JavaScript 实现笛卡尔积算法详解

/**
 * Created by Hawk on 2016/6/18.
 */
var DescartesUtils = {

  /**
   * 如果传入的参数只有一个数组，求笛卡尔积结果
   * @param arr1 一维数组
   * @returns {Array}
   */
  descartes1:function(arr1){
    // 返回结果，是一个二维数组
    var result = [];
    var i = 0;
    for (i = 0; i < arr1.length; i++) {
      var item1 = arr1[i];
      result.push([item1]);
    }
    return result;
  },

  /**
   * 如果传入的参数只有两个数组，求笛卡尔积结果
   * @param arr1 一维数组
   * @param arr2 一维数组
   * @returns {Array}
   */
  descartes2: function(arr1, arr2) {
    // 返回结果，是一个二维数组
    var result = [];
    var i = 0, j = 0;
    for (i = 0; i < arr1.length; i++) {
      var item1 = arr1[i];
      for (j = 0; j < arr2.length; j++) {
        var item2 = arr2[j];
        result.push([item1, item2]);
      }
    }
    return result;
  },

  /**
   *
   * @param arr2D 二维数组
   * @param arr1D 一维数组
   * @returns {Array}
   */
  descartes2DAnd1D: function(arr2D, arr1D) {
    var i = 0, j = 0;
    // 返回结果，是一个二维数组
    var result = [];

    for (i = 0; i < arr2D.length; i++) {
      var arrOf2D = arr2D[i];
      for (j = 0; j < arr1D.length; j++) {
        var item1D = arr1D[j];
        result.push(arrOf2D.concat(item1D));
      }
    }

    return result;
  },

  descartes3: function(list) {
    var listLength = list.length;
    var i = 0, j = 0;
    // 返回结果，是一个二维数组
    var result = [];
    // 为了便于观察，采用这种顺序
    var arr2D = DescartesUtils.descartes2(list[0], list[1]);
    for (i = 2; i < listLength; i++) {
      var arrOfList = list[i];
      arr2D = DescartesUtils.descartes2DAnd1D(arr2D, arrOfList);
    }
    return arr2D;
  },

  //笛卡儿积组合
  descartes: function(list)
  {
    if (!list) {
      return [];
    }
    if (list.length <= 0) {
      return [];
    }
    if (list.length == 1) {
      return DescartesUtils.descartes1(list[0]);
    }
    if (list.length == 2) {
      return DescartesUtils.descartes2(list[0], list[1]);
    }
    if (list.length >= 3) {
      return DescartesUtils.descartes3(list);
    }
  }

};

<!DOCTYPE html>
<html>
<head>
  <meta charset="UTF-8">
  <title></title>
  <script type="text/javascript" src="descartes.js"></script>
</head>
<body>


<div id="resultDiv"></div>
<script type="text/javascript">
  var arr1 = [1,2,3];
  var arr2 = ["a", "b", "c", "d"];
  var list = [arr1, arr2];
  var list2 = [
    [1,2,3],
    ["a", "b", "c"],
    ["A", "B"],
    ["啊","把","车","的"]
  ];
  var result = DescartesUtils.descartes(list2);

  var html = "";
  for (var i = 0; i < result.length; i++) {
    html = html + result[i].join(",") + "<br>";
  }
  document.getElementById("resultDiv").innerHTML = html;
</script>
</body>
</html>