【排序】各类排序算法的时间性能比较

• 用 https://www.luogu.com.cn/paste/nzx555us 中代码
• 在此题运行
• 时限 \(\tt 1s\)，空间限制 \(\tt 256MB\)。

	插入排序	冒泡排序	选择排序	希尔排序	快速排序	归并排序	堆排序	计数排序	桶排序	基数排序	std::sort
\(n=10^3\) 随机数据 \(a_i \le 10^5\)	\(\tt 4ms\)	\(\tt 7ms\)	\(\tt 6ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)
\(n=10^3\) 完全正序 \(a_i \le 10^5\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)
\(n=10^3\) 完全倒序 \(a_i \le 10^5\)	\(\tt 4ms\)	\(\tt 8ms\)	\(\tt 8ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)	\(\tt 4ms\)
\(n=10^4\) 随机数据 \(a_i \le 10^5\)	\(\tt 80ms\)	\(\tt 373ms\)	\(\tt 200ms\)	\(\tt 7ms\)	\(\tt 6ms\)	\(\tt 6ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 8ms\)	\(\tt 5ms\)	\(\tt 6ms\)
\(n=10^4\) 随机数据 \(a_i \le 10^5\)	\(\tt 80ms\)	\(\tt 372ms\)	\(\tt 198ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 6ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 6ms\)
\(n=10^4\) 完全正序 \(a_i \le 10^5\)	\(\tt 79ms\)	\(\tt 5ms\)	\(\tt 4ms\)	\(\tt 5ms\)	\(\tt 5ms\)	\(\tt 6ms\)	\(\tt 6ms\)	\(\tt 5ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 5ms\)
\(n=10^4\) 完全倒序 \(a_i \le 10^5\)	\(\tt 101ms\)	\(\tt 407ms\)	\(\tt 394ms\)	\(\tt 5ms\)	\(\tt 5ms\)	\(\tt 5ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 7ms\)	\(\tt 5ms\)	\(\tt 5ms\)
\(n=10^5\) 随机数据 \(a_i \le 10^6\)	TLE	TLE	TLE	\(\tt 52ms\)	\(\tt 28ms\)	\(\tt 29ms\)	\(\tt 40ms\)	\(\tt 19ms\)	\(\tt 44ms\)	\(\tt 22ms\)	\(\tt 30ms\)
\(n=10^6\) 随机数据 \(a_i \le 10^7\)	TLE	TLE	TLE	\(\tt 683ms\)	\(\tt 275ms\)	\(\tt 294ms\)	\(\tt 438ms\)	\(\tt 174ms\)	\(\tt 517ms\)	\(\tt 216ms\)	\(\tt 313ms\)
\(n=10^6\) 随机数据 \(a_i \le 10^8\)	TLE	TLE	TLE	\(\tt 726ms\)	\(\tt 290ms\)	\(\tt 311ms\)	\(\tt 456ms\)	MLE	\(\tt 610ms\)	\(\tt 244ms\)	\(\tt 321ms\)
总时间	\(\tt \color{red}{352ms}\)	\(\color{red}{\tt 1176ms}\)	\(\color{red}{\tt 814ms}\)	\(\tt 1497ms\)	\(\tt 626ms\)	\(\tt 669ms\)	\(\tt 973ms\)	\(\color{red}{\tt 225ms}\)	\(\tt 1212ms\)	\(\tt 514ms\)	\(\tt 698ms\)

总结：当值域较小时，计数排序无疑是最佳选择，在所有 AC 的算法中时间的比较：

基数排序 \(<\) 快速排序 \(<\) 归并排序 \(<\) std::sort \(<\) 堆排序 \(<\) 桶排序 \(<\) 希尔排序。