Cartesian tree ($O(n)$)
(graph/cartesian_tree.hpp)

• View this file on GitHub
• Last update: 2020-07-16 00:31:29+09:00
• Include: #include "graph/cartesian_tree.hpp"

Depends on

• utils/macros.hpp

Verified with

• graph/cartesian_tree.yosupo.test.cpp
• graph/cartesian_tree.yukicoder-1031.test.cpp

Code

#pragma once
#include <functional>
#include <vector>
#include "utils/macros.hpp"

/**
 * @brief Cartesian tree ($O(n)$)
 * @note the smallest value is the root
 * @note if a is not distinct, the way for tie-break is undefined
 * @return the binary tree as the list of parents
 */
template <class T, class Comparator = std::less<int> >
std::vector<int> construct_cartesian_tree(const std::vector<T> & a, const Comparator & cmp = Comparator()) {
    int n = a.size();
    std::vector<int> parent(n, -1);
    REP3 (i, 1, n) {
        int p = i - 1;  // parent of i
        int l = -1;  // left child of i
        while (p != -1 and cmp(a[i], a[p])) {
            int pp = parent[p];  // parent of parent of i
            if (l != -1) {
                parent[l] = p;
            }
            parent[p] = i;
            l = p;
            p = pp;
        }
        parent[i] = p;
    }
    return parent;
}

#line 2 "graph/cartesian_tree.hpp"
#include <functional>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 5 "graph/cartesian_tree.hpp"

/**
 * @brief Cartesian tree ($O(n)$)
 * @note the smallest value is the root
 * @note if a is not distinct, the way for tie-break is undefined
 * @return the binary tree as the list of parents
 */
template <class T, class Comparator = std::less<int> >
std::vector<int> construct_cartesian_tree(const std::vector<T> & a, const Comparator & cmp = Comparator()) {
    int n = a.size();
    std::vector<int> parent(n, -1);
    REP3 (i, 1, n) {
        int p = i - 1;  // parent of i
        int l = -1;  // left child of i
        while (p != -1 and cmp(a[i], a[p])) {
            int pp = parent[p];  // parent of parent of i
            if (l != -1) {
                parent[l] = p;
            }
            parent[p] = i;
            l = p;
            p = pp;
        }
        parent[i] = p;
    }
    return parent;
}

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