Question

erica has two arrays of integers. the first consists of dinstinct positive integers

Answer 1

An algorithm which for any input positive integer, gives all possible distinct arrays of positive non-zero integers that can sum to it.

e.g Inputting 4 returns (1,1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,3), (3,1), (2,2), (4

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Answer 2

Here is some idea.

If I'm not mistaken the number of the arrays is 2N-1 and the arrays map to bit patterns codding integers form 0 to 2N-1-1 as follows:

I'll show an example for N = 4

The first array is all ones. Imagine every bit in the bit pattern corresponds to the boundary between two array cells

1 1 1 1 <- array elements
| | | <- sections
0 0 0 <- bit pattern
Every 1 in the bit pattern means merging two neighbouring cells

1 (1+1) 1 <- array elements (1 2 1)
| | | <- sections
0 1 0 <- bit pattern


1 (1+1+1) <- array elements (1 3)
| | | <- sections
0 1 1 <- bit pattern


(1+1) (1+1)<- array elements (2 2)
| | | <- sections
1 0 1 <- bit pattern


(1+1+1+1) <- array elements (4)
| | | <- sections
1 1 1 <- bit pattern
To enumerate all arrays you can generate integers from 0 to 2N-1-1 and for every bit pattern you get, generate the corresponding array. It might be helpful to convert the integer to the string of zeros and ones of length N-1. You decode the pattern as follows:

First cell contains 1 initially. Going through the pattern from left to right, for every bit, if it's 1 add 1 to the current cell, if it's 0 create new cell containing 1.

The pattern 1 1 0 0 1 0 1 for N = 8 would be decoded to an array

(3 1 2 2)
Here is some C++ code without argument validation and processing the pattern from right to left. It just changes the order of arrays produced and is simpler to code.

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