SPL Programming - 4.3 [Sequence] Multi-layer sequence

 

The members of a sequence can also be sequences, and a multi-layer sequence can be formed in this way. For example, [[1,2,3],[2,3,1],[3,1,2]] is a legal sequence, and each member is also a sequence.

Let’s look at how members of a multi-layer sequence can be referenced:

A
1 =[[1,2,3],[4,5,6],[7,8,9,10]]
2 =A1(2)
3 =A1(3)(2)
4 >A1(1)(3)=0
5 =A1.len()
6 =A1(3).len()
7 >A1(2)=0

Try to execute the above code and observe the running results to understand the actions of member reference and assignment of multi-layer sequence.

The result of A2 is sequence [4,5,6]; A3 gets the second member of the third member sequence, namely 8; After A4 is executed, the third member of the first member sequence becomes 0, which used to be 3; A5 is the length of the sequence, which is 3, and A6 is the length of the third member sequence, which is 4; After A7 is executed, the second member sequence will be changed to 0, and this member will no longer be a sequence.

Multi layer sequence can also be displayed on the interface. After the above code is executed, click A1 to see its value on the right.

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The sequence members will also be displayed as a sequence. At this time, double-click a sequence member (such as the third member pointed by the arrow), the members of this member sequence will be displayed:

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The sequence composed of n sequences of length m can be understood as a two-dimensional structure, and each member sequence can be written as a row, and it can be regarded as a table of n rows and m columns. Therefore, some programming languages also call a two-layer sequence as a two-dimensional array, and even have done some special processing, and can support the writing method of x(i,j) to access the member of the i-th row and j-th column. There is no special understanding in SPL, it is simply understood as the j-th member of the i-th member sequence, that is, written as x(i)(j).

Obviously, there can be more of these levels, in terms of array, there can be more dimensions.

We use the two-layer sequence to calculate the Pascal triangle:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

……

Pascal triangle is composed of N rows of numbers. The n-th row has n numbers. The m-th number of the n-th row is the sum of the (m-1)-th and m-th numbers of the (n-1)-th row. The n-th row number of Pascal triangle is exactly the coefficient of term xi in (1+x)n, that is:

(1+x)1= 1+1x

(1+x)2= 1+2x+1x2

(1+x)3= 1+3x+3x2+1x3

(1+x)4= 1+4x+6x2+4x3+1x4

……+

The code is simple:

A B C D
1 5 =\[0\]*(A1+1) >B1(1)=\[1\] >B1(2)=\[1,1\]
2 for 3,A1+1 >B1(A2)=\[1\]*A2
3 for 2,A2-1 >B1(A2)(B3)=B1(A2-1)(B3-1)+B1(A2-1)(B3)

Calculate to the (A1+1)-th row, the result is a 2-layer sequence, which is saved in B1.

B1 generates a sequence of length A1+1, which is ready to be filled in. C1 and D1 are filled in the first two rows. The A2 loop is calculated from the third row. B2 generates a sequence of length A2, with members all be 1, for the current row, and then calculates from the second column to the A2-1 column, because the first and A2 columns of this row are all 1, and it is unnecessary to calculate them.