THINK++ — Engineering Visualized

Loop in Loop

Nested Loops

A loop inside another loop. The inner loop completes all its iterations for each single iteration of the outer loop. Time complexity is typically O(n²).

2D MATRIX TRAVERSAL

for (int i = 0; i < rows; i++) {
    for (int j = 0; j < cols; j++) {
        cout << matrix[i][j] << " ";
    }
    cout << endl;
}

Pattern: Right triangle

for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= i; j++)
        cout << "* ";
    cout << endl;
}
// *
// * *
// * * *

COMPLEXITY WARNING

2 nested loops = O(n²), 3 nested = O(n³). For n=10⁵, O(n²) ≈ 10¹⁰ operations — far too slow. Always check constraints before nesting.

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