a20150604

追求高效的纯批置换算法: 从生成一个元素的全排列, 逐次进阶扩展到 2, 3, .... 个元素, 排除命令行窗口显示耗时, 仅数据生成时间 < 1秒 (i3 处理器)

@echo off & setlocal enabledelayedexpansion & mode 160, 1000
set z=1;
set z
for /L %%j in (2 1 6) do (
    set /a k=%%j-1
    set x=
    for /L %%i in (1 1 !k!) do (
        set t=!z:%%i=%%j!
        set x=!x!!t:;=%%i;!
    )
    set z=!z:;=%%j;!!x!
    set z
)
echo;complete 6

REM 7个元素的全排列用带分隔符的单变量存储超出批处理变量存储极限, 只能另行处理
REM 数字形式
REM echo;!z:;=7;!
REM for /L %%i in (1 1 6) do (
    REM set t=!z:%%i=7!
    REM echo;!t:;=%%i;!
REM )

set t7=!z:;=e;!
for /L %%i in (1 1 6) do (
    set t%%i=!z:%%i=e!
    set t%%i=!t%%i:;=%%i;!
)
for /L %%i in (1 1 7) do (
    for %%Q in (1:b 2:a 3:t 4:h 5:o 6:m) do for /f "tokens=1-2 delims=:" %%W in ("%%Q") do set t%%i=!t%%i:%%W=%%X!
    echo;!t%%i:;= !
)

echo;complete 7
pause
exit
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a20150604

Wolfram 语言

Permutations[{b,a,t,h,o,m,e}]
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格式处理一下

StringJoin /@ Permutations[Characters["bathome"]]
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a20150604

8 楼置换算法的 JS 和 VBS 版

JS

Z = "1;";
for( j = 2; j <= 7; j++ ) {
    t = Z;
    Z = Z.replace(/;/g, j + ";")
    for ( i = 1; i <= j - 1; i++ ) Z = Z + t.replace(RegExp(i, "g"), j).replace(/;/g, i + ";");
}
for( i = 1; i <= 7; i++ ) Z = Z.replace(RegExp(i, "g"), "bathome".substr(i - 1, 1));
console.log(Z);
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VBS

Z = "1;"
For j = 2 To 7
    t = Z
    Z = Replace(Z, ";", j & ";")
    For i = 1 To j - 1
      Z = Z & Replace(Replace(t, i, j), ";", i & ";")
    Next
Next
For i = 1 To 7
    Z = Replace(Z, i, Mid("bathome", i, 1))
Next
WScript.Echo Z
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a20150604

http://www.cs.utsa.edu/~wagner/knuth/

Donald E. Knuth  
  The Art of Computer
Programming
Volume 4,
Combinatorial Algorithms