查找给定数字 n - javascript python 的所有偶数因式分解

Question

目前我正在实现一种算法，该算法依赖于查找给定数字 n 的所有偶数因式分解，包括 n。

我已经尝试了一些方法，但总的来说我无法很好地处理这个问题。递归处理它也许是个好主意，但我还不太擅长 javascript，尤其是语言的高级方面可能会派上用场。

function evens(n) {
evens = []
for (var i = 2; i < n/2 - 1; i++){
    if (i % 2 != 0){
        continue;
    }
    else {
        if ((n/i) % 2 == 0) {
            evens.push([n/i, i])
        }
    }
}
return evens
}

这是一些代码，但考虑到所有正确的基本情况，我还不能递归地实现它。我还认为可以用树状结构来完成，其中路径是偶数因子，但是我的cs知识很差。

也欢迎 Python 中的建议，但 javascript 最好。

只是为了让一切更清楚：例如，136 的所有偶数分解是 [[68, 2], [34, 2, 2], [34, 4], [136]]。

感谢您的帮助:)

Answer 1

在cdlane正确指出我方案的缺陷后，我收回了原方案，将cdlane优雅的python方案移植到javascript。

function even_factorization(n) {
  let solutions = [];

  function even_divisors(n) {
      var divisors = [];
      for (let i = 2; i <= n; i += 2) {
        if (n % i === 0) divisors.push(i);
      }
      return divisors;
  }

  function remove_similarities(combos) {
    for (let i = 0; i < combos.length; i++) {
      for (let j = i + 1; j < combos.length; j++) {
        if (combos[i].sort((a,b) => a - b).join(" ") === combos[j].sort((a,b) => a - b).join(" ")) {
          combos.splice(j--,1);
        }
      }
    }
    return combos;
  }

  even_divisors(n).forEach(divisor => {
    if (divisor === n)
      solutions.push([divisor]);
    else {
        even_factorization(n / divisor).forEach(solution => {
          solutions.push([divisor, ...solution]);
        });
    }
  });

  return remove_similarities(solutions);
}

运行 218960 returns...

[[2,2,2,27370],[2,2,10,5474],[2,2,14,3910],[2,2,34,1610],[2,2 ,46,1190],[2,2,70,782],[2,2,170,322],[2,2,230,238],[2,2,54740],[2,4,27370],[2,10,14,782], [2,10,34,322],[2,10,46,238],[2,10,10948],[2,14,34,230],[2,14,46,170],[2,14,7820],[2 ,20,5474],[2,28,3910],[2,34,46,70],[2,34,3220],[2,46,2380],[2,68,1610],[2 ,70,1564],[2,92,1190],[2,140,782],[2,170,644],[2,230,476],[2,238,460],[2,322,340],[2,109480],[4,10,5474],[4 ,14,3910],[4,34,1610],[4,46,1190],[4,70,782],[4,170,322],[4,230,238],[4,54740],[8,27370],[10 ,14,34,46],[10,14,1564],[10,28,782],[10,34,644],[10,46,476],[10,68,322],[10,92,238],[10,21896 ],[14,20,782],[14,34,460],[14,46,340],[14,68,230],[14,92,170],[14,15640],[20,34,322],[20,46,238], [20,10948],[28,34,230],[28,46,170],[28,7820],[34,46,140],[34,70,92],[34,6440],[40,5474], [46,68,70],[46,4760],[56,3910],[68,3220],[70,3128],[92,2380],[136,1610],[140,1564], [170,1288],[184,1190],[230,952],[238,920],[280,782],[322,680],[340,644],[460,476],[218960]]

...和运行 136 returns...

[[2,2,34],[2,68],[4,34],[136]]

Answer 2

Maybe its a good idea to handle it recursively

这是我在 Python 中的递归解决方案的尝试：

def even_factorization(n):
    solutions = []

    def even_divisors(n):  # 136 generates [2, 4, 8, 34, 68, 136]
        return (d for d in range(2, n + 1, 2) if n % d == 0)

    def remove_similarities(array):  # [[2, 2, 34], [2, 34, 2], [34, 2, 2]] -> [[2, 2, 34]]
        return list(map(list, set(map(lambda a: tuple(sorted(a)), array))))

    for divisor in even_divisors(n):
        if divisor == n:
            solutions.append([divisor])
        else:
            for solution in even_factorization(n // divisor):
                solutions.append([divisor] + solution)

    return remove_similarities(solutions)  # return 'solutions' to see raw data

对于 136 returns:

[[2, 2, 34], [4, 34], [2, 68], [136]]

218960 returns:

[[184, 1190], [8, 27370], [4, 54740], [2, 70, 1564], [56, 3910], [2, 2, 170, 322],
[280, 782], [70, 3128], [4, 46, 1190], [2, 2, 34, 1610], [2, 14, 34, 230],
[2, 14, 7820], [20, 34, 322], [10, 14, 34, 46], [14, 92, 170], [20, 46, 238],
[218960], [2, 322, 340], [10, 68, 322], [34, 46, 140], [10, 14, 1564],
[2, 10, 10948], [10, 92, 238], [4, 170, 322], [92, 2380], [14, 20, 782],
[10, 21896], [238, 920], [28, 34, 230], [10, 28, 782], [2, 2, 46, 1190],
[2, 28, 3910], [10, 34, 644], [34, 6440], [2, 92, 1190], [46, 4760], [2, 170, 644],
[2, 68, 1610], [4, 70, 782], [340, 644], [2, 34, 46, 70], [2, 20, 5474],
[14, 68, 230], [2, 34, 3220], [4, 34, 1610], [4, 10, 5474], [28, 7820],
[14, 34, 460], [322, 680], [10, 46, 476], [2, 2, 54740], [4, 230, 238],
[2, 2, 2, 27370], [34, 70, 92], [2, 140, 782], [14, 15640], [2, 10, 46, 238],
[2, 10, 14, 782], [2, 14, 46, 170], [2, 238, 460], [136, 1610], [2, 2, 10, 5474],
[20, 10948], [4, 14, 3910], [40, 5474], [2, 2, 70, 782], [2, 2, 230, 238],
[230, 952], [68, 3220], [2, 46, 2380], [2, 230, 476], [2, 10, 34, 322],
[140, 1564], [460, 476], [170, 1288], [2, 4, 27370], [46, 68, 70], [14, 46, 340],
[2, 109480], [28, 46, 170], [2, 2, 14, 3910]]

查找给定数字 n - javascript python 的所有偶数因式分解

Finding all even factorizations of a given number n - javascript python

javascript

python

python-3.x

number-theory

factorization