# find all pairs in an array, that sum up to particular number with best complexity

Here we discuss two possible algorithms

• algorithm with the time complexity O(n) and with no additional space complexity
• algorithm which uses additional hashmap data structure which reduces the time complexity to O(2n) at the cost of additional space complexity O(n)
• brute force algorithm with time complexity of O(n^2)

Algorithm with the time complexity O(n) and with no additional space complexity

```        /**
* Find the pair in an array whose sum with complexity O(n). This assumes
* the array passed is sorted array and there are no duplicates in the array
*
* @param arr
*            input array of elements
* @param k
*            sum for which pair of array elements needs to be searched
*/
public void getPair2(int[] arr, int k) {
int start = 0;
int end = arr.length - 1;
int sum = 0;

// output array to record matching pairs
StringBuilder arrs = new StringBuilder();

while (start < end) {
sum = arr[start] + arr[end];
if (sum == k) {
// we have found one pair, add it to our output array
arrs.append(arr[start] + "," + arr[end] + ";");
start++;
end--;
} else if (sum < k) {
// if the sum of the pair is less than the sum we are searching
// then increment the start pointer which would give us the sum
// more than our current sum as the array is sorted
start++;
} else {
// if the sum of the pair is greater than the sum we are searching
// then decrement the end pointer which would give us the sum
// less than our current sum as the array is sorted
end--;
}
}
System.out.println(arrs.toString());
}
```

Output: 1,5;2,4;

Algorithm which uses additional hashmap data structure which reduces the time complexity to O(2n) at the cost of additional space complexity O(n)

```/**
* Find the pair in an array whose sum with complexity O(2n)
*
* @param arr
*            input array of elements
* @param k
*            sum for which pair of array elements needs to be searched
* @return string of combination of array pairs
*/
public String getPair(int[] arr, int k) {
HashMap<Integer, Integer> hm = new HashMap<Integer, Integer>();
String result = "";

/**
* First store array elements into hashmap with key as the value of the
* array This has time complexity of O(n) and space complexity of O(n)
*/
for (int i = 0; i < arr.length; i++) {
hm.put(arr[i], arr[i]);
}

/**
* Try getting the hashmap value at key (sum-array_element) If it
* exists, it means array_element and sum-array_element is the pair
* thats forms sum 'k' This has time complexity of O(n)
*/
for (int i = 0; i < arr.length; i++) {
if (hm.get(k - arr[i]) != null) {
result += arr[i] + "," + (k - arr[i]) + ";";
}
}
return result;
}
```

Output: Pair of elements at O(2n) time complexity and O(n) space complexity: 4,2;2,4;5,1;1,5;

Brute force algorithm with time complexity of O(n^2)

```/**
* Find the pair in an array whose sum with complexity O(n^2)
*
* @param arr
*            input array of elements
* @param k
*            sum for which pair of array elements needs to be searched
* @return string of combination of array pairs
*/
public String findPair(int[] arr, int k) {
int i = 0, j = arr.length - 1;
String result = "";
while (i < j) {
while (i < j) {
if (arr[i] + arr[j] == k) {
result += arr[i] + "," + arr[j] + ";";
}
j--;
}
i++;
j = arr.length - 1;
}
return result;
}
```

Output: Pair of elements at O(n^2) time complexity and no additional space complexity: 4,2;5,1;

### 7 Responses to find all pairs in an array, that sum up to particular number with best complexity

1. anand says:

Your solutions which use hashmap and brute force do not work for array = {1,2,3} and sum = 2 / sum = 4 / sum = 6
It will give you (1,1) / (1,3),(2,2) /(3,3) as solutions.
(1,1) and (2,2) cannot be solutions as those are not pairs but just single element.

Am I missing something here ?

2. Miloud L C says:

great explanation! thank you!

3. shoba says:

If arr={0,1,2,3} and k=4, your hashmap algorithm will also return (2,2) as a pair which is not the case

• adding a condition should help
if (hm.get(k – arr[i]) != null && (k – arr[i]) != arr[i])

anyways I will try it out and update the code when I get some time.

Thanks for pointing it out.

4. Yash Sangani says:

Cell
{
int index ;//which contains the array index
int val; //which contains the array value at that index
}

5. vimal says:

u said all pairs that sum upto a given number so for array {1,2,3,4} and k=4 answer should be {1,2}, {1,3} not just {1,3}. Right ??

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