Sorting a set of objects by a user's preference

Question

Given a set of n objects in no specific order (n = 5 in this example):

{
    apple,
    orange,
    banana,
    cherry,
    cabbage
}
         


        

Answer 1

1. Keep all of the items in an array. Use a separate array / hashmap for relations between pairs. Then use your favorite comparison-based search algorithm (say quicksort).

2. When two elements are to be compared, find out relative precedence using the map. If there is no known precedence, ask the user.

3. When a new precedence is added, adjust the precedence order of the whole matrix. For example when the user says apple < banana and then separately banana < cherry, add apple < cherry to the hashmap.

The comparison-based search algorithms are designed to optimize number of comparisons and this translates to optimization of the number of questions asked to the user in this case.