a, b, nd -> right, (l + r) >> 1, r);
return max(lv, rv);
}
long long _query_min(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return INF;
if (a <= l && r <= b) return nd -> min_v;
nd -> push();
long long lv = _query_min(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_min(a, b, nd -> right, (l + r) >> 1, r);
return min(lv, rv);
}
long long _query_sum(int a, int b, Node *nd, int l, int r) {
if (b <= l || r <= a) return 0;
if (a <= l && r <= b) return nd -> sum;
nd -> push();
long long lv = _query_sum(a, b, nd -> left, l, (l + r) >> 1);
long long rv = _query_sum(a, b, nd -> right, (l + r) >> 1, r);
return lv + rv;
}
SegmentTreeBeats(int n, long long val = 0) : n(n) {
n0 = 1; while (n0 < n) n0 <<= 1;
Node *nds = new Node[2 * n0];
root = nds;
nds[0].len = n0;
for (int i = 0; i < n0 - 1; ++i) {
nds[i].left = &nds[2 * i + 1];
nds[i].right = &nds[2 * i + 2];
nds[2 * i + 1].len = nds[2 * i + 2].len = nds[i].len >> 1;
}
for (int i = 0; i < n; ++i) nds[n0 - 1 + i].init(val);
for (int i = n; i < n0; ++i) nds[n0 - 1 + i].init_empty();
for (int i = n0 - 2; i >= 0; i--) nds[i].update();
}
SegmentTreeBeats(const vector<long long> &v) : n((int)v.size()) {
n0 = 1; while (n0 < n) n0 <<= 1;
Node *nds = new Node[2 * n0];
root = nds;
nds[0].len = n0;
for (int i = 0; i < n0 - 1; ++i) {
nds[i].left = &nds[2 * i + 1];
nds[i].right = &nds[2 * i + 2];
nds[2 * i + 1].len = nds[2 * i + 2].len = nds[i].len >> 1;
}
for (int i = 0; i < n; ++i) nds[n0 - 1 + i].init(v[i]);
for (int i = n; i < n0; ++i) nds[n0 - 1 + i].init_empty();
for (int i = n0 - 2; i >= 0; i--) nds[i].update();
}
void update_min(int a, int b, long long x) { _update_min(x, a, b, root, 0, n0); }
void update_max(int a, int b, long long x) { _update_max(x, a, b, root, 0, n0); }
void add_val(int a, int b, long long x) { _add_val(x, a, b, root, 0, n0); }
void update_val(int a, int b, long long x) { _update_val(x, a, b, root, 0, n0); }
long long query_max(int a, int b) { return _query_max(a, b, root, 0, n0); }
long long query_min(int a, int b) { return _query_min(a, b, root, 0, n0); }
long long query_sum(int a, int b) { return _query_sum(a, b, root, 0, n0); }
};
// clang-format on