// Combinations and permutations.

// Counts can be verified at http://www.calculatorsoup.com/calculators/discretemathematics/permutations.php

// noprotect

​

var combinations = function(arr) {

  var result = [];

  for (var i=0; i<arr.length; i++) {

    var item1 = arr[i];

    for (var j=i+1; j<arr.length; j++) {

      var item2 = arr[j];

      result.push([item1, item2]);

    }

  }

  return result;

}

​

var permutations = function(arr) {

  var result = [];

  for (var i=0; i<arr.length; i++) {

    var item1 = arr[i];

    for (var j=0; j<arr.length; j++) {

      var item2 = arr[j];

      if (item1 !== item2) {

        result.push([item1, item2]);

      }

    }

  }

  return result;  

}

​

var combinationsn = function(arr, n) {

  var result = [];

​

  var indexes = [];

  for (var i=0; i<n; i++) {

      indexes.push(i);

  }

  var i=0;

  while (i < arr.length) {

    var items = [];

    for (var j=0; j<indexes.length; j++) {

      var index = indexes[j];

      items.push(arr[index]);

    }

​

    var idx = indexes.length - 1;

    var lastIndex = indexes[idx];

    while (lastIndex == arr.length - 1 && idx > 0) {

      idx--;

      lastIndex = indexes[idx];

    }

    if (indexes[idx] < arr.length - 1) {

      indexes[idx]++;

​

      var count = 0;

      for (var k=idx + 1; k<indexes.length; k++) {

        indexes[k] = indexes[idx + count] + 1;

        if (indexes[k] >= arr.length) {

          indexes[k] = arr.length - 1;

        }

        count++;

      }

​

      i = 0;

    }

​

    var skip = false;

    for (var k=0; k<items.length - 1; k++) {

      for (var l=k+1; l<items.length; l++) {

        if (items[k] === items[l]) {

          skip = true;

          break;

        }

      }

    }

​

    if (n == 1) {

      for (var k=0; k<result.length; k++) {

        if (result[k][0] === items[0]) {

          skip = true;

          break;

        }

      }

    }

​

    if (!skip) {

      result.push(items);

    }

    i++;

  }

​

  return result;

}

​

var permutationsn = function(arr, n) {

  var result = [];

​

  var indexes = [];

  for (var i=0; i<n; i++) {

      indexes.push(i);

  }

  var i=0;

  while (i < arr.length) {

    var items = [];

    for (var j=0; j<indexes.length; j++) {

      var index = indexes[j];

      items.push(arr[index]);

    }

​

    var idx = indexes.length - 1;

    var lastIndex = indexes[idx];

    while (lastIndex == arr.length - 1 && idx > 0) {

      idx--;

      lastIndex = indexes[idx];

    }

    if (indexes[idx] < arr.length - 1) {

      indexes[idx]++;

​

      for (var k=idx + 1; k<indexes.length; k++) {

        indexes[k] = 0;

      }

​

      i = 0;

    }

​

    var skip = false;

    for (var k=0; k<items.length - 1; k++) {

      for (var l=k+1; l<items.length; l++) {

        if (items[k] === items[l]) {

          skip = true;

          break;

        }

      }

    }

​

    if (n == 1) {

      for (var k=0; k<result.length; k++) {

        if (result[k][0] === items[0]) {

          skip = true;

          break;

        }

      }

    }

​

    if (!skip) {

      result.push(items);

    }

    i++;

  }

​

  return result;

}

​

var factorial = function(n) {

  var result = 1;

​

  for (var i=n; i>0; i--) {

    result *= i;

  }

​

  return result;

}

​

var combinationCount = function(n, k) {

  var result = 1;

​

  var divisor = (factorial(k) * factorial(n - k));

  if (divisor) {

    result = factorial(n) / divisor;

  }

​

  return result;

}

​

var permutationCount = function(n, k) {

  var result = 1;

​

  var divisor = factorial(n - k);

  if (divisor) {

    result = factorial(n) / divisor;

  }

​

  return result;

}

​

var list = ['x','y','a','b','c','d','e','f'];

var c = combinations(list);

console.log(c.length + ' combinations.');

console.log(c);

​

var p = permutations(list);

console.log(p.length + ' permutations.');

console.log(p);

​

for (var i=1; i<=list.length; i++) {

  console.log(combinationsn(list, i).length == combinationCount(list.length, i));

}

​

for (var i=1; i<=list.length; i++) {

  console.log(permutationsn(list, i).length == permutationCount(list.length, i));

}