# Pseudocode Syntax Reference

Math operators are used the same as they are in formal mathematical writing.

-> indicates a return type. Only used for function declarations.

• If nothing is returned, this symbol is unused.

Any kind of indexing, range, interval is inclusive and 1-based unless explicitly stated.

• Example: A[1...N]: List<number> means the list A has N elements and can be indexed by 1, 2, 3, ... N.

Angle brackets <T> indicate the use of type parameters. For example, List<Vertex> means elements of this list are vertices.

function MergeSort(A[1...n]):
	if n > 1:
		mid = floor(n / 2)
		MergeSort(A[1 ... mid])
		MergeSort(A[mid + 1 ... n])
		Merge(A, mid)

In this pseudocode:

• Array A can be indexed by integers in [1, n]
• mid was declared and assigned the value floor(n / 2)
• floor, Merge are function calls
• Returns nothing

const prices = [...]

// Backtracking
function CutRod(rod_len) -> number:
	if rod_len == 0:
		return 0
	if rod_len == 1:
		return prices[1]
	
	best = 0
	for cut_len = 1 to rod_len:
		cut_profit = CutRod(rod_len - cut_len) + prices[cut_len]
		if cut_profit > best:
			best = cut_profit

	return best

Here we have an global constant prices = [...]. The function returns a number. int or float are explicitly stated when it is important (e.g. if the function returns an index, it must be an int).

Any object will be created on the heap through its constructor and are passed around by reference. (anything other than numbers, booleans, and strings)

queue = Queue()

Let’s use this syntax to state each dimension's size of the array:

Array(shape=(dimension1, dimension2, dimension3, ...))

For example:

B = Array(shape=(5, 6))

This means B can be indexed by:

• 1 through 5 on the 1st axis
• 1 through 6 on the 2nd axis.