Comparisons, selection and current state

Initially x = 3. In this pseudocode, x = 5 is a condition that tests equality, while x ← 5 is an assignment. If only the condition x = 5 is tested, what happens?

Checking a comparison does not replace either number

Check the comparison, including its boundary

A condition has a true or false result. Here < means less than, ≤ means less than or equal to, > means greater than, and ≥ means greater than or equal to

Equality is included in ≤ and ≥ but not in < or >. At x = 4, x > 4 is false and x ≥ 4 is true

The equality test = is true when both values are the same. The not-equal test ≠ is true when they differ

For one IF/ELSE decision, evaluate the condition once and run only its matching branch. The other branch is skipped

A strict boundary takes the false branch

Initially x = 4

Each numbered row is one separate IF/ELSE decision: test its condition once using the current x, then run only the matching true or false column

The arrow ← assigns a value; = in a test checks equality without changing x. The comparisons ≤ and ≥ include equality, while < and > exclude it; ≠ means not equal

What is the final value of x after all numbered decisions have run?

Before step 1: x = 4. The test 4 < 4 is false, so use only the If false column. Read the current 4 and calculate 4 + 1 = 5. After step 1: x = 5

After all numbered decisions, the final value is x = 5

Do not include equality in greater than

The two separate examples start with the same selected x. One tests x > 4; the other tests x ≥ 4. In each example, a true result runs x ← x + 2 and a false result runs x ← x + 1. Predict the outcomes for starting values 3, 4 and 5. The truth flag uses 1 for true and 0 for false

With starting x = 4, why do the final values differ?

Include equality in at most

Equal and not equal are opposite tests

If x is 5, the test x = 5 is true and x ≠ 5 is false

If x is 3, the test x = 5 is false and x ≠ 5 is true

These symbols describe this pseudocode model. A programming language may use different spelling for the same comparison, so use that language's stated rules when writing code

Trace a false equality test

Trace a true not-equal test

Start with x = 3. A single decision tests x < 4. Its true branch runs x ← x + 2; its false branch runs x ← x + 1. After the true branch makes x equal to 5, should the false branch also run?

The decision was already made using the value before its selected action

A later separate condition sees the current state

Two numbered IF/ELSE rows are two separate decisions. Finish the selected branch of the first row, then test the next row

The second test uses the value after the first row, not automatically the original input

A false test does not stop the sequence. Follow its false column and continue to the next numbered row

This is not an ELSE IF chain. In such a chain, a later alternative is considered only if earlier alternatives have not been selected

An update can make the next condition true

Initially x = 2

Each numbered row is one separate IF/ELSE decision: test its condition once using the current x, then run only the matching true or false column

Continue to the next numbered row after that branch, even if the preceding test was false. The next row is not an ELSE IF and it uses any updated value of x

The arrow ← assigns a value; = in a test checks equality without changing x. The comparisons ≤ and ≥ include equality, while < and > exclude it; ≠ means not equal

What is the final value of x after all numbered decisions have run?

Before step 1: x = 2. The test 2 < 3 is true, so use only the If true column. Read the current 2 and calculate 2 + 4 = 6. After step 1: x = 6

Before step 2: x = 6. The test 6 > 5 is true, so use only the If true column. Read the current 6 and calculate 6 + 2 = 8. After step 2: x = 8

After all numbered decisions, the final value is x = 8

An update can make the next condition false

Test equality against the updated value

No assignment means no change

If the selected branch says No assignment, keep the current value of x

Skipping an assignment does not replace x with zero or erase the variable

A later row still runs and can use that unchanged value. If a selected branch does contain x ← 2, it replaces x before the next condition is tested

Keep a value through a branch with no assignment

Replace before testing the next boundary

Test current state, select once, then continue

Evaluate the stated comparison and check whether equality is included

Run only one branch for that decision; do not retest it after the selected action

Use the resulting state for the next separate numbered condition

Keep x unchanged when the selected branch has no assignment