cplib-cpp
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segmenttree/test/rmq_nonrecursive.test.cpp
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- Last update: 2022-01-08 20:23:44+09:00
- Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A
Depends on
Code
#include "../point-update-range-get_nonrecursive.hpp"
#include <iostream>
using namespace std;
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A"
int main() {
int N, Q;
cin >> N >> Q;
vector<int> A(N, (1LL << 31) - 1);
RangeMinimumQuery<int> rmq(A, A[0]);
while (Q--) {
int c, x, y;
cin >> c >> x >> y;
if (c == 0)
rmq.update(x, y);
else
cout << rmq.get(x, y + 1) << endl;
}
}#line 2 "segmenttree/point-update-range-get_nonrecursive.hpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <iostream>
#include <stack>
#include <vector>
// CUT begin
// Nonrecursive Segment Tree (point-update, range-get)
// - Conditions for operations:
// - merge_data: [TDATA, TDATA] -> TDATA, e(x, y) == e(y, x)
// - data2ret: [TDATA, TQUERY] -> TRET
// - merge_ret: [TRET, TRET] -> TRET, g(defaultRET, x) == x, g(x, y) = g(y, x)
// - commutability f(e(x, y), q) == g(f(x, q), f(y, q))
template <typename TDATA, typename TRET, typename TQUERY> struct NonrecursiveSegmentTree {
int N;
TRET defaultRET;
virtual TDATA merge_data(const TDATA &, const TDATA &) = 0;
virtual TRET data2ret(const TDATA &, const TQUERY &) = 0;
virtual TRET merge_ret(const TRET &, const TRET &) = 0;
std::vector<TDATA> data;
inline TDATA &at(int i) { return data[i]; }
inline void _merge(int i) { at(i) = merge_data(at(i << 1), at((i << 1) + 1)); }
void initialize(const std::vector<TDATA> &seq, TRET RET_ZERO) {
N = seq.size();
defaultRET = RET_ZERO;
data = seq;
data.insert(data.end(), seq.begin(), seq.end());
for (int i = N - 1; i; i--) _merge(i);
}
NonrecursiveSegmentTree() = default;
void update(int pos, const TDATA &x) {
assert(pos >= 0 and pos < N);
at(pos + N) = x;
for (int i = pos + N; i > 1;) i >>= 1, _merge(i);
}
// [l, r), 0-indexed
TRET get(int l, int r, TQUERY query = NULL) {
assert(l >= 0 and r <= N);
TRET retl = defaultRET, retr = defaultRET;
l += N, r += N;
while (l < r) {
if (l & 1) retl = merge_ret(retl, data2ret(data[l++], query));
if (r & 1) retr = merge_ret(data2ret(data[--r], query), retr);
l >>= 1, r >>= 1;
}
return merge_ret(retl, retr);
}
// Calculate smallest r that satisfies condition(g(f(x_l, q), ..., f(x_{r - 1}, q)) == true
// Assumption: Monotonicity of g(x_l, ..., x_r) about r (l: fixed)
// Complexity: O(log N)
int binary_search(int l, std::function<bool(TRET)> condition, TQUERY query = NULL) {
std::stack<int> rs;
l += N;
int r = N * 2;
TRET retl = defaultRET;
if (condition(retl)) return l - N;
while (l < r) {
if (l & 1) {
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
l++;
retl = ret_tmp;
}
if (r & 1) rs.push(--r);
l >>= 1, r >>= 1;
}
while (!rs.empty()) {
l = rs.top();
rs.pop();
TRET ret_tmp = merge_ret(retl, data2ret(data[l], query));
if (condition(ret_tmp)) {
while (l * 2 < N * 2) {
ret_tmp = merge_ret(retl, data2ret(data[l * 2], query));
if (condition(ret_tmp))
l *= 2;
else
retl = ret_tmp, l = l * 2 + 1;
}
return l - N;
}
retl = ret_tmp;
}
return N;
}
template <typename T1, typename T2, typename T3>
friend std::ostream &operator<<(std::ostream &os, NonrecursiveSegmentTree<T1, T2, T3> s) {
os << "[SegmentTree (len: " << s.N << ')';
for (int i = 0; i < s.N; i++) os << s.at(i + s.N) << ',';
os << "]";
return os;
}
};
// Range Minimum Query
// - get: return min(x_l, ..., x_{r - 1})
template <typename T> struct RangeMinimumQuery : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return std::min(vl, vr); };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return std::min(vl, vr); };
RangeMinimumQuery(const std::vector<T> &seq, T defaultmin)
: SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, defaultmin);
};
};
// Range Maximum Query
// - get: return max(x_l, ..., x_{r - 1})
template <typename T> struct RangeMaximumQuery : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return std::max(vl, vr); };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return std::max(vl, vr); };
RangeMaximumQuery(const std::vector<T> &seq, T defaultmax)
: SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, defaultmax);
};
};
template <typename T> struct PointUpdateRangeSum : public NonrecursiveSegmentTree<T, T, bool> {
using SegTree = NonrecursiveSegmentTree<T, T, bool>;
T merge_data(const T &vl, const T &vr) override { return vl + vr; };
T data2ret(const T &v, const bool &q) override { return v; }
T merge_ret(const T &vl, const T &vr) override { return vl + vr; };
PointUpdateRangeSum(const std::vector<T> &seq, T zero) : SegTree::NonrecursiveSegmentTree() {
SegTree::initialize(seq, zero);
};
};
// Range Counting less than q Query
// - get: return (#{i | l <= i < r, x_i < q}, total sum of them).
template <typename T>
struct CountAndSumLessThan
: public NonrecursiveSegmentTree<std::vector<std::pair<T, T>>, std::pair<int, T>, T> {
using TDATA = std::vector<std::pair<T, T>>;
using TRET = std::pair<int, T>;
using TQUERY = T;
TDATA merge_data(const TDATA &vl, const TDATA &vr) override {
TDATA ret = vl;
ret.insert(ret.end(), vr.begin(), vr.end());
std::sort(ret.begin(), ret.end());
if (ret.size()) {
ret[0].second = ret[0].first;
for (size_t i = 1; i < ret.size(); i++)
ret[i].second = ret[i - 1].second + ret[i].first;
}
return ret;
}
TRET data2ret(const TDATA &vec, const TQUERY &q) override {
int i = std::lower_bound(vec.begin(), vec.end(), std::make_pair(q, q)) - vec.begin();
if (!i)
return std::make_pair(0, 0);
else
return std::make_pair(i, vec[i - 1].second);
}
TRET merge_ret(const TRET &l, const TRET &r) override {
return std::make_pair(l.first + r.first, l.second + r.second);
}
using SegTree = NonrecursiveSegmentTree<TDATA, TRET, TQUERY>;
CountAndSumLessThan(const std::vector<T> &seq) : SegTree::NonrecursiveSegmentTree() {
std::vector<TDATA> init;
for (auto x : seq) init.emplace_back(TDATA{std::pair<T, T>(x, x)});
SegTree::initialize(init, TRET(0, 0));
}
};
#line 3 "segmenttree/test/rmq_nonrecursive.test.cpp"
using namespace std;
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_2_A"
int main() {
int N, Q;
cin >> N >> Q;
vector<int> A(N, (1LL << 31) - 1);
RangeMinimumQuery<int> rmq(A, A[0]);
while (Q--) {
int c, x, y;
cin >> c >> x >> y;
if (c == 0)
rmq.update(x, y);
else
cout << rmq.get(x, y + 1) << endl;
}
}