Python | Three element sum in list

23 Nov, 2021
The problem of getting the number of pairs that lead to a particular solution has been dealt with many times, this article aims at extending that to 3 numbers and discussing several ways in which this particular problem can be solved. Let’s discuss certain ways in which this can be performed.Method #1: Using Nested loopsThis is the naive method in which this particular problem can be solved and takes the outer loop to iterate for each element and the inner loop checks for the remaining difference adding the pairs to the result. 
Python3
# Python3 code to demonstrate# 3 element sum# using nested loops # initializing listtest_list = [4, 1, 3, 2, 6, 5] # initializing sumsum = 9 # printing original listprint("The original list : " + str(test_list)) # using nested loops# 3 element sumres = []for i in range(0, len(test_list)-2):    for j in range(i + 1, len(test_list)-1):        for k in range(j + 1, len(test_list)):            if test_list[i] + test_list[j] + test_list[k] == sum:                temp = []                temp.append(test_list[i])                temp.append(test_list[j])                temp.append(test_list[k])                res.append(tuple(temp)) # print resultprint("The 3 sum element list is : " + str(res))
The original list : [4, 1, 3, 2, 6, 5]
The 3 sum element list is : [(4, 3, 2), (1, 3, 5), (1, 2, 6)]
 
 Method #2 : Using itertools.combination() This particular problem can also be done in a concise manner using the inbuilt function of a function. The combination function finds all the combinations taking K arguments leading to a particular sum.  
Python3
# Python3 code to demonstrate# 3 element sum# using itertools.combination()from itertools import combinations # function to get the sumdef test(val):    return sum(val) == 9 # initializing listtest_list = [4, 1, 3, 2, 6, 5] # initializing sumsummation = 9 # printing original listprint("The original list : " + str(test_list)) # using itertools.combination()# 3 element sumres = list(filter(test, list(combinations(test_list, 3)))) # print resultprint("The 3 sum element list is : " + str(res))
The original list : [4, 1, 3, 2, 6, 5]
The 3 sum element list is : [(4, 3, 2), (1, 3, 5), (1, 2, 6)]
 
Method #3: Using itertools.combination() and additional check to improve runtime for 1000 items. also, it only checks if a match exists or not, if a match is found then output the combination.
Python3
import itertools def solve(nums, k):  # rule out cases where no of elements are less then 3  if len(nums)<=2:    return False  else:    # get all unique combinations    permut = itertools.combinations(nums, 3)     #rule out the loop if even the max * 3 < target    max_value = max(nums)    if max_value*3 < k:      return False    else:      #check until a match is found      for i in permut:        if i[0]+i[1]+i[2]==k:          return True        return False  nums = [4,1,3,1]k=5print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [2, 4, 3, 0, 1]k = 0print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [0]k = 0print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [1, 0]k = 1print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [2, 0, 1]k = 3print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [13, 76, 35, 89, 15, 76, 54, 4, 66, 4,        9, 25, 9, 48, 26, 76, 95, 80, 19, 66,        74, 15, 18, 96, 36, 78, 80, 42, 42, 76,        85, 74, 96, 9, 95, 29, 58, 43, 57, 14,        38, 21, 55, 56, 18, 25, 3, 11, 76, 77,        72, 36, 44, 88, 93, 2, 95, 86, 77, 47,        3, 51, 34, 46, 70, 90, 4, 24, 58, 6, 91,        93, 59, 69, 89, 5, 58, 87, 23, 15, 98, 24,        62, 64, 15, 43, 93, 68, 17, 4, 78, 6, 2,        10, 52, 17, 28, 82, 20, 44, 78, 91, 1, 79,        17, 23, 27, 66, 88, 57, 60, 78, 68, 6,        35, 43, 73, 37, 12, 22, 47, 59, 40, 36,        0, 70, 91, 68, 33, 54, 44, 78, 23, 69, 60,        44, 32, 15, 20, 28, 36, 55, 73, 12, 55, 26,        43, 57, 63, 46, 0, 43, 24, 91, 86, 61, 15,        10, 29, 8, 51, 84, 94, 18, 5, 63, 90, 4,        38, 28, 84, 67, 18, 33, 85, 93, 31, 38,        97, 14, 79, 11, 92, 3, 8, 27, 65, 39, 1,        83, 38, 8, 83, 53, 53, 44, 57, 64, 78, 1,        44, 72, 100, 86, 85, 16, 5, 27, 24, 2, 56,        74, 16, 90, 65, 8, 93, 64, 72, 45, 47, 7,        83, 100, 99, 62, 89, 38, 38, 42, 98, 18,        29, 88, 48, 35, 0, 82, 56, 22, 64, 13, 54,        66, 32, 9, 2, 52, 80, 28, 19, 9, 38, 98, 38,        21, 41, 65, 78, 63, 97, 71, 99, 41, 89, 78,        48, 47, 72, 67, 79, 45, 43, 92, 30, 28, 42,        52, 56, 24, 46, 55, 82, 22, 86, 67, 43, 84,        41, 26, 66, 26, 32, 8, 93, 65, 10, 47, 19,        70, 84, 43, 99, 74, 78, 51, 59, 58, 38, 75,        86, 24, 48, 27, 72, 32, 15, 28, 98, 11, 70,        74, 91, 89, 90, 74, 69, 60, 78, 6, 67, 34,        100, 70, 98, 70, 60, 12, 58, 26, 21, 44, 64,        15, 82, 81, 52, 9, 82, 94, 99, 43, 22, 14,        16, 27, 68, 72, 69, 45, 60, 10, 91, 31, 58, 91,        71, 42, 19, 43, 42, 80, 61, 50, 2, 81, 45, 40,        44, 100, 68, 74, 19, 0, 33, 24, 58, 59, 1, 26,        65, 69, 19, 60, 12, 50, 82, 44, 18, 96, 77, 43,        33, 31, 53, 9, 36, 86, 24, 46, 11, 26, 3, 43, 8,        42, 17, 55, 60, 56, 33, 66, 90, 64, 42, 73,        61, 34, 13, 43, 9, 59, 46, 0, 68, 93, 60, 78,        92, 76, 45, 20, 31, 47, 21, 44, 2, 23, 78, 72,        62, 65, 56, 26, 80, 65, 87, 61, 88, 22, 38, 70,        98, 48, 25, 95, 55, 3, 32, 28, 50, 13, 57, 18,        95, 11, 23, 57, 21, 93, 35, 38, 75, 79, 39, 87,        30, 95, 73, 37, 47, 43, 15, 73, 59, 0, 29, 29,        30, 50, 13, 73, 1, 32, 7, 46, 7, 24, 43, 21, 84,        1, 6, 96, 33, 69, 2, 70, 98, 2, 90, 31, 66, 74, 58, 66, 56, 33,        5, 78, 19, 21, 98, 76, 1, 55, 97, 39, 43, 43, 44, 7, 61, 84, 31,        0, 67, 46, 39, 23, 7, 31, 29, 2, 71, 7, 35, 60, 20, 94, 23, 81,        40, 79, 11, 46, 71, 25, 42, 54, 10, 21, 11, 72, 86, 48, 53, 67,        36, 55, 49, 98, 65, 37, 27, 63, 20, 86, 60, 29, 63, 75, 91, 30,        55, 23, 82, 88, 53, 62, 44, 25, 27, 99, 39, 4, 40, 41, 35, 35, 61,        62, 10, 98, 9, 82, 21, 39, 82, 89, 41, 71, 26, 51, 2, 73, 30, 49,        92, 16, 66, 60, 68, 2, 99, 91, 15, 77, 43, 44, 46, 69, 79, 100, 47,        9, 66, 33, 25, 15, 5, 77, 86, 81, 82, 69, 10, 0, 98, 4, 90, 30, 89,        87, 83, 97, 35, 96, 71, 15, 50, 12, 82, 79, 91, 79, 28, 62, 24, 75,        77, 68, 59, 87, 29, 81, 66, 92, 85, 4, 17, 48, 69, 28, 37, 55, 39,        11, 92, 57, 26, 64, 91, 44, 37, 3, 44, 57, 13, 75, 21, 39, 17, 29,        18, 74, 43, 93, 53, 6, 61, 71, 89, 99, 13, 92, 23, 99, 18, 13, 38,        14, 9, 82, 10, 7, 41, 24, 40, 61, 42, 26, 2, 43, 38, 3, 50, 43, 75,        47, 95, 16, 41, 40, 43, 14, 26, 40, 79, 11, 30, 16, 39, 46, 45, 25,        44, 79, 21, 48, 48, 23, 38, 79, 62, 71, 8, 53, 12, 72, 64, 71, 50,        90, 38, 77, 6, 48, 74, 77, 53, 85, 82, 19, 18, 43, 97, 67, 56, 25,        46, 87, 27, 99, 21, 13, 56, 71, 87, 73, 25, 0, 52, 82, 18, 65, 34,        96, 33, 99, 43, 45, 2, 59, 29, 53, 34, 78, 27, 41, 74, 74, 59, 96,        74, 45, 74, 44, 28, 62, 4, 90, 62, 31, 89, 72, 88, 69, 5, 29, 26,        81, 66, 96, 53, 87, 72, 89, 9, 30, 71, 75, 83, 46, 71, 57, 12, 77,        24, 44, 71, 34, 42, 11, 67, 9, 69, 47, 95, 93, 72, 12, 40, 98, 83,        25, 27, 91, 21, 31, 0, 44, 56, 1, 76, 30, 100, 18, 46, 35, 72, 61,        39, 90, 25, 78, 42, 77, 13, 72, 32, 3, 84, 63, 59, 100, 60, 22, 57,        50, 40, 63, 65, 2, 27, 88, 63, 40, 97, 94, 69, 72, 98, 2, 68, 13,        62, 76, 97, 14, 36, 15, 91, 80, 55, 45, 67, 50, 13, 49, 54, 72,        84, 36, 69, 74, 35, 30, 47, 64, 91, 24, 16, 41, 41, 19, 96, 25,        38, 60, 43, 86, 6, 23, 81, 71, 73, 56, 12, 44, 67, 28, 39, 1,        52, 40, 28, 45, 44, 53, 63, 7, 66, 45, 44, 68, 6, 98, 100, 95]k = 787 print("Test case :-\nk=",k," \nnums = ",nums[0:10],".....")print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------") nums = [0, 0, 0]k = 0print("Test case :-\nk=",k," \nnums = ",nums)print("-----------------------------------------")Solution.solve(nums, k)print("-----------------------------------------")
Output : 
Test case :-
k= 5  
nums =  [4, 1, 3, 1]
-----------------------------------------
Found match :  (1, 3, 1) 5
-----------------------------------------
Test case :-
k= 0  
nums =  [2, 4, 3, 0, 1]
-----------------------------------------
Match not found.
-----------------------------------------
Test case :-
k= 0  
nums =  [0]
-----------------------------------------
Match not found.
-----------------------------------------
Test case :-
k= 1  
nums =  [1, 0]
-----------------------------------------
Match not found.
-----------------------------------------
Test case :-
k= 3  
nums =  [2, 0, 1]
-----------------------------------------
Found match :  (2, 0, 1) 3
-----------------------------------------
Test case :-
k= 787  
nums =  [13, 76, 35, 89, 15, 76, 54, 4, 66, 4] .....
-----------------------------------------
Match not found.
-----------------------------------------
Test case :-
k= 0  
nums =  [0, 0, 0]
-----------------------------------------
Found match :  (0, 0, 0) 0
-----------------------------------------
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