動態規律查找

如何用程序得到一組數字的動態規律，前提已知該規律只有加法。

例如：1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 41, 27, 37, 47, 67

可直觀的發現這幾組規律： [1, 2, 3], [11, 12, 13], [21, 22, 23], [31, 32, 33] 和 [27], [37], [47]

下面用代碼實現：

a = [1,2,3,11,12,13,21,22,23,31,32,33,41,27,37,47,67]
data = []
for i in range(1,len(a)):
    data.append( a[i]-a[i-1] )

for pos in range(1, len(data)//3):
    for i in range(len(data)-pos):
        if data[i]  == data[i+pos]:
            getp = True
            p = [a[i:i+pos]]
            r = 1

            while r < (len(data)-i)//pos:
                
                for j in range(pos):
                    if data[i+j] != data[i+pos*r+j]:
                        getp = False
                        break

                if not getp:
                    break
                
                else:
                    p.append(a[i+pos*r :i+pos*r +pos])
                    r += 1

            if len(p) > 1:
                print(p)

輸出：

[[1], [2]]
[[11], [12]]
[[21], [22]]
[[31], [32]]
[[27], [37]]
[[1, 2, 3], [11, 12, 13], [21, 22, 23], [31, 32, 33]]
[[2, 3, 11], [12, 13, 21], [22, 23, 31]]
[[3, 11, 12], [13, 21, 22], [23, 31, 32]]
[[11, 12, 13], [21, 22, 23], [31, 32, 33]]
[[12, 13, 21], [22, 23, 31]]
[[13, 21, 22], [23, 31, 32]]
[[21, 22, 23], [31, 32, 33]]

該方法可以用來檢測信號週期