Swap by addition and subtraction

Standard swapping algorithms require the use of a temporary storage area - standard intuitive algorithms to swap x and y involve:

• copying  y aside to a temporary storage area
• setting  y to be x
• copying the temporary storage value back to x.

However, this algorithm requires only the mathematical operations of addition and subtraction. The algorithm follows (where A and B are the values stored in the variables X and Y respectively):

X has A, Y has B.

Step 1: Add X and Y and store in X

Now X has A + B, Y has B.

Step 2: Subtract Y from X and store in Y

Now X has A + B, Y has A.

Step 3: Subtract Y from X and store in X

Now X has B, Y has A. Swap done.

The algorithm looks much simpler when it is written in pseudocode.

X := X + Y

Y := X - Y

X := X - Y

Limitation: Due to the addition operation in the first step, this swap algorithm would fail for the case of (A+B) overflow, i.e., when the sum exceeds the maximum allowable number for a given number of bits.