python - 逆笛卡尔积 - 给定乘积，找到索引

Question

我有一个函数，可以计算多个输入数组的笛卡尔积的第 n 个元素:

def prod(arrs, n):
    out = []

    for i,arr in enumerate(arrs):
        denom = numpy.prod([ len(p) for p in arrs[i+1:] ], dtype=int)
        idx = n // denom % len(arr)
        out.append( arr[idx] )

    return out

这个功能很好用:

a = [ 1000, 1100, 1200, 1300, 1400 ]
b = [ 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 ]
c = [ -2, -1, 0, 1, 2 ]

for n in range(20, 30):
    i = prod([a, b, c], n)
    print(i)

[1000, 3.0, -2]
[1000, 3.0, -1]
[1000, 3.0, 0]
[1000, 3.0, 1]
[1000, 3.0, 2]
[1000, 3.5, -2]
[1000, 3.5, -1]
[1000, 3.5, 0]
[1000, 3.5, 1]
[1000, 3.5, 2]

现在我需要“向后退”。

也就是说，给定输入数组 [ a, b, c ] 和单个排列，找出该排列是笛卡尔积中的哪个元素。 (可以假设每个数组仅包含不同的元素。)

例如:

def n_from_prod(arrs, arr):
    # TODO: calculate n 

n = n_from_prod([a, b, c], [1000, 3.5, -2])

assert n == 25

问题:

给定多个输入数组的笛卡尔积的单个排列，我如何找到该排列中的 n(系列中的哪个数字)？

Answer 1

假设a,b,c已排序；否则你必须使用 index 或类似的:

def get_idx(x,a,b,c):
    return np.ravel_multi_index([np.searchsorted(A,B) for B,A in zip(x,(a,b,c))],[*map(len,(a,b,c))])

测试:

import itertools as it

[get_idx(p,a,b,c) for p in it.product(a,b,c)]
# [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149]