'''
Given an integer array, output all the unique pairs that sum up to a specific value k.

Example
pair_sum([1,2,3,4,5,6,7],7)
Returns: (3, 4), (2, 5), (1, 6)
'''
 
#using Sorting
def pair_sum(list,k):
    ''' 
    Funtion return all the unique pairs of list elements that sum up to k
    Syntax: insert(list,k)
    Time Complexity: O(nlogn)   
    ''' 
    list.sort() #sorting the list

    length=len(list)
    pairs=[] #for storing the list of pairs that sum up to k
    i=0 #pointing to begining of the list  (Smallest number in the list)
    j=length-1 #pointing to ending of the list (Largest number in the list)

    #making iterations until i and j points to the same element
    while i<=j:     
        
        #if sum of list[i] & list[j] is equal to k that means it is one of the desired pair 
        if list[i]+list[j]==k:
            pairs.append((list[i],list[j]))
            i+=1
            j-=1

        #if these pair sum is less than k
        #we know that the list is sorted and hence j is pointing to Largest number in the list
        #so it is due to value of number pointed by i that is causes there sum to be lesser than k
        #Thus we increment the pointer i so that the sum of values pointed by i and j may gets equal to k
        elif list[i]+list[j]<k:
            i+=1

        #if these pair sum is greater than k
        #we know that the list is sorted and hence i is pointing to Smallest number in the list
        #so it is due to value of number pointed by j that is causes there sum to be greater than k
        #Thus we dicrement the pointer j so that the sum of values pointed by i and j may gets equal to k       
        else:
            j-=1

    return pairs    


#using Set
def pair_sum(list,k):
    ''' 
    Funtion return all the unique pairs of list elements that sum up to k
    Syntax: insert(list,k)
    Time Complexity: O(n)   
    '''
    pairs=[] #for storing the list of pairs that sums up to k
    seen=set() #for storing the elements of the list which are alredy seened

    for current in list:

        target=k-current #stores the desiered value or target value ( which when added to current element of the list yiedls to the sum k )
        
        #if target value is found in the seen set 
        #then the sum of target and list current element is equal to k 
        #Thus we add target & current element touple onto the pairs list
        if target in seen:
            pairs.append((min(target,current),max(target,current))) #formating the pairs touple so like (min_value_of_pairs,max_value_of_pairs)
        
        #if target value is not found in the seen set
        #means the sum of any element of seen set with the current element doesnot yields to k
        #Thus we simply add current element of the list to the seen set in a hop that may be this added_current_element_values can be summed up with upcomming element to produce  k  
        else:
            seen.add(current)
    
    return pairs


list=[1,2,3,4,5,6,7]
pairs=pair_sum([1,2,3,4,5,6,7],7)
print(pairs)