feat(DataStructures): add segment tree

Author: mgechev

src/data-structures/segment-tree.js

@@ -0,0 +1,105 @@
+/**
+ * Implementation of a segment tree.
+ *
+ * @example
+ * var SegmentTree = require('path-to-algorithms/src/data-structures'+
+ * '/segment-tree').SegmentTree;
+ *
+ * var tree = SegmentTree.indexArray([-1, 2, 4, 0], Infinity, function (a, b) {
+ *   return Math.min(a, b);
+ * });
+ *
+ * @public
+ * @constructor
+ * @param {any} placeholder A placeholder value dpendent on the aggregate.
+ * @param {Function} aggregate Generates the values for the intermediate nodes.
+ * @module data-structures/segment-tree
+ */
+(function (exports) {
+
+  'use strict';
+
+  /**
+   * SegmentTree constructor.
+   *
+   * @public
+   * @constructor
+   * @param {any} invalidValue Invalid value to be returned depending
+   *  on the aggregate.
+   * @param {Function} aggregate Function to generate the intermediate
+   *  values in the tree.
+   */
+  function SegmentTree(invalidValue, aggregate) {
+    this._data = [];
+    this._original = null;
+    this._invalidValue = invalidValue;
+    this._aggregate = aggregate;
+  }
+
+  /**
+   * Creates a segment tree using an array passed as element.
+   *
+   * @static
+   * @public
+   * @param {Array} array Array to be indexed.
+   * @param {Function} aggregate Function used for generation of
+   *  intermediate nodes.
+   */
+  SegmentTree.indexArray = function (array, placeholder, aggregate) {
+    var segmentize = function (original, data, lo, hi, idx) {
+      if (lo === hi) {
+        data[idx] = original[lo];
+      } else {
+        var mid = Math.floor((lo + hi) / 2);
+        var left = 2 * idx + 1;
+        var right = 2 * idx + 2;
+        segmentize(original, data, lo, mid, left);
+        segmentize(original, data, mid + 1, hi, right);
+        data[idx] = aggregate(data[left], data[right]);
+      }
+    };
+    var result = [];
+    if (array && array.length) {
+      segmentize(array, result, 0, array.length - 1, 0);
+    }
+    var tree = new SegmentTree(placeholder, aggregate);
+    tree._data = result;
+    tree._original = array;
+    return tree;
+  };
+
+  /**
+   * Queries the SegmentTree in given range based on the set aggregate.
+   *
+   * @param {Number} start The start index of the interval.
+   * @param {Number} end The end index of the interval.
+   */
+  SegmentTree.prototype.query = function (start, end) {
+    if (start > end) {
+      throw new Error('The start index should be smaller by the end index');
+    }
+    var findEl = function (originalArrayStart, originalArrayEnd, current) {
+      if (start > originalArrayEnd) {
+        return this._invalidValue;
+      }
+      if (end < originalArrayStart) {
+        return this._invalidValue;
+      }
+      if (start === originalArrayStart && end === originalArrayEnd ||
+          originalArrayStart === originalArrayEnd) {
+        return this._data[current];
+      }
+      var originalArrayMid =
+        Math.floor((originalArrayStart + originalArrayEnd) / 2);
+      return this._aggregate(
+        findEl(originalArrayStart, originalArrayMid, 2 * current + 1),
+        findEl(originalArrayMid + 1, originalArrayEnd, 2 * current + 2)
+      );
+    }.bind(this);
+    return findEl(0, this._original.length - 1, 0, this._aggregate);
+  };
+
+  exports.SegmentTree = SegmentTree;
+
+}(typeof window === 'undefined' ? module.exports : window));
+

test/data-structures/segment-tree.spec.js

@@ -0,0 +1,89 @@
+'use strict';
+
+var SegmentTree = require('../../src/data-structures/segment-tree.js')
+  .SegmentTree;
+
+var defaultAggregate = function (a, b) {
+  return Math.min(a, b);
+};
+
+describe('Segment Tree', function () {
+
+  describe('indexing', function () {
+
+    it('should be a constructor function', function () {
+      expect(typeof SegmentTree).toBe('function');
+    });
+
+    it('should start with null original array', function () {
+      expect(new SegmentTree()._original).toBe(null);
+    });
+
+    it('should start with empty array as data', function () {
+      expect(new SegmentTree()._data).not.toBe(null);
+      expect(new SegmentTree()._data.length).toBe(0);
+    });
+
+    it('should work with empty arrays', function () {
+      var tree = SegmentTree.indexArray([], Infinity, defaultAggregate);
+      expect(tree._data).toBeTruthy();
+      expect(tree._data.length).toBe(0);
+    });
+
+    it('should index arrays with one element', function () {
+      var tree = SegmentTree.indexArray([1], Infinity, defaultAggregate);
+      expect(tree._data).toBeTruthy();
+      expect(tree._data.length).toBe(1);
+    });
+
+    it('should index any array', function () {
+      var tree = SegmentTree.indexArray([1, 2, 3], Infinity, defaultAggregate);
+      expect(tree._data).toEqual([1, 1, 3, 1, 2]);
+
+      tree = SegmentTree.indexArray([1, 2, 3, 6], Infinity, defaultAggregate);
+      expect(tree._data).toEqual([1, 1, 3, 1, 2, 3, 6]);
+    });
+
+  });
+
+  describe('should find the proper value at given interval', function () {
+
+    it('should properly find the minimum when in range', function () {
+      var tree = SegmentTree.indexArray([1], Infinity, defaultAggregate);
+      expect(tree.query(0, 0)).toBe(1);
+
+      tree = SegmentTree.indexArray([1, 2], Infinity, defaultAggregate);
+      expect(tree.query(0, 0)).toBe(1);
+      expect(tree.query(0, 1)).toBe(1);
+      expect(tree.query(1, 1)).toBe(2);
+
+      tree = SegmentTree.indexArray([1, -1, 2], Infinity, defaultAggregate);
+      expect(tree.query(0, 2)).toBe(-1);
+      expect(tree.query(0, 1)).toBe(-1);
+      expect(tree.query(1, 1)).toBe(-1);
+      expect(tree.query(1, 2)).toBe(-1);
+      expect(tree.query(2, 2)).toBe(2);
+    });
+
+    it('should properly find the minimum when outside range', function () {
+      var tree = SegmentTree.indexArray([1], Infinity, defaultAggregate);
+      expect(tree.query(0, 2)).toBe(1);
+
+      tree = SegmentTree.indexArray([1, 2, 3], Infinity, defaultAggregate);
+      expect(tree.query(0, 20)).toBe(1);
+      expect(tree.query(2, 20)).toBe(3);
+      expect(Number.isFinite(tree.query(20, 25))).toBe(false);
+    });
+
+    it('should throw when the start index is bigger than end', function () {
+      var tree = SegmentTree.indexArray([1], Infinity, defaultAggregate);
+      expect(function () {
+        tree.query(2, 1);
+      }).toThrow();
+      expect(function () {
+        tree.query(1, 1);
+      }).not.toThrow();
+    });
+  });
+});
+