Some boundaries you should know to approximate time and space complexity of your algorithm.

• $2^{10} = 1,024 \approx 10^{3}, 2^{20} = 1,048,576 \approx 10^{6}$
• 32-bit signed integers (int) and 64-bit signed integers (long long) have upper limits of $2^{31} − 1 \approx 2 \times 10^{9}$ (safe for up to $\approx 9$ decimal digits) and $2^{63} − 1 \approx 9 \times 10^{18}$ (safe for up to $\approx 18$ decimal digits) respectively.
• Unsigned integers can be used if only non-negative numbers are required. 32-bit unsigned integers (unsigned int) and 64-bit unsigned integers (unsigned long long) have upper limits of $2^{32} − 1 \approx 4 \times 10^{9}$ and $2^{64} − 1 \approx 1.8 \times 10^{19}$ respectively.
• There are $n!$ permutations and $2^{n}$ subsets (or combinations) of n elements.
• The best time complexity of a comparison-based sorting algorithm is $Ω(n\log_{2}{n})$.

Notes:

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