This C# Algorithms Online Test
Separates Good From Bad Hires

Binary search tree (BST) is a binary tree where the value of each node is larger or equal to the values in all the nodes in that node's left subtree and is smaller than the values in all the nodes in that node's right subtree.

Write a function that, efficiently with respect to time used, checks if a given binary search tree contains a given value.

For example, for the following tree:

• n1 (Value: 1, Left: null, Right: null)
• n2 (Value: 2, Left: n1, Right: n3)
• n3 (Value: 3, Left: null, Right: null)

Call to Contains(n2, 3) should return true since a tree with root at n2 contains number 3.

A playlist is considered a repeating playlist if any of the songs contain a reference to a previous song in the playlist. Otherwise, the playlist will end with the last song which points to null.

Implement a function IsRepeatingPlaylist that, efficiently with respect to time used, returns true if a playlist is repeating or false if it is not.

For example, the following code prints "True" as both songs point to each other.

Song first = new Song("Hello");
Song second = new Song("Eye of the tiger");
    
first.NextSong = second;
second.NextSong = first;

Console.WriteLine(first.IsRepeatingPlaylist());

Write a function that, when passed a list and a target sum, returns, efficiently with respect to time used, two distinct zero-based indices of any two of the numbers, whose sum is equal to the target sum. If there are no two numbers, the function should return null.

For example, FindTwoSum(new List<int>() { 3, 1, 5, 7, 5, 9 }, 10) should return a Tuple<int, int> containing any of the following pairs of indices:

• 0 and 3 (or 3 and 0) as 3 + 7 = 10
• 1 and 5 (or 5 and 1) as 1 + 9 = 10
• 2 and 4 (or 4 and 2) as 5 + 5 = 10

Implement function CountNumbers that accepts a sorted array of unique integers and, efficiently with respect to time used, counts the number of array elements that are less than the parameter lessThan.

For example, SortedSearch.CountNumbers(new int[] { 1, 3, 5, 7 }, 4) should return 2 because there are two array elements less than 4.

A TrainComposition is built by attaching and detaching wagons from the left and the right sides, efficiently with respect to time used.

For example, if we start by attaching wagon 7 from the left followed by attaching wagon 13, again from the left, we get a composition of two wagons (13 and 7 from left to right). Now the first wagon that can be detached from the right is 7 and the first that can be detached from the left is 13.

Implement a TrainComposition that models this problem.

As a part of the route planner, the RouteExists method is used as a quick filter if the destination is reachable, before using more computationally intensive procedures for finding the optimal route.

The roads on the map are rasterized and produce a matrix of boolean values - true if the road is present or false if it is not. The roads in the matrix are connected only if the road is immediately left, right, below or above it.

Finish the RouteExists method so that it returns true if the destination is reachable or false if it is not. The fromRow and fromColumn parameters are the starting row and column in the mapMatrix. The toRow and toColumn are the destination row and column in the mapMatrix. The mapMatrix parameter is the above mentioned matrix produced from the map.

For example, for the given rasterized map, the code below should return true since the destination is reachable:

bool[,] mapMatrix = {
	{true, false, false},
	{true, true, false},
	{false, true, true}
};

RouteExists(0, 0, 2, 2, mapMatrix);