Given a dictionary of recipes how can I sort the dictionary such that all ingredient keys appear before they are in recipe values

Question

Given a dictionary of recipes {item: [ingredient_1, ingredient_2], ...} how can I sort the item keys efficiently such that we would never have item_n appear after another item_(n-m), m > 1, that used item_n as an ingredient.

for example:

{"cake" : ["egg", "sugar", "flour"], "flour": ["wheat", "titanium_dioxide"]}

should be sorted to

{"flour": ["wheat", "titanium_dioxide"], "cake" : ["egg", "sugar", "flour"]}

Asked By: Goods

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Source

Answer 1

Use this simple algorithm:

For each ingredient in an item, if the ingredient has it’s own entry in the dictionary (as a separate item_2), define an edge where ingredient is the source and item is the destination. When you do that for all ingredients/items, you basically get a directed graph.
If the graph is cyclic, no such valid ordering exists.
If the graph is acyclic (that is, a DAG), use topological sort to get a valid ordering of items that need to be completed first (as a pre-requisite to some following item).

Answered By: Abhinav Mathur

Answer 2

Initialize an empty result list.

Initialize an empty hash table (or map or whatever) and call it references. Iterate through all the recipes, and every time you come across a recipe name or ingredient name, set references[name] = 0.

Iterate through all the recipes again. Every time you come across an ingredient, increment references[ingredient] in the hash table.

Now a loop.

If `references` is empty, you have completed successfully.
Create an empty string array called `zeroes`.  
For each key `k` in `references`:
    if `references[k] == 0`:
        Remove `references[k]`
        Append k to `zeroes`
If `zeroes` is empty, there is a cyclic dependency, so fail.
For each key `k` in `zeroes`:
    If there is a recipe for `k`:
        In the recipe for `k`, for each ingredient `i`:
            decrement `references[i]`
        Add the recipe for `k` to the result list.
Restart the loop

If the loop completes successfully, the sorted recipes will be in the result list.

Answered By: NovaDenizen

Given a dictionary of recipes how can I sort the dictionary such that all ingredient keys appear before they are in recipe values

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