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Author: ishriayush

binary-space-partitioning.cpp

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+// Language: cpp
+// Path: Tree/binary-space-partitioning.cpp
+// Implementation of the binary space partitioning tree.
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// A node of the tree.
+struct Node {
+    int x, y;
+    Node *left, *right;
+    Node(int x, int y) : x(x), y(y), left(NULL), right(NULL) {}
+};
+
+// A comparator for sorting the points by x-coordinate.
+struct XComparator {
+    bool operator()(const Node *a, const Node *b) {
+        return a->x < b->x;
+    }
+};
+
+// A comparator for sorting the points by y-coordinate.
+struct YComparator {
+    bool operator()(const Node *a, const Node *b) {
+        return a->y < b->y;
+    }
+};
+
+// Builds a binary space partitioning tree for the given points.
+Node *build(vector<Node *> &points, int depth) {
+    if (points.empty()) return NULL;
+    if (points.size() == 1) return points[0];
+    if (depth % 2 == 0) {
+        sort(points.begin(), points.end(), XComparator());
+    } else {
+        sort(points.begin(), points.end(), YComparator());
+    }
+    int mid = points.size() / 2;
+    Node *node = points[mid];
+    vector<Node *> left(points.begin(), points.begin() + mid);
+    vector<Node *> right(points.begin() + mid + 1, points.end());
+    node->left = build(left, depth + 1);
+    node->right = build(right, depth + 1);
+    return node;
+}
+
+// Prints the tree in the inorder traversal order.
+void print(Node *node) {
+    if (node == NULL) return;
+    print(node->left);
+    printf("(%d, %d), ", node->x, node->y);
+    print(node->right);
+}
+
+int main() {
+    vector<Node *> points;
+    points.push_back(new Node(2, 3));
+    points.push_back(new Node(5, 4));
+    points.push_back(new Node(9, 6));
+    points.push_back(new Node(4, 7));
+    points.push_back(new Node(8, 1));
+    points.push_back(new Node(4, 2));
+    Node *root = build(points, 0);
+    print(root);
+    return 0;
+}