用O [n ^ 2]的3个数组找出给出结果A [i] + B [j] = C [k]的所有组合

Question

There are 3 arrays, every array has a size of N . Find the combinations that give A[i]+B[j]=C[k] at only O[n^2].

Answer 1

There is a simpler problem: given two arrays and a number find all combinations from the arrays which give sum=number. It can be solved in O(n).

We can use its solution as part of solution for the larger one:

(I'm assuming that all elements are different - it simplifies things a bit)

sort(A)
sort(B)
sort(C)
for(int indexC=0;indexC<N;++indexC)
    int indexA=0
    int indexB=N-1
    while(indexA<0)
        //find all combinations in A,B with sum=C[indexC]
        int sum=A[indexA]+B[indexB]
        if(sum==C[indexC])
            OutputCombination(indexA,indexB,indexC)
        if(sum<C[indexC])
            ++indexA
        else if(sum>C[indexC])
            --indexB
        else
            ++indexA
            --indexB

Answer 2

Update : Question was later modified to ask specifically for an implementation in Java. The algorithm and explanation in Python remain valid, but I've also added Java implementation below.

---

Use a hashmap (or a set) to test for existence in C with time complexity O(1) (on average). Then all you need is to iterate over all pairs (a,b) | a <- A, b <- B (a,b) | a <- A, b <- B , for a total time complexity of O(n^2) .

For example, in Python you could do it like this:

c = set(C)
for a in A:
    for b in B:
        if a + b in c:
            print a, b, a + b

Quick test:

>>> A = [1,2,3]
>>> B = [3,4,5]
>>> C = [1,4,7]
>>> c = set(C)
>>> for a in A:
...     for b in B:
...         if a + b in c:
...             print a, b, a + b
... 
1 3 4
2 5 7
3 4 7

Or, a shorter version with a list comprehension:

>>> c = set(C)
>>> [(a,b,a+b) for a in A for b in B if a+b in c]
[(1, 3, 4), (2, 5, 7), (3, 4, 7)]

---

The Java implementation is essentially the same. The key observation is to use java.util.HashSet for checking if the sum A[i]+B[j] is present in the array C :

import java.util.HashSet;

class Pairs {
    public static void main(String[] args) {
        Integer[] A = new Integer[]{1,2,3};
        Integer[] B = new Integer[]{3,4,5};
        Integer[] C = new Integer[]{1,4,7};

        HashSet<Integer> c = new HashSet<Integer>();
        for (int i = 0; i < C.length; i++) {
            c.add(C[i]);
        }

        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < B.length; j++) {
                if (c.contains(A[i] + B[j])) {
                    System.out.format("%d %d %d%n", A[i], B[j], A[i]+B[j]);
                }
            }
        }
    }
}