Question

How can I randomly remove a key with value 0 efficiently ?

Dictionary<string, int> dict = new Dictionary<Edge, int>();
dict.add("a",0);
dict.add("b",0);
dict.add("c",0);
dict.add("d",1);

The size of dictionary is 10000.

Answer 1

Something like this should do it:

IEnumerable<string, int> pairsToRemove = dictionary.Where(pair => pair.Value == 0);

To generate a random index, you could use:

int indexToRemove = [RandomNumber] % pairsToRemove.Length() -1;

Find the indexToRemove th element from pairsToRemove and remove it from the dictionary.

As to efficiency:
The complexity should be O(n)[get all items with value 0] + O(.6N)[finding ith value to remove] + O(log(n))[deletion] assuming the random number generation is constant time.

The problem is, there is no way to perform a value lookup on a dictionary in better than O(n) time. So that will be your bottleneck.