查找三个数字之和可被给定数字整除的数字

Question

How can I search through an array and find every combination of three values whose sum is divisible by a given number(x) in java.

In other words, every combination where (n1+n2+n3) % x == 0.

I know this would be a simple solution using a triple for loop but I need something with a time complexity of O(N^2).

Any idea's?

Answer 1

1 - Hash every (element % x) in the list.

2 - Sum every pair of elements in the list (lets call the sum y) and do modded_y = y % x.

3 - Check if x - modded_y is in the hash table. If it is and it's not one of the other 2 numbers then you found a possible combination. Keep iterating and hashing the combinations you found so that they don't repeat.

This is called a meet in the middle strategy.

It's complexity is O(n + (n^2 * 1)) = O(n^2)

Answer 2

I will call the given array A1.

1) create two structs

 struct pair{ int first; int second; bool valid; } 

 struct third{ int value; int index; } 

2) using a nested loop, initialize an array B1 of all possible Pairs.

3) Loop through B1. if (A1[B1[i].first] + A1[B1[i].second])%x==0 then set B1[i].valid to true

4) create an array A3 of Thirds that stores the index and value of every element from A1 that is divisible by x.

5) using a nested loop, go through each element of A3 and each element of B1. If B1.valid = true print A1[B1[i].first] and A1[B1[i].second] with an element from A1[A3.index].

that should give you all combinations without using any triple loops.