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10
1+2+3+4.
Class 6 · English Medium · Pearson Edexcel · ICT
Data, logic and algorithms
Trace a loop and explain a loop invariant.
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Learn the idea
A loop invariant is a property preserved at a stated point in each iteration. It helps explain correctness beyond a few test cases. A termination argument explains why the loop ends. Tests can reveal errors but do not by themselves prove every input works.
Worked example
To sum1 to n: total=0; for k=1..n add k. After processing k, total equals1+...+k. The next addition preserves that relation, and the finite counter supplies termination.
- Define the initial state.
- Show preservation in one step.
- Explain termination and edge cases.
Your written practice
Show your working on paper and enter your answer here. If it does not match, compare the model and try again.
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7
One per integer1 through7.
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6
Include0 as well as1..5.
Write in your own words. A guardian or teacher should review this response.
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After each processed number, total is the sum of all numbers processed so far.
Name the point in the loop.
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Its condition could remain true indefinitely if progress toward stopping is not guaranteed.
Explain how a variable approaches a stopping condition.
Apply the idea
Write a paper trace and invariant for counting items meeting a condition.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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