我试图写一个函数,它做以下工作:

以一个整数数组作为参数(例如[1,2,3,4]) 创建一个包含[1,2,3,4]的所有可能排列的数组,每个排列的长度为4

下面的函数(我在网上找到的)通过接受一个字符串作为参数,并返回该字符串的所有排列来实现这一点

我不知道如何修改它,使它与整数数组一起工作,(我认为这与一些方法在字符串上的工作方式不同于在整数上的工作方式有关,但我不确定…)

let permArr = [];
let usedChars = [];

function permute(input) {
    const chars = input.split("");
    for (let i = 0; i < chars.length; i++) {
        const ch = chars.splice(i, 1);
        usedChars.push(ch);
        if (chars.length === 0) {
            permArr[permArr.length] = usedChars.join("");
        }
        permute(chars.join(""));
        chars.splice(i, 0, ch);
        usedChars.pop();
    }
    return permArr
};

注意:我希望函数返回整数数组,而不是字符串数组。

我真的需要解决方案是在JavaScript。我已经知道如何在python中做到这一点


当前回答

以下非常高效的算法使用Heap的方法生成运行时复杂度为O(N!)的N个元素的所有排列:

function permute(permutation) { var length = permutation.length, result = [permutation.slice()], c = new Array(length).fill(0), i = 1, k, p; while (i < length) { if (c[i] < i) { k = i % 2 && c[i]; p = permutation[i]; permutation[i] = permutation[k]; permutation[k] = p; ++c[i]; i = 1; result.push(permutation.slice()); } else { c[i] = 0; ++i; } } return result; } console.log(permute([1, 2, 3]));

同样的算法实现为一个空间复杂度为O(N)的生成器:

function* permute(permutation) { var length = permutation.length, c = Array(length).fill(0), i = 1, k, p; yield permutation.slice(); while (i < length) { if (c[i] < i) { k = i % 2 && c[i]; p = permutation[i]; permutation[i] = permutation[k]; permutation[k] = p; ++c[i]; i = 1; yield permutation.slice(); } else { c[i] = 0; ++i; } } } // Memory efficient iteration through permutations: for (var permutation of permute([1, 2, 3])) console.log(permutation); // Simple array conversion: var permutations = [...permute([1, 2, 3])];

性能比较

请随意将您的实现添加到以下benchmark.js测试套件中:

function permute_SiGanteng(input) { var permArr = [], usedChars = []; function permute(input) { var i, ch; for (i = 0; i < input.length; i++) { ch = input.splice(i, 1)[0]; usedChars.push(ch); if (input.length == 0) { permArr.push(usedChars.slice()); } permute(input); input.splice(i, 0, ch); usedChars.pop(); } return permArr } return permute(input); } function permute_delimited(inputArr) { var results = []; function permute(arr, memo) { var cur, memo = memo || []; for (var i = 0; i < arr.length; i++) { cur = arr.splice(i, 1); if (arr.length === 0) { results.push(memo.concat(cur)); } permute(arr.slice(), memo.concat(cur)); arr.splice(i, 0, cur[0]); } return results; } return permute(inputArr); } function permute_monkey(inputArray) { return inputArray.reduce(function permute(res, item, key, arr) { return res.concat(arr.length > 1 && arr.slice(0, key).concat(arr.slice(key + 1)).reduce(permute, []).map(function(perm) { return [item].concat(perm); }) || item); }, []); } function permute_Oriol(input) { var permArr = [], usedChars = []; return (function main() { for (var i = 0; i < input.length; i++) { var ch = input.splice(i, 1)[0]; usedChars.push(ch); if (input.length == 0) { permArr.push(usedChars.slice()); } main(); input.splice(i, 0, ch); usedChars.pop(); } return permArr; })(); } function permute_MarkusT(input) { function permutate(array, callback) { function p(array, index, callback) { function swap(a, i1, i2) { var t = a[i1]; a[i1] = a[i2]; a[i2] = t; } if (index == array.length - 1) { callback(array); return 1; } else { var count = p(array, index + 1, callback); for (var i = index + 1; i < array.length; i++) { swap(array, i, index); count += p(array, index + 1, callback); swap(array, i, index); } return count; } } if (!array || array.length == 0) { return 0; } return p(array, 0, callback); } var result = []; permutate(input, function(a) { result.push(a.slice(0)); }); return result; } function permute_le_m(permutation) { var length = permutation.length, result = [permutation.slice()], c = new Array(length).fill(0), i = 1, k, p; while (i < length) { if (c[i] < i) { k = i % 2 && c[i], p = permutation[i]; permutation[i] = permutation[k]; permutation[k] = p; ++c[i]; i = 1; result.push(permutation.slice()); } else { c[i] = 0; ++i; } } return result; } function permute_Urielzen(arr) { var finalArr = []; var iterator = function (arrayTaken, tree) { for (var i = 0; i < tree; i++) { var temp = arrayTaken.slice(); temp.splice(tree - 1 - i, 0, temp.splice(tree - 1, 1)[0]); if (tree >= arr.length) { finalArr.push(temp); } else { iterator(temp, tree + 1); } } } iterator(arr, 1); return finalArr; } function permute_Taylor_Hakes(arr) { var permutations = []; if (arr.length === 1) { return [ arr ]; } for (var i = 0; i < arr.length; i++) { var subPerms = permute_Taylor_Hakes(arr.slice(0, i).concat(arr.slice(i + 1))); for (var j = 0; j < subPerms.length; j++) { subPerms[j].unshift(arr[i]); permutations.push(subPerms[j]); } } return permutations; } var Combinatorics = (function () { 'use strict'; var version = "0.5.2"; /* combinatory arithmetics */ var P = function(m, n) { var p = 1; while (n--) p *= m--; return p; }; var C = function(m, n) { if (n > m) { return 0; } return P(m, n) / P(n, n); }; var factorial = function(n) { return P(n, n); }; var factoradic = function(n, d) { var f = 1; if (!d) { for (d = 1; f < n; f *= ++d); if (f > n) f /= d--; } else { f = factorial(d); } var result = [0]; for (; d; f /= d--) { result[d] = Math.floor(n / f); n %= f; } return result; }; /* common methods */ var addProperties = function(dst, src) { Object.keys(src).forEach(function(p) { Object.defineProperty(dst, p, { value: src[p], configurable: p == 'next' }); }); }; var hideProperty = function(o, p) { Object.defineProperty(o, p, { writable: true }); }; var toArray = function(f) { var e, result = []; this.init(); while (e = this.next()) result.push(f ? f(e) : e); this.init(); return result; }; var common = { toArray: toArray, map: toArray, forEach: function(f) { var e; this.init(); while (e = this.next()) f(e); this.init(); }, filter: function(f) { var e, result = []; this.init(); while (e = this.next()) if (f(e)) result.push(e); this.init(); return result; }, lazyMap: function(f) { this._lazyMap = f; return this; }, lazyFilter: function(f) { Object.defineProperty(this, 'next', { writable: true }); if (typeof f !== 'function') { this.next = this._next; } else { if (typeof (this._next) !== 'function') { this._next = this.next; } var _next = this._next.bind(this); this.next = (function() { var e; while (e = _next()) { if (f(e)) return e; } return e; }).bind(this); } Object.defineProperty(this, 'next', { writable: false }); return this; } }; /* power set */ var power = function(ary, fun) { var size = 1 << ary.length, sizeOf = function() { return size; }, that = Object.create(ary.slice(), { length: { get: sizeOf } }); hideProperty(that, 'index'); addProperties(that, { valueOf: sizeOf, init: function() { that.index = 0; }, nth: function(n) { if (n >= size) return; var i = 0, result = []; for (; n; n >>>= 1, i++) if (n & 1) result.push(this[i]); return (typeof (that._lazyMap) === 'function')?that._lazyMap(result):result; }, next: function() { return this.nth(this.index++); } }); addProperties(that, common); that.init(); return (typeof (fun) === 'function') ? that.map(fun) : that; }; /* combination */ var nextIndex = function(n) { var smallest = n & -n, ripple = n + smallest, new_smallest = ripple & -ripple, ones = ((new_smallest / smallest) >> 1) - 1; return ripple | ones; }; var combination = function(ary, nelem, fun) { if (!nelem) nelem = ary.length; if (nelem < 1) throw new RangeError; if (nelem > ary.length) throw new RangeError; var first = (1 << nelem) - 1, size = C(ary.length, nelem), maxIndex = 1 << ary.length, sizeOf = function() { return size; }, that = Object.create(ary.slice(), { length: { get: sizeOf } }); hideProperty(that, 'index'); addProperties(that, { valueOf: sizeOf, init: function() { this.index = first; }, next: function() { if (this.index >= maxIndex) return; var i = 0, n = this.index, result = []; for (; n; n >>>= 1, i++) { if (n & 1) result[result.length] = this[i]; } this.index = nextIndex(this.index); return (typeof (that._lazyMap) === 'function')?that._lazyMap(result):result; } }); addProperties(that, common); that.init(); return (typeof (fun) === 'function') ? that.map(fun) : that; }; /* permutation */ var _permutation = function(ary) { var that = ary.slice(), size = factorial(that.length); that.index = 0; that.next = function() { if (this.index >= size) return; var copy = this.slice(), digits = factoradic(this.index, this.length), result = [], i = this.length - 1; for (; i >= 0; --i) result.push(copy.splice(digits[i], 1)[0]); this.index++; return (typeof (that._lazyMap) === 'function')?that._lazyMap(result):result; }; return that; }; // which is really a permutation of combination var permutation = function(ary, nelem, fun) { if (!nelem) nelem = ary.length; if (nelem < 1) throw new RangeError; if (nelem > ary.length) throw new RangeError; var size = P(ary.length, nelem), sizeOf = function() { return size; }, that = Object.create(ary.slice(), { length: { get: sizeOf } }); hideProperty(that, 'cmb'); hideProperty(that, 'per'); addProperties(that, { valueOf: function() { return size; }, init: function() { this.cmb = combination(ary, nelem); this.per = _permutation(this.cmb.next()); }, next: function() { var result = this.per.next(); if (!result) { var cmb = this.cmb.next(); if (!cmb) return; this.per = _permutation(cmb); return this.next(); } return (typeof (that._lazyMap) === 'function')?that._lazyMap(result):result; } }); addProperties(that, common); that.init(); return (typeof (fun) === 'function') ? that.map(fun) : that; }; /* export */ var Combinatorics = Object.create(null); addProperties(Combinatorics, { C: C, P: P, factorial: factorial, factoradic: factoradic, permutation: permutation, }); return Combinatorics; })(); function permute_Technicalbloke(inputArray) { if (inputArray.length === 1) return inputArray; return inputArray.reduce( function(accumulator,_,index){ permute_Technicalbloke([...inputArray.slice(0,index),...inputArray.slice(index+1)]) .map(value=>accumulator.push([inputArray[index],value])); return accumulator; },[]); } var suite = new Benchmark.Suite; var input = [0, 1, 2, 3, 4]; suite.add('permute_SiGanteng', function() { permute_SiGanteng(input); }) .add('permute_delimited', function() { permute_delimited(input); }) .add('permute_monkey', function() { permute_monkey(input); }) .add('permute_Oriol', function() { permute_Oriol(input); }) .add('permute_MarkusT', function() { permute_MarkusT(input); }) .add('permute_le_m', function() { permute_le_m(input); }) .add('permute_Urielzen', function() { permute_Urielzen(input); }) .add('permute_Taylor_Hakes', function() { permute_Taylor_Hakes(input); }) .add('permute_Combinatorics', function() { Combinatorics.permutation(input).toArray(); }) .add('permute_Technicalbloke', function() { permute_Technicalbloke(input); }) .on('cycle', function(event) { console.log(String(event.target)); }) .on('complete', function() { console.log('Fastest is ' + this.filter('fastest').map('name')); }) .run({async: true}); <script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/platform/1.3.4/platform.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/benchmark/2.1.4/benchmark.min.js"></script>

Chrome 48的运行时结果:

99.152ms此算法 153.115 MarkusT女士 401.255 js-combinatorics女士 497.037 Urielzen女士 925.669 Oriol女士 1026.571 SiGanteng女士 2529.841毫秒分隔 3992.622毫秒的猴子 4514.665 Oriol女士

其他回答

下面的函数排列任意类型的数组,并对发现的每个排列调用指定的回调函数:

/*
  Permutate the elements in the specified array by swapping them
  in-place and calling the specified callback function on the array
  for each permutation.

  Return the number of permutations.

  If array is undefined, null or empty, return 0.

  NOTE: when permutation succeeds, the array should be in the original state
  on exit!
*/
  function permutate(array, callback) {
    // Do the actual permuation work on array[], starting at index
    function p(array, index, callback) {
      // Swap elements i1 and i2 in array a[]
      function swap(a, i1, i2) {
        var t = a[i1];
        a[i1] = a[i2];
        a[i2] = t;
      }

      if (index == array.length - 1) {
        callback(array);
        return 1;
      } else {
        var count = p(array, index + 1, callback);
        for (var i = index + 1; i < array.length; i++) {
          swap(array, i, index);
          count += p(array, index + 1, callback);
          swap(array, i, index);
        }
        return count;
      }
    }

    if (!array || array.length == 0) {
      return 0;
    }
    return p(array, 0, callback);
  }

如果你这样称呼它:

  // Empty array to hold results
  var result = [];
  // Permutate [1, 2, 3], pushing every permutation onto result[]
  permutate([1, 2, 3], function (a) {
    // Create a copy of a[] and add that to result[]
    result.push(a.slice(0));
  });
  // Show result[]
  document.write(result);

我认为它将完全满足您的需要-用数组[1,2,3]的排列填充一个名为result的数组。结果是:

[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,2,1],[3,1,2]]

JSFiddle上的代码稍微清晰一些:http://jsfiddle.net/MgmMg/6/

下面是递归函数=> https://recursion.vercel.app/的可视化

 var permute = function (nums) {
  let answer = [];

  var permuter = function (arr, permutation = []) {
    if (arr.length === 0) {
      return answer.push(permutation);
    } else {
      for (let i = 0; i < arr.length; i++) {
        let currentArr = arr.slice();
        let next = currentArr.splice(i, 1);
        permuter(currentArr, permutation.concat(next)); ///we use concat because splice returns an array.
      }
    }
  };

  permuter(nums);

  return answer;
};

我尝试着做一个简洁而可读的版本,并且是纯函数式编程。

function stringPermutations ([...input]) {
  if (input.length === 1) return input;

  return input
    .map((thisChar, index) => {
      const remainingChars = [...input.slice(0, index), ...input.slice(index + 1)];
      return stringPermutations(remainingChars)
        .map(remainder => thisChar + remainder);
    })
    .reduce((acc, cur) => [...acc, ...cur]);
}

注意,参数格式化将输入字符串转换为数组。不知道这是不是有点太神奇了。我不确定在野外见过。为了真正的可读性,我可能会用input =[…]输入]作为函数的第一行。

我想你可能会喜欢这个:

const permute1 = (arr: any[]): any[][] =>
  arr.reduce(
    (acc, curr) =>
      acc.length > 0
        ? acc
            .map((p) =>
              Array.from({ length: p.length + 1 }, (_, i) =>
                p.slice(0, i).concat(curr, p.slice(i))
              )
            )
            .flat()
        : [[curr]],
    []
  );

const permutations = array => { let permut = []; helperFunction(0, array, permut); return permut; }; const helperFunction = (i, array, permut) => { if (i === array.length - 1) { permut.push(array.slice()); } else { for (let j = i; j < array.length; j++) { swapElements(i, j, array); helperFunction(i + 1, array, permut); swapElements(i, j, array); } } }; function swapElements(a, b, array) { let temp = array[a]; array[a] = array[b]; array[b] = temp; } console.log(permutations([1, 2, 3]));