Problem: Given an array a of n integers, find all such elements a[i], a[j], a[k], and a[l], such that a[i] + a[j] + a[k] + a[l] = target? Output all unique quadruples.

Solution: of course one way would be to just use 4 nested loops to iterate over all possible quadruples, but this is quite slow O(n^4). Another way is to iterate over all triples, put the sums into a set and then in another pass over elements a[i] check if we have any triple with sum (T - a[i]). This would give us O(n^3), and we need to keep track of which elements gave us the required sums. Another step is to iterate over all pairs and put results into a map from integer to indexes of elements, which produce this sum. Then in another pass over this map we can see if we can get a sum of T using two different values from the map (and they shouldn't be using the same element twice). This approach has time complexity O(n^2).