From a4c035b6dc599febe142e20a97119bb181370d64 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= <git@maximilian-kessler.de>
Date: Sat, 16 Apr 2022 12:29:01 +0200
Subject: [PATCH] store covered length at each node separately

---
 segment_tree.cpp |  9 +++++----
 segment_tree.h   | 30 ++++++++++++++++++------------
 2 files changed, 23 insertions(+), 16 deletions(-)

diff --git a/segment_tree.cpp b/segment_tree.cpp
index c0811d8..9c9e20e 100644
--- a/segment_tree.cpp
+++ b/segment_tree.cpp
@@ -6,7 +6,7 @@
 #include "segment_tree.h"
 
 SegmentTree::SegmentTree(const std::vector<RectCoord> &coords):
-    _covered_cross_section_length(0), _nodes() {
+   _nodes() {
 
     assert(!coords.empty());
 
@@ -15,7 +15,7 @@ SegmentTree::SegmentTree(const std::vector<RectCoord> &coords):
     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});
+    _nodes.resize(2 * num_meta_nodes + 1, {0, coords[num_leaf_nodes].coord, coords[num_leaf_nodes].coord, 0});
 
     // We initialize the tree from bottom up, keeping track of the index ranges
     // and the length of the corresponding segment
@@ -37,7 +37,7 @@ SegmentTree::SegmentTree(const std::vector<RectCoord> &coords):
 
 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);
+        add_coverage(node_idx);
     } else {
         if(interval.left < left_child(node_idx).right_coord) {
             add_interval(interval, left_child_idx(node_idx));
@@ -45,12 +45,13 @@ void SegmentTree::add_interval(Interval interval, Index node_idx) {
         if(right_child(node_idx).left_coord < interval.right) {
             add_interval(interval, right_child_idx(node_idx));
         }
+        update_covered_length(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);
+        remove_coverage(node_idx);
     } else {
         if(interval.left < left_child(node_idx).right_coord) {
             remove_interval(interval, left_child_idx(node_idx));
diff --git a/segment_tree.h b/segment_tree.h
index 99aeb77..69ac54d 100644
--- a/segment_tree.h
+++ b/segment_tree.h
@@ -13,13 +13,13 @@ struct TreeNode {
     unsigned coverage;
     Coordinate left_coord;
     Coordinate right_coord;
+    Unit covered_length;
     inline Unit segment_length();
 };
 
 
 class SegmentTree {
     std::vector<TreeNode> _nodes;
-    Unit _covered_cross_section_length;
 public:
     /**
      *
@@ -36,8 +36,9 @@ private:
     inline static Index right_child_idx(Index node_idx);
     inline TreeNode& left_child(Index node_idx);
     inline TreeNode& right_child(Index node_idx);
-    inline void update_added(Index node_idx);
-    inline void update_removed(Index node_idx);
+    inline void add_coverage(Index node_idx);
+    inline void remove_coverage(Index node_idx);
+    inline void update_covered_length(Index node_idx);
     void add_interval(Interval interval, Index node_idx);
     void remove_interval(Interval interval, Index node_idx);
 
@@ -58,7 +59,7 @@ TreeNode& SegmentTree::right_child(Index node_idx) {
 }
 
 Unit SegmentTree::length_covered_intervals() {
-    return _covered_cross_section_length;
+    return _nodes.front().covered_length;
 }
 
 void SegmentTree::add_interval(Interval interval) {
@@ -69,18 +70,14 @@ void SegmentTree::remove_interval(Interval interval) {
     remove_interval(interval, 0);
 }
 
-void SegmentTree::update_added(Index node_idx) {
+void SegmentTree::add_coverage(Index node_idx) {
     ++(_nodes[node_idx].coverage);
-    if(_nodes[node_idx].coverage == 1) {
-        _covered_cross_section_length += _nodes[node_idx].segment_length();
-    }
+    update_covered_length(node_idx);
 }
 
-void SegmentTree::update_removed(Index node_idx) {
+void SegmentTree::remove_coverage(Index node_idx) {
     --(_nodes[node_idx].coverage);
-    if(_nodes[node_idx].coverage == 0) {
-        _covered_cross_section_length -= _nodes[node_idx].segment_length();
-    }
+    update_covered_length(node_idx);
 }
 
 Index SegmentTree::left_child_idx(Index node_idx) {
@@ -91,6 +88,15 @@ Index SegmentTree::right_child_idx(Index node_idx) {
     return 2*node_idx + 2;
 }
 
+void SegmentTree::update_covered_length(Index node_idx) {
+    if (_nodes[node_idx].coverage > 0) {
+        _nodes[node_idx].covered_length = _nodes[node_idx].segment_length();
+    } else {
+        _nodes[node_idx].covered_length = \
+        left_child(node_idx).covered_length + right_child(node_idx).covered_length;
+    }
+}
+
 
 Unit TreeNode::segment_length() {
     return right_coord - left_coord;