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Last modified: July 25, 2019

In this quick tutorial, we'll show how to implement an algorithm for finding all pairs of numbers in an array whose sum equals a given number. We'll focus on **two approaches to the problem**.

In the first approach, we'll find all such pairs regardless of uniqueness. In the second, we'll find only the unique number combinations, removing redundant pairs.

For each approach, we'll present two implementations — a traditional implementation using *for *loops, and a second using the Java 8 Stream API.

We'll iterate through an array of integers, finding all pairs (*i* and *j*) that sum up to the given number (*sum*) using a brute-force, nested-loop approach. **This algorithm will have a runtime complexity of O(n^{2}).**

For our demonstrations, we'll look for all pairs of numbers whose sum is equal to *6*, using the following *input* array:

```
int[] input = { 2, 4, 3, 3 };
```

In this approach, our algorithm should return:

`{2,4}, {4,2}, {3,3}, {3,3}`

In each of the algorithms, when we find a target pair of numbers that sum up to the target number, we'll collect the pair using a utility method, *addPairs(i, j)*.

**The first way we might think to implement the solution is by using the traditional for loop:**

```
for (int i = 0; i < input.length; i++) {
for (int j = 0; j < input.length; j++) {
if (j != i && (input[i] + input[j]) == sum) {
addPairs(input[i], sum-input[i]));
}
}
}
```

This can be a bit rudimentary, so **let's also write an implementation using the Java 8 Stream API**.

Here, we use the method *IntStream.range *to generate a sequential stream of numbers. Then, we filter them for our condition:* number 1 + number 2 = sum*:

```
IntStream.range(0, input.length)
.forEach(i -> IntStream.range(0, input.length)
.filter(j -> i != j && input[i] + input[j] == sum)
.forEach(j -> addPairs(input[i], input[j]))
);
```

For this example, we'll have to **develop a smarter algorithm that returns only the unique number combinations, omitting redundant pairs**.

To achieve this, we'll add every element to a hash map (without sorting), checking first if the pair has already been shown. If not, we'll retrieve and mark it as shown (set *value* field as *null*).

Accordingly, using the same *input* array as before, and a target sum of *6*, our algorithm should return only the different number combinations:

`{2,4}, {3,3}`

**If we use a traditional for loop, we'll have:**

```
Map<Integer, Integer> pairs = new HashMap();
for (int i : input) {
if (pairs.containsKey(i)) {
if (pairs.get(i) != null) {
addPairs(i, sum-i);
}
pairs.put(sum - i, null);
} else if (!pairs.containsValue(i)) {
pairs.put(sum-i, i);
}
}
```

Note that this implementation improves on the previous complexity, as **we use only one for loop, so we'll have O(n)**.

Now let's solve the problem using Java 8 and the Stream API:

```
Map<Integer, Integer> pairs = new HashMap();
IntStream.range(0, input.length).forEach(i -> {
if (pairs.containsKey(input[i])) {
if (pairs.get(input[i]) != null) {
addPairs(input[i], sum - input[i]);
}
pairs.put(sum - input[i], null);
} else if (!pairs.containsValue(input[i])) {
pairs.put(sum - input[i], input[i]);
}
});
```

In this article, we explained several different ways to find all pairs that sum up a given number in Java. We saw two different solutions, each using two Java core methods.

As usual, all the code samples shown in this article can be found on GitHub — this is a Maven project, so it should be easy to compile and run it.

It seems that even though the solution for getting all unique pairs uses just one “for loop”, it does not mean that its completely is O(n). There is “containsValue” that makes it O(n^2).

Hey Andrew,

I’m not sure if your notation is meant to refer to n-squared or n multiplied by 2.

To be n-squared, that would require 2 loops. If you meant O(n*2) – that’s still O(n) since it still depends linearly on the size of n.

Cheers.