What is the complexity of this loop? I can’t wrap my head around it.

Question

Asked: June 16, 20262026-06-16T04:37:12+00:00 2026-06-16T04:37:12+00:00

for (i = 0; i < n; ++i) { 
    for (j = i; j < n; ++j) {
        for (k = 0; k < j; ++k) {
            // Do something
        }
    }

}

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Editorial Team · Answer 1 · 2026-06-16T04:37:14+00:00

Editorial Team

O(n^3), I believe. See Square pyramidal number.

i loop has n iterations.

j loop: (1 + 2 + … + n), starting with n iterations, and finishing with 1.

k loop: (1² + 2² + … n²), j times per each iteration of the j loop.

And finally:

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