rectangle-union-area/segment_tree.cpp

//
// Created by maximilian on 16.04.22.
//
#include <cassert>
#include <bit>
#include "segment_tree.h"

SegmentTree::SegmentTree(const std::vector<RectCoord> &coords):
    _covered_cross_section_length(0), _nodes() {

    assert(!coords.empty());

    // reserve nodes for a full binary tree with at least as many leaves as intervals
    size_t num_leaf_nodes = coords.size() -1;
    size_t num_meta_nodes = std::bit_ceil(num_leaf_nodes) - 1;

    // Initialize all nodes with zero coverage and dummy interval
    _nodes.resize(2 * num_meta_nodes + 1, {0, coords[num_leaf_nodes].coord, coords[num_leaf_nodes].coord});

    // We initialize the tree from bottom up, keeping track of the index ranges
    // and the length of the corresponding segment

    for(Index leaf_node_idx = 0 ; leaf_node_idx < num_leaf_nodes ; ++leaf_node_idx) {
        _nodes[leaf_node_idx + num_meta_nodes].left_coord = coords[leaf_node_idx].coord;
        _nodes[leaf_node_idx + num_meta_nodes].right_coord = coords[leaf_node_idx +1].coord;
    }
    // Note that there are remaining leafs that represent dummy ranges
    for(Index node_idx = num_meta_nodes - 1; node_idx != -1 ; --node_idx) {
        _nodes[node_idx].left_coord = left_child(node_idx).left_coord;
        _nodes[node_idx].right_coord = right_child(node_idx).right_coord;
    }

    assert(_nodes.front().left_coord == coords.front().coord);
    assert(_nodes.front().right_coord == coords.back().coord);
    assert(_nodes.front().segment_length() == coords.back().coord - coords.front().coord);
}

void SegmentTree::add_interval(Interval interval, Index node_idx) {
    if (interval.left <= _nodes[node_idx].left_coord && _nodes[node_idx].right_coord <= interval.right) {
        update_added(node_idx);
    } else {
        if(interval.left < left_child(node_idx).right_coord) {
            add_interval(interval, left_child_idx(node_idx));
        }
        if(right_child(node_idx).left_coord < interval.right) {
            add_interval(interval, right_child_idx(node_idx));
        }
    }
}

void SegmentTree::remove_interval(Interval interval, Index node_idx) {
    if (interval.left <= _nodes[node_idx].left_coord && _nodes[node_idx].right_coord <= interval.right) {
        update_removed(node_idx);
    } else {
        if(interval.left < left_child(node_idx).right_coord) {
            remove_interval(interval, left_child_idx(node_idx));
        }
        if(right_child(node_idx).left_coord < interval.right) {
            remove_interval(interval, right_child_idx(node_idx));
        }
    }
}