Find all pairs of integers within an array which sum to a specified value

Question

Design an algorithm to find all pairs of integers within an array which sum to a specified value.

I have tried this problem using a hash

Answer 1

1. If the array is sorted:

   Let i = 0, j = end of array, sum = the value you are looking for, then do:

   If i+j = sum, then output (i,j).
   If i+j < sum, then move i to the right one position.
   If i+j > sum, then move j to the left one position.

   Time complexity: O(n). Space complexity: O(1).

2. If the array is not sorted, there are a few ways to approach this problem:

   1. Sort the array and then use the above approach.

   2. HashMap:

      Store all elements in a HashMap.

      a+b=sum, so b=sum-a. For each element a of the array, look up b from the HashMap.

      HashMap lookup takes amortized O(1).

      Time complexity: O(n). Space complexity: O(n).

   3. BitMap:

      Iterate through the input to create a bitmap where each bit corresponds to an element value. Say the input is {2,5,8}, then we toggle the bitmap array's indices 2, 5 and 8 from binary 0 to 1. This takes O(1) per element, thus O(n) in total.

      Go through the input again. We know b=sum-a, so for every element a in the input, look up its b, which can be done in O(1) since it's a bitmap index. This also takes O(n) in total.

      Time complexity: O(n) + O(n) = O(n). Space complexity: bitmap space = O(n).