Algorithms - Writing for Computer Science - page 144

ₐ ≤ ≤

3. (Summation.) sum 0. For each j , where 1 j n ,

ₐ

(a) c 1; the variable c is a temporary accumulator.

(b) For each k , where 1

≤ k ≤ m ,set c ₐ c × A jk .

(c) sum ₐ sum + c .

This is cumbersome and no more informative than the equivalent mathematical
expression. It is safe to assume that most programmers know how to use loops
to implement sums and products.

ₐ j = 1 k = 1 A jk .
Written this way, it is unclear that a separate variable sum is even required: the
mathematical expression may suffice in future references to the same value. Giving
this step explicitly, however, might help if, say, the matrix A was sparse and stored
as a list rather than as a two-dimensional array, thus requiring an explanation of how
to compute the summation efficiently.
In specifications of algorithms, use text rather than mathematics if the former is
sufficiently clear.
2. for 1

3. (Summation.) Set sum

≤ i ≤| s |

(a) set c ₐ s [ i ]

(b) set A c ₐ A c + 1

2. For each character c in string s , increment A c .

Figures

Figures are an effective way of conveying the intricacies of data structures; and
even quite simple structures can require complex descriptions. General guidelines
for figures are given in Chap. 11 .

A single rotation can be used to bring a node one level closer to the root. In a
left-rotation, a parent node x and its right child y are exchanged as follows:
as B is the left child of y , assign B to be the new right child of x and assign
x to be the new left child of y . The left child of x and the right child of y
remain unchanged. The complementary operation is a right-rotation. Left- and
right-rotations are shown in the following diagram.

y

x

right rotate

x

y

A

C

left rotate

A B B C