Nested Loops
Nested loops place one loop inside another. In normal execution, the inner loop completes before the outer loop advances.
Summary
Nested loops place one loop inside another. In normal execution, the inner loop completes before the outer loop advances. To determine total work, count inner-loop body executions across all outer iterations.
| Traversal | Inner-loop behavior | Total body executions |
|---|---|---|
| Rectangular | Fixed iterations for each of outer iterations | |
| Triangular | iterations on outer iteration , from through |
đ§ Key Concepts
- Nested loops
- Outer loop
- Rectangular traversal
- Triangular traversal
- Dependent bounds
- Time complexity
- Auxiliary space
- Break statement
- Continue statement
đ§ Quick Check
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An outer loop runs times, and its inner loop runs times per outer iteration. With no early exits, how many times does the innermost body execute?
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Nested Loops
đ Overview Nested loops place one loop inside another to repeat work across multiple levels of iteration. Their total work depends on how often the inner loop runs during each outer-loop iteration.
đ§ Key Idea Count inner-loop executions across all outer-loop iterations. Multiply iteration counts for fixed, independent bounds; add the changing counts when the inner bound depends on the outer index.
âď¸ Core Details: - In normal execution, the inner loop completes all its iterations before the outer loop advances. - For fixed bounds, the innermost body executes times, where is the outer iteration count and is the inner iteration count. - An inner loop running
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