如何生成时间序列的所有排列？

Question

我想生成一个时间序列的所有排列的数组。假设数字可以是0,5,10,25，第一个排列是[0,0,0,0,0,0,0]。下一个排列可以是[0,0,0,0,0,0,5]等等，直到[25,25,25,25,25,25,25]。在这种情况下应该有4^6 = 4096个排列，因为有4个数字和7个插槽。

有人可以帮助我了解如何开始解决这个问题吗？我想用javascript写这个。感谢您的考虑。

Answer 1

请参阅附件脚本，我只是放在一起。它应该适用于你的情况。我限制了4种排列，但应该很容易扩展到7个。我希望你看到这种模式。

var array = new Array(); 
 
var values = [0,5,10,25]; 
 

 
for(var i = 0; i < Math.pow(4,4); i++) { 
 
    
 
    // calculate which indexes to retrieve value from loops through 1..4 
 
    var entry = [ 
 
    Math.floor(i/Math.pow(4,0)) % 4, // increment this with every i 
 
    Math.floor(i/Math.pow(4,1)) % 4, // increment this with every 4 * i 
 
    Math.floor(i/Math.pow(4,2)) % 4, // increment this with every 16 * i 
 
    Math.floor(i/Math.pow(4,3)) % 4 // increment this with every 64 * i etc 
 
    ]; 
 
    
 
    array.push([values[entry[0]], values[entry[1]], values[entry[2]],values[entry[3]]]); 
 
    
 
} 
 

 
document.write(JSON.stringify(array));

Answer 2

下面，我创建了一个循环来生成所有排列。这是一个迭代的解决方案。

更新：我减少了我的代码到以下几点：

function permutations(series, size) { 
    return zeroFill(Math.pow(series.length,size)).map(function(r,i) { 
    return zeroFill(size).map(function(c,j) { 
     return series[Math.floor(i/Math.pow(series.length,j))%series.length]; 
    }).reverse(); 
    }); 
} 
function zeroFill(n) { 
    return new Array(n+1).join('0').split(''); 
} 

因为这是一个非常内存密集型的过程，我从列表中删除25并降低每个处理进入的5长度。

var out = document.getElementById('output'); 
 
var permutations = generate([0, 5, 10], 5); 
 

 
printResults(permutations); 
 

 
// Generate permutations. 
 
function generate(series, size) { 
 
    var result = []; 
 
    var len = series.length; 
 
    var limit = Math.pow(len, size); 
 

 
    for (var i = 0; i < limit; i++) { 
 
    var entry = []; 
 
    for (var j = 0; j < size; j++) { 
 
     entry[size-j] = series[Math.floor(i/Math.pow(len, j)) % len]; 
 
    } 
 
    result.push(entry); 
 
    } 
 
    return result; 
 
} 
 

 
// Utility Functions - These are for display purposes. 
 
function printResults(list) { 
 
    var width = ('' + list.length).length; 
 
    list.forEach(function(list, index) { 
 
    print('[' + FormatNumberLength(index, width) + '] ' + numberJoin(list, 3)); 
 
    }); 
 
} 
 
function print(text) { 
 
    out.innerHTML += text + '<br />'; 
 
} 
 
function numberJoin(intList, width) { 
 
    return intList.map(function(value) { 
 
    return FormatNumberLength(value, width); 
 
    }).join(' '); 
 
} 
 
function FormatNumberLength(num, length, useZero) { 
 
    var c = useZero ? '0' : ' '; 
 
    var r = "" + num; 
 
    while (r.length < length) r = c + r; 
 
    return r; 
 
}

#output { 
 
    font-family: monospace; 
 
    white-space: pre; 
 
}

<div id="output"></div>

预期结果

[ 0] 0 0 0 0 0 
[ 1] 0 0 0 0 5 
[ 2] 0 0 0 0 10 
[ 3] 0 0 0 5 0 
[ 4] 0 0 0 5 5 
[ 5] 0 0 0 5 10 
[ 6] 0 0 0 10 0 
[ 7] 0 0 0 10 5 
[ 8] 0 0 0 10 10 
[ 9] 0 0 5 0 0 
[ 10] 0 0 5 0 5 
[ 11] 0 0 5 0 10 
[ 12] 0 0 5 5 0 
[ 13] 0 0 5 5 5 
[ 14] 0 0 5 5 10 
[ 15] 0 0 5 10 0 
[ 16] 0 0 5 10 5 
[ 17] 0 0 5 10 10 
[ 18] 0 0 10 0 0 
[ 19] 0 0 10 0 5 
[ 20] 0 0 10 0 10 
[ 21] 0 0 10 5 0 
[ 22] 0 0 10 5 5 
[ 23] 0 0 10 5 10 
[ 24] 0 0 10 10 0 
[ 25] 0 0 10 10 5 
[ 26] 0 0 10 10 10 
[ 27] 0 5 0 0 0 
[ 28] 0 5 0 0 5 
[ 29] 0 5 0 0 10 
[ 30] 0 5 0 5 0 
[ 31] 0 5 0 5 5 
[ 32] 0 5 0 5 10 
[ 33] 0 5 0 10 0 
[ 34] 0 5 0 10 5 
[ 35] 0 5 0 10 10 
[ 36] 0 5 5 0 0 
[ 37] 0 5 5 0 5 
[ 38] 0 5 5 0 10 
[ 39] 0 5 5 5 0 
[ 40] 0 5 5 5 5 
[ 41] 0 5 5 5 10 
[ 42] 0 5 5 10 0 
[ 43] 0 5 5 10 5 
[ 44] 0 5 5 10 10 
[ 45] 0 5 10 0 0 
[ 46] 0 5 10 0 5 
[ 47] 0 5 10 0 10 
[ 48] 0 5 10 5 0 
[ 49] 0 5 10 5 5 
[ 50] 0 5 10 5 10 
[ 51] 0 5 10 10 0 
[ 52] 0 5 10 10 5 
[ 53] 0 5 10 10 10 
[ 54] 0 10 0 0 0 
[ 55] 0 10 0 0 5 
[ 56] 0 10 0 0 10 
[ 57] 0 10 0 5 0 
[ 58] 0 10 0 5 5 
[ 59] 0 10 0 5 10 
[ 60] 0 10 0 10 0 
[ 61] 0 10 0 10 5 
[ 62] 0 10 0 10 10 
[ 63] 0 10 5 0 0 
[ 64] 0 10 5 0 5 
[ 65] 0 10 5 0 10 
[ 66] 0 10 5 5 0 
[ 67] 0 10 5 5 5 
[ 68] 0 10 5 5 10 
[ 69] 0 10 5 10 0 
[ 70] 0 10 5 10 5 
[ 71] 0 10 5 10 10 
[ 72] 0 10 10 0 0 
[ 73] 0 10 10 0 5 
[ 74] 0 10 10 0 10 
[ 75] 0 10 10 5 0 
[ 76] 0 10 10 5 5 
[ 77] 0 10 10 5 10 
[ 78] 0 10 10 10 0 
[ 79] 0 10 10 10 5 
[ 80] 0 10 10 10 10 
[ 81] 5 0 0 0 0 
[ 82] 5 0 0 0 5 
[ 83] 5 0 0 0 10 
[ 84] 5 0 0 5 0 
[ 85] 5 0 0 5 5 
[ 86] 5 0 0 5 10 
[ 87] 5 0 0 10 0 
[ 88] 5 0 0 10 5 
[ 89] 5 0 0 10 10 
[ 90] 5 0 5 0 0 
[ 91] 5 0 5 0 5 
[ 92] 5 0 5 0 10 
[ 93] 5 0 5 5 0 
[ 94] 5 0 5 5 5 
[ 95] 5 0 5 5 10 
[ 96] 5 0 5 10 0 
[ 97] 5 0 5 10 5 
[ 98] 5 0 5 10 10 
[ 99] 5 0 10 0 0 
[100] 5 0 10 0 5 
[101] 5 0 10 0 10 
[102] 5 0 10 5 0 
[103] 5 0 10 5 5 
[104] 5 0 10 5 10 
[105] 5 0 10 10 0 
[106] 5 0 10 10 5 
[107] 5 0 10 10 10 
[108] 5 5 0 0 0 
[109] 5 5 0 0 5 
[110] 5 5 0 0 10 
[111] 5 5 0 5 0 
[112] 5 5 0 5 5 
[113] 5 5 0 5 10 
[114] 5 5 0 10 0 
[115] 5 5 0 10 5 
[116] 5 5 0 10 10 
[117] 5 5 5 0 0 
[118] 5 5 5 0 5 
[119] 5 5 5 0 10 
[120] 5 5 5 5 0 
[121] 5 5 5 5 5 
[122] 5 5 5 5 10 
[123] 5 5 5 10 0 
[124] 5 5 5 10 5 
[125] 5 5 5 10 10 
[126] 5 5 10 0 0 
[127] 5 5 10 0 5 
[128] 5 5 10 0 10 
[129] 5 5 10 5 0 
[130] 5 5 10 5 5 
[131] 5 5 10 5 10 
[132] 5 5 10 10 0 
[133] 5 5 10 10 5 
[134] 5 5 10 10 10 
[135] 5 10 0 0 0 
[136] 5 10 0 0 5 
[137] 5 10 0 0 10 
[138] 5 10 0 5 0 
[139] 5 10 0 5 5 
[140] 5 10 0 5 10 
[141] 5 10 0 10 0 
[142] 5 10 0 10 5 
[143] 5 10 0 10 10 
[144] 5 10 5 0 0 
[145] 5 10 5 0 5 
[146] 5 10 5 0 10 
[147] 5 10 5 5 0 
[148] 5 10 5 5 5 
[149] 5 10 5 5 10 
[150] 5 10 5 10 0 
[151] 5 10 5 10 5 
[152] 5 10 5 10 10 
[153] 5 10 10 0 0 
[154] 5 10 10 0 5 
[155] 5 10 10 0 10 
[156] 5 10 10 5 0 
[157] 5 10 10 5 5 
[158] 5 10 10 5 10 
[159] 5 10 10 10 0 
[160] 5 10 10 10 5 
[161] 5 10 10 10 10 
[162] 10 0 0 0 0 
[163] 10 0 0 0 5 
[164] 10 0 0 0 10 
[165] 10 0 0 5 0 
[166] 10 0 0 5 5 
[167] 10 0 0 5 10 
[168] 10 0 0 10 0 
[169] 10 0 0 10 5 
[170] 10 0 0 10 10 
[171] 10 0 5 0 0 
[172] 10 0 5 0 5 
[173] 10 0 5 0 10 
[174] 10 0 5 5 0 
[175] 10 0 5 5 5 
[176] 10 0 5 5 10 
[177] 10 0 5 10 0 
[178] 10 0 5 10 5 
[179] 10 0 5 10 10 
[180] 10 0 10 0 0 
[181] 10 0 10 0 5 
[182] 10 0 10 0 10 
[183] 10 0 10 5 0 
[184] 10 0 10 5 5 
[185] 10 0 10 5 10 
[186] 10 0 10 10 0 
[187] 10 0 10 10 5 
[188] 10 0 10 10 10 
[189] 10 5 0 0 0 
[190] 10 5 0 0 5 
[191] 10 5 0 0 10 
[192] 10 5 0 5 0 
[193] 10 5 0 5 5 
[194] 10 5 0 5 10 
[195] 10 5 0 10 0 
[196] 10 5 0 10 5 
[197] 10 5 0 10 10 
[198] 10 5 5 0 0 
[199] 10 5 5 0 5 
[200] 10 5 5 0 10 
[201] 10 5 5 5 0 
[202] 10 5 5 5 5 
[203] 10 5 5 5 10 
[204] 10 5 5 10 0 
[205] 10 5 5 10 5 
[206] 10 5 5 10 10 
[207] 10 5 10 0 0 
[208] 10 5 10 0 5 
[209] 10 5 10 0 10 
[210] 10 5 10 5 0 
[211] 10 5 10 5 5 
[212] 10 5 10 5 10 
[213] 10 5 10 10 0 
[214] 10 5 10 10 5 
[215] 10 5 10 10 10 
[216] 10 10 0 0 0 
[217] 10 10 0 0 5 
[218] 10 10 0 0 10 
[219] 10 10 0 5 0 
[220] 10 10 0 5 5 
[221] 10 10 0 5 10 
[222] 10 10 0 10 0 
[223] 10 10 0 10 5 
[224] 10 10 0 10 10 
[225] 10 10 5 0 0 
[226] 10 10 5 0 5 
[227] 10 10 5 0 10 
[228] 10 10 5 5 0 
[229] 10 10 5 5 5 
[230] 10 10 5 5 10 
[231] 10 10 5 10 0 
[232] 10 10 5 10 5 
[233] 10 10 5 10 10 
[234] 10 10 10 0 0 
[235] 10 10 10 0 5 
[236] 10 10 10 0 10 
[237] 10 10 10 5 0 
[238] 10 10 10 5 5 
[239] 10 10 10 5 10 
[240] 10 10 10 10 0 
[241] 10 10 10 10 5 
[242] 10 10 10 10 10