State, assignment and sequence

In this pseudocode, what does x ← 5 do?

The arrow points towards the target that receives the value

Keep a record of the current state

An algorithm is a precise set of steps for carrying out a task. These first examples are short sequences with no branches or loops

A variable has a name and a current stored value. The state is the collection of current values being tracked

For x ← x + 2, first read the old x, add 2, then store the result in x. This is an update instruction, not an algebraic equation claiming x equals x + 2

The next instruction uses the updated state. Record the state after each step instead of trying to apply all statements at once

These tasks explicitly use numeric values; they do not describe links between mutable objects or other data types

Use the updated value at the next step

Use this complete initial state and execute the numbered instructions once, from top to bottom

The arrow ← means assignment, not an algebraic equation: first evaluate its right side using the values just before that step, then replace only the target variable on the left

All values here are numbers. Copying a variable copies its current numerical value, not a live link or spreadsheet formula

What is the final value of x after every instruction has run?

Before step 1: x = 3. x ← x + 2 uses the current value 3 of x, giving 3 + 2 = 5 and stores 5 in x. After step 1: x = 5

Before step 2: x = 5. x ← x + 1 uses the current value 5 of x, giving 5 + 1 = 6 and stores 6 in x. After step 2: x = 6

The requested final state is x = 6

Replace before adding

Start with x = 5 in both cases. Replace then add runs x ← 2 followed by x ← x + 4. Add then replace runs those two instructions in the opposite order. Predict the state after each step before changing the selector

With Add then replace selected, why is the final value 2 rather than 9?

Keep the last stored value

Copy the value at that moment

For numeric values here, y ← x reads the current value of x and stores that value in y

A later assignment to x does not automatically change y. The earlier instruction copied a number, not a live connection

Keep separate state entries for x and y. Update only the target named on the left of each arrow

This differs from a spreadsheet cell retaining a formula that recalculates from another cell; use the rules of the model actually stated

An earlier copy retains its number

Use this complete initial state and execute the numbered instructions once, from top to bottom

The arrow ← means assignment, not an algebraic equation: first evaluate its right side using the values just before that step, then replace only the target variable on the left

All values here are numbers. Copying a variable copies its current numerical value, not a live link or spreadsheet formula

Enter the final values of x and y after every instruction has run

Before step 1: x = 2, y = 5. y ← x uses the current value 2 of x and stores 2 in y. After step 1: x = 2, y = 2

Before step 2: x = 2, y = 2. x ← x + 3 uses the current value 2 of x, giving 2 + 3 = 5 and stores 5 in x. After step 2: x = 5, y = 2

The requested final state is x = 5, y = 2

Change the source after copying it

Read the arrow direction

An overwrite can lose a value needed later

Starting with x = 2 and y = 7, consider these two instructions

The first instruction replaces x with 7. The second reads that updated x, so both variables finish with 7

The original value 2 is no longer in either variable. These two assignments do not swap the original values

Trace the supplied instructions, not their hoped-for purpose

Preserve a needed value before overwriting it

A temporary variable can retain the original x while x is replaced

For the following sequence, start with x = 2, y = 7 and temp = 0

The first instruction saves the original x in temp. The next two put the original y into x and the saved original x into y

Follow the saved value through the sequence

Use this complete initial state and execute the numbered instructions once, from top to bottom

The arrow ← means assignment, not an algebraic equation: first evaluate its right side using the values just before that step, then replace only the target variable on the left

All values here are numbers. Copying a variable copies its current numerical value, not a live link or spreadsheet formula

Enter the final values of x and y after every instruction has run

Before step 1: x = 2, y = 7, temp = 0. temp ← x uses the current value 2 of x and stores 2 in temp. After step 1: x = 2, y = 7, temp = 2

Before step 2: x = 2, y = 7, temp = 2. x ← y uses the current value 7 of y and stores 7 in x. After step 2: x = 7, y = 7, temp = 2

Before step 3: x = 7, y = 7, temp = 2. y ← temp uses the current value 2 of temp and stores 2 in y. After step 3: x = 7, y = 2, temp = 2

The requested final state is x = 7, y = 2

Trace a temporary value with different starting values

Start with numeric x = 4 and y = 0. Execute y ← x once, then execute x ← 9. No later instruction targets y. What is y at the end?

The earlier assignment copied x's value at that time

Read current state and update one target at a time

An assignment evaluates its right side from the current state before replacing its target

Instructions run in order; the next instruction sees any earlier updates

A copied numeric value does not become a live link. Preserve a value before overwriting it if it will be needed later