算法导论1 Problems 答案

1-1

以每月\(30\)天，每年有\(365\)天，一个世纪有\(36525\)天计算。

\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline &\text{1 second}&\text{1 minute}&\text{1 hour}&\text{1 day}&\text{1 month}&\text{1 year}&\text{1 century}\\ \hline \lg n&2^{10^6}&2^{6\times 10^7}&2^{3.6\times 10^9}&2^{8.64\times 10^{10}}&2^{2.592\times10^{12}}&2^{3.1104\times 10^{13}}&2^{3.15576\times 10^{15}}\\ \hline \sqrt{n}&10^{12}&3.6\times 10^{15}&1.296\times 10^{19}&7.46496\times 10^{21}&\approx 6.71846\times 10^{24}&\approx 9.67459\times 10^{26}&\approx 9.96882\times 10^{30}\\ \hline n&10^6&6\times 10^7&3.6\times 10^9&8.64\times 10^{10}&2.592\times10^{12}&3.1104\times 10^{13}&3.15576\times 10^{15}\\ \hline n\lg n&62746&\approx2.80142\times10^{6}&\approx1.33378\times10^{8}&\approx2.75515\times10^{9}&\approx7.18709\times10^{10}&\approx7.87090\times10^{11}&\approx6.86565\times10^{13}\\ \hline n^2&1000&\approx 7745&6000&\approx 293938&\approx 1.60997\times 10^6&\approx 5.57710\times 10^6&\approx 5.61762\times 10^7\\ \hline n^3&100&391&1532&4420&13736&31448&146679\\ \hline 2^n&19&25&31&36&41&44&51\\ \hline n!&9&11&12&13&15&16&17\\ \hline \end{array}\)