I don't think you have a complete statement of the problem. Why, in the first example, are arrangements like 1 1 2 excluded? And you only accept the arrangements in a particular order. How do you define the order?
the data ascended by column,when the first column is the same, sort by the second column,...
Thanks - and I realize now that 1 1 2 is not excluded; I just wasn't looking carefully.
The best way to generate such a sequence is using depth-first search or recursion. By prohibiting the usage of IFs, all solutions are inefficient (because we can't cut the tree, and are forced to follow all branches).
High school cafeteria
Find best placement for ordered dominoes (harder)
Fibonacci-Sum of Squares
Convert given decimal number to binary number.
Return fibonacci sequence do not use loop and condition version 3
Project Euler: Problem 14 Longest Collatz sequence(harder version)
Generate a vector like 1,2,2,3,3,3,4,4,4,4
Return fibonacci sequence do not use loop and condition
Determine if input is a perfect number
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