Sometimes, we desire to get the elements that sum to a particular element. But in cases we are not able to find that, our aim changes to be one to find the closest one. This can have application in many domains. Lets discuss certain ways in which this task can be performed.
Method #1 : Using dictionary comprehension + max() The combination of above functionalities can be used to perform this task. In this, we perform the logic part in dictionary comprehension and closest pair is extracted using max(). The list should be sorted to perform this method.
Python3
# Python3 code to demonstrate # Closest Sum Pair in List# using dictionary comprehension + max()# Initializing listtest_list = [7, 8, 10, 3, 18, 1]# printing original listprint("The original list is : " + str(test_list))# Initializing K K = 12# Closest Sum Pair in List# using dictionary comprehension + max()test_list.sort()res = { i + j :(i, j) for i in test_list for j in test_list if i != j and i + j < K}res = max(res)# printing result print ("The closest sum pair is : " + str(res)) |
The original list is : [7, 8, 10, 3, 18, 1] The closest sum pair is : 11
Time Complexity: O(n*n) where n is the number of elements in the list “test_list”.
Auxiliary Space: O(n) where n is the number of elements in the list “test_list”.
Method #2 : Using loop + combinations() This is yet another way in which this task can be performed. In this, we iterate through the list, compute all possible pairs and return the closest possible sum generated using min(). This return actual pairs.
Python3
# Python3 code to demonstrate # Closest Sum Pair in List# using loop + combinationsfrom itertools import combinations# Initializing listtest_list = [7, 8, 10, 3, 18, 1]# printing original listprint("The original list is : " + str(test_list))# Initializing K K = 12# Closest Sum Pair in List# using dictionary comprehension + max()res = {}for ele in combinations(test_list, 2): ele_sum = sum(ele) try: res[ele_sum].append(ele) except KeyError: res[ele_sum] = [ele]res = res[min(res, key = lambda ele: abs(ele - K))]# printing result print ("The closest sum pair is : " + str(res)) |
The original list is : [7, 8, 10, 3, 18, 1] The closest sum pair is : [(8, 3), (10, 1)]
Time Complexity: O(n), where n is the length of the dictionary
Auxiliary Space: O(n) additional space of size n is created where n is the number of elements in the res dictionary
Method #3: Using sorting + two pointer technique
This is yet another way in which this task can be performed. In this, we first sort the list and apply two pointer technique to get the closest sum.
Python3
# Python3 code to demonstrate # Closest Sum Pair in List# using sorting + two pointer technique # Initializing listtest_list = [7, 8, 10, 3, 18, 1] # printing original listprint("The original list is : " + str(test_list)) # Initializing K K = 12 # Closest Sum Pair in List# using sorting + two pointer techniquetest_list.sort()l, r, n = 0, len(test_list) - 1, len(test_list)res = test_list[l] + test_list[r]while l < r: if test_list[l] + test_list[r] < K: l += 1 else: r -= 1 if abs(test_list[l] + test_list[r] - K) < abs(res - K): res = test_list[l] + test_list[r] # printing result print ("The closest sum pair is : " + str(res)) |
The original list is : [7, 8, 10, 3, 18, 1] The closest sum pair is : 11
Time Complexity: O(NLogN)
Auxiliary Space: O(1)
