PL-HW1-SchemeProgramming

Some examples of functional programming and Scheme programming language in specific.

Examples

Example 1

A binary tree in Scheme language can be defined as below (Note that no node can have only one child):

• (leaf integer-value)
• (node left-subtree right-subtree)

Write the function, sum, in a way that returns the sum of all leaf values given a binary tree as input.

Example test case:
Input: (display(sum '(node (leaf 1) (node (leaf 2) (leaf 3)))))
Output: 6

Example 2

In Scheme language, the 2D array, A_m*n, is illustrated as below:

• ((a₁₁ a₁₂ ... a_1n) (a₂₁ a₂₂ ... a_2n) (a_m1 a_m2 ... a_mn))

Write a function to get two arrays as input and return their multiplication.

Example test case:
Input: (display (multiply '(((1 2) (3 4)) ((5 6) (7 8)))))
Output: ((19 22) (43 50))

Example 3

Write a function as depicted below to return the sum of rows and columns of a given array.

• (rowSum '((a₁₁ a₁₂ ... a_1n) (a₂₁ a₂₂ ... a_2n) (a_m1 a_m2 ... a_mn)) )
• (colSum '((a₁₁ a₁₂ ... a_1n) (a₂₁ a₂₂ ... a_2n) (a_m1 a_m2 ... a_mn)) )

Example test case:
Input: (display (rowSum '((0 1 2 3 4)(5 6 7 8 9)(0 1 2 3 4)(5 6 7 8 9))))
Output: (10 35 10 35)