Question

我需要一些帮助在JavaScript中实现Radix sort algorthim。

我在网上发现了this example，其中包含以下代码，但我不明白我是如何调用该函数的，因为它似乎是为该网站量身定制的：

// Radix sort a (base 2)
// Numbers must be in the range 0 to 2**31 - 1
function radixSort() {
  readArray('i');
  var b0 = new obj();  // Bin for 0 digits
  var b1 = new obj();  // Bin for 1 digits

  for (var i=0; i<32; ++i) {
    if (form.step.checked) {  // Single step
      writeArray('i','a');

      if (!confirm("Sort on bit "+i))
        return;    
    }

    var mask = 1<<i;     // Digit (2**i)
    var biggest = 2<<i;  // If all of a is smaller, we're done
    var zeros=0;         // Number of elements in b0, b1
    var ones=0;
    var found=false;     // Any digits past i?

    for (var j=0; j<n; ++j) { // Sort into bins b0, b1
      if ((a[j] & mask) == 0)
        b0[zeros++] = a[j];
      else
        b1[ones++] = a[j];

      if (a[j]>=biggest)  // Any more digits to sort on?
        found=true;
    }

    for (j=0; j<zeros; ++j)  // Concatenate b0, b1 back to a
      a[j]=b0[j];

    for (j=0; j<ones; ++j)
      a[j+zeros]=b1[j];

    form.imoves.value = parseInt(form.imoves.value)+n;

    if (!found)
      break;
  }

  writeArray('i','a');
}

Answer 1

术语“基数排序”是一个棘手的问题。实际上有两种不同的排序以类似的方式工作 - MSB（最高有效位）基数和LSB（最低有效位）基数。（有时您会看到B替换为数字D）。以下是两者的实现。

MSB基数：

//arguments to sort an array:
//arr: array to be sorted
//begin: 0
//end: length of array
//bit: maximum number of bits required to represent numbers in arr
function sort(arr, begin, end, bit)
{
  var i, j, mask;
  i = begin;
  j = end;
  mask = 1 << bit;
  while(i < j)
  {
    while(i < j && !(arr[i] & mask))
    {
      ++i;
    }
    while(i < j && (arr[j - 1] & mask))
    {
      --j;
    }
    if(i < j)
    {
      j--;
      var tmp = arr[i];
      arr[i] = arr[j];
      arr[j] = tmp;
      i++;
    }
  }
  if(bit && i > begin)
  {
    sort(arr, begin, i, bit - 1);
  }
  if(bit && i < end)
  {
    sort(arr, i, end, bit - 1);
  }
}
sort(arr, 0, arr.length, 32);  //Here I've assumed that the values in arr are integers that fit in 32 bits

LSB基数：

function insert(arr, i, j)
{
  tmp = arr[i];
  arr.splice(i, 1);
  arr.splice(j, 0, tmp);
}

//arguments to sort an array:
//arr: array to be sorted
function sort(arr)
{
  var bit, end, i, mask;
  bit = 0;
  while(true) 
  {
    mask = 1 << bit;
    i = 0;
    end = arr.length;
    while(i < end)
    {
      if(arr[i] & mask)
      {
        insert(arr, i, arr.length - 1);
        end--;
      }
      else
      {
        i++;
      }
    }
    bit++;
    if(end === arr.length)
    {
      break;
    }
  }
}

我从http://visualsort.appspot.com/中删除了这些算法。然后我将它们编译为http://jashkenas.github.com/coffee-script/的javascript，并编写了插入方法/重新格式化以便于阅读。

Answer 2

您提供的链接已不再可用，但我希望我的实施对您或任何感兴趣的人都尽可能清晰。

我正在实施CRLS第3版第8.2节中引入的基数排序版本

让我们从伪代码开始：

/**
 * @param k: the max of input, used to create a range for our buckets
 * @param exp: 1, 10, 100, 1000, ... used to calculate the nth digit
 */
Array.prototype.countingSort = function (k, exp) {
    /* eslint consistent-this:0 */
    /* self of course refers to this array */
    const self = this;

    /**
     * let's say the this[i] = 123, if exp is 100 returns 1, if exp 10 returns 2, if exp is 1 returns 3
     * @param i
     * @returns {*}
     */
    function index(i) {
        if (exp)
            return Math.floor(self[i] / exp) % 10;
        return i;
    }

    const LENGTH = this.length;

    /* create an array of zeroes */
    let C = Array.apply(null, new Array(k)).map(() => 0);
    let B = [];

    for (let i = 0; i < LENGTH; i++)
        C[index(i)]++;

    for (let i = 1; i < k; i++)
        C[i] += C[i - 1];

    for (let i = LENGTH - 1; i >= 0; i--) {
        B[--C[index(i)]] = this[i];
    }

    B.forEach((e, i) => {
        self[i] = e
    });
}

这是唯一棘手的部分，其余部分非常简单

Array.prototype.radixSort = function () {
    const MAX = Math.max.apply(null, this);

    /* let's say the max is 1926, we should only use exponents 1, 10, 100, 1000 */
    for (let exp = 1; MAX / exp > 1; exp *= 10) {
        this.countingSort(10, exp);
    }
}

现在，您可以在此处测试此方法

let a = [589, 111, 777, 65, 124, 852, 345, 888, 553, 654, 549, 448, 222, 165];
a.radixSort()
console.log(a);

最后，如书中所提到的，这种特殊算法的工作原理只是因为count-sort是一种就地排序算法，这意味着如果两个元素相关联，它们在输入数组中的出现顺序就会被保留。

Answer 3

我的版本更详细，但对于大型数据集执行速度非常快：

      var testArray = [ 331, 454, 230, 34, 343, 45, 59, 453, 345, 231, 9 ];

  function radixBucketSort (arr) {
    var idx1, idx2, idx3, len1, len2, radix, radixKey;
    var radices = {}, buckets = {}, num, curr;
    var currLen, radixStr, currBucket;

    len1 = arr.length;
    len2 = 10;  // radix sort uses ten buckets

    // find the relevant radices to process for efficiency        
    for (idx1 = 0;idx1 < len1;idx1++) {
      radices[arr[idx1].toString().length] = 0;
    }

    // loop for each radix. For each radix we put all the items
    // in buckets, and then pull them out of the buckets.
    for (radix in radices) {          
      // put each array item in a bucket based on its radix value
      len1 = arr.length;
      for (idx1 = 0;idx1 < len1;idx1++) {
        curr = arr[idx1];
        // item length is used to find its current radix value
        currLen = curr.toString().length;
        // only put the item in a radix bucket if the item
        // key is as long as the radix
        if (currLen >= radix) {
          // radix starts from beginning of key, so need to
          // adjust to get redix values from start of stringified key
          radixKey = curr.toString()[currLen - radix];
          // create the bucket if it does not already exist
          if (!buckets.hasOwnProperty(radixKey)) {
            buckets[radixKey] = [];
          }
          // put the array value in the bucket
          buckets[radixKey].push(curr);          
        } else {
          if (!buckets.hasOwnProperty('0')) {
            buckets['0'] = [];
          }
          buckets['0'].push(curr);          
        }
      }
      // for current radix, items are in buckets, now put them
      // back in the array based on their buckets
      // this index moves us through the array as we insert items
      idx1 = 0;
      // go through all the buckets
      for (idx2 = 0;idx2 < len2;idx2++) {
        // only process buckets with items
        if (buckets[idx2] != null) {
          currBucket = buckets[idx2];
          // insert all bucket items into array
          len1 = currBucket.length;
          for (idx3 = 0;idx3 < len1;idx3++) {
            arr[idx1++] = currBucket[idx3];
          }
        }
      }
      buckets = {};
    }
  }
  radixBucketSort(testArray);
  console.dir(testArray);

协助在JavaScript中实现Radix Sort

3 个答案: