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 pointer 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->next(second);
second->next(first);

std::cout << std::boolalpha << 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 (-1, -1).

For example, findTwoSum({ 3, 1, 5, 7, 5, 9 }, 10) should return a std::pair<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 vector of unique integers and, efficiently with respect to time used, counts the number of vector elements that are less than the parameter lessThan.

For example, for vector v containing { 1, 3, 5, 7 }, countNumbers(v, 4) should return 2 because there are two vector 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.