Btree insert only implemented.

2022/03/algorithms/btree.js

@@ -0,0 +1,151 @@
+"use strict";
+
+// const fs = require('fs');
+// const {EOL} = require('os');
+
+let enable_logging = false;
+
+function log(...s) {
+	if (!enable_logging) {
+		return;
+	}
+	console.log.apply(null, s);
+}
+
+function make_node(k) {
+	return {
+		level: k,
+		// temporarily allowing having one more element before split
+		keys: [],    // k node can have k-1 keys, they are sorted
+		children: [] // k node can have k children
+	};
+};
+
+function binary_search(arr, el) {
+	if (!arr.length) {
+		log('Arr is empty');
+		return 0;
+	}
+
+	if (el < arr[0]) {
+		log(`El ${el} is smaller than ${arr[0]}`);
+		return 0;
+	}
+
+	if (el > arr[arr.length - 1]) {
+		log(`El ${el} is bigger than ${arr[arr.length - 1]}`);
+		return arr.length;
+	}
+
+	let i = 0;
+	let j = arr.length - 1;
+	let p;
+	while (i < j - 1) {
+		p = (i + j) >> 1; // dividing by 2 but javascript can't do it without Math.floor
+		if (arr[p] <= el) {
+			i = p;
+		} else {
+			j = p;
+		}
+	}
+
+	return i+1;
+}
+
+function btree_insert(node, el) {
+	log(`Adding ${el} into`, node);
+	if (!node) {
+		return [null, el, null];
+	}
+
+	const idx = binary_search(node.keys, el);
+	log(`Got index ${idx}`);
+	const child = node.children[idx];
+	let result = btree_insert(child, el);
+	if (!result) {
+		log('No merging root from sub');
+		return null; // we are all good
+	} 
+
+	let [left, root, right] = result;
+	log(`Got new root ${root} and sub trees`, left, right);
+	node.keys.splice(idx, 0, root);
+	node.children[idx] = left;
+	node.children.splice(idx+1, 0, right);
+
+	log(`Node size: ${node.keys.length}, node level: ${node.level}`);
+	if (node.keys.length > node.level) {
+		let h = node.level >> 1;
+		log(`Splitting`);
+		log(node.keys, `h index ${h}`);
+		let left = make_node(node.level);
+		let right = make_node(node.level);
+		let root = node.keys[h];
+		console.log(`Children`, node.children);
+		left.keys = node.keys.slice(0, h);
+		left.children = node.children.slice(0, h+1);
+		right.keys = node.keys.slice(h+1);
+		right.children = node.children.slice(h+1);
+		log('Result', left, root, right);
+		return [left, root, right];
+	} else {
+		return null;
+	}
+}
+
+function make_tree(t, result) {
+	if (!result) {
+		return t;
+	}
+
+	let [left, el, right] = result;
+	let root = make_node(t.level);
+	root.keys[0] = el;
+	root.children[0] = left;
+	root.children[1] = right;
+	return root;
+}
+
+function display_tree(t, path = '') {
+	if (!t) {
+		return;
+	}
+
+	for (let i = 0; i < t.keys.length; i++) {
+		display_tree(t.children[i], path + "/" + i);
+		console.log(path + " " + t.keys[i]);
+	}
+	display_tree(t.children[t.keys.length], path + "/" + t.keys.length);
+}
+
+// let arr = [1, 3, 5, 7];
+
+// const el = -2;
+// const pos = binary_search(arr, el);
+// arr.splice(pos, 0, el);
+// log(`Binary search`, arr);
+
+let t = make_node(2);
+// t = make_tree(t, btree_insert(t, 1));
+// t = make_tree(t, btree_insert(t, 2));
+// t = make_tree(t, btree_insert(t, 3));
+// t = make_tree(t, btree_insert(t, 4));
+// t = make_tree(t, btree_insert(t, 5));
+// t = make_tree(t, btree_insert(t, 6));
+// t = make_tree(t, btree_insert(t, 7));
+
+display_tree(t);
+// enable_logging = true;
+t = make_tree(t, btree_insert(t, 1));
+t = make_tree(t, btree_insert(t, 2));
+t = make_tree(t, btree_insert(t, 3));
+t = make_tree(t, btree_insert(t, 4));
+t = make_tree(t, btree_insert(t, 5));
+t = make_tree(t, btree_insert(t, 6));
+t = make_tree(t, btree_insert(t, 7));
+t = make_tree(t, btree_insert(t, 8));
+t = make_tree(t, btree_insert(t, 5));
+t = make_tree(t, btree_insert(t, 5));
+// console.log(t);
+//enable_logging = false;
+display_tree(t);