Complexity estimator
Read the constraint (e.g. n ≤ 2·10⁵) and the time limit, and instantly see which algorithm complexities fit, are risky, or will TLE — so you pick the right approach before you start coding.
Operation budget ≈ 1.0×10⁸ comfortable · 1.0×10⁹ ceiling— aim for O(n log² n) or better
| Complexity | ~Operations | Verdict | Typical use |
|---|---|---|---|
| O(1) | 1 | ✓ fits | — |
| O(log n) | 18 | ✓ fits | — |
| O(√n) | 448 | ✓ fits | — |
| O(n) | 2.0×10⁵ | ✓ fits | — |
| O(n log n) | 3.5×10⁶ | ✓ fits | sort / heap / segment tree |
| O(n √n) | 8.9×10⁷ | ✓ fits | Mo's algorithm, sqrt decomp |
| O(n log² n) | 6.2×10⁷ | ✓ fits | — |
| O(n²) | 4.0×10¹⁰ | ✗ TLE | nested loops / simple DP |
| O(n² log n) | 7.0×10¹¹ | ✗ TLE | — |
| O(n³) | 8.0×10¹⁵ | ✗ TLE | Floyd-Warshall, matrix DP |
| O(2^n · n) | ∞ | ✗ TLE | bitmask DP (n ≤ ~22) |
| O(n!) | ∞ | ✗ TLE | brute permutations (n ≤ ~11) |
Heuristic: ~10⁸ simple C++ ops/sec comfortable, ~10⁹ as a risky ceiling. Constant factors, cache, and language overhead shift this — treat it as a starting point, not a guarantee.