Python - Distinct Positive Integers Sum to K

Python – Distinct Positive Integers Sum to K

Last Updated : 01 Nov, 2020

Given a sum K then extracts distinct positive numbers that reach the sum.

Input : K = 17
Output : [1, 2, 3, 4, 7]
Explanation : List summation equals 17.

Input : K = 21
Output : [1, 2, 3, 4, 11]
Explanation : List summation equals 21.

Method #1 : Using loop

In this, we take the smallest possible values that can reach K, for the last value, we subtract the remaining value from K from summed valued till the point.

Python3

# Python3 code to demonstrate working of 
# Distinct Positive Integers Sum to K 
# Using loop 
  
# initializing K 
K = 19
  
# printing K 
print("The value of K : " + str(K)) 
  
res = [] 
idx = 0
for ele in range(1, K): 
    idx += ele 
      
    # checking for last element point  
    if K - idx < ele + 1: 
          
        # appending initial elements 
        res.extend(list(range(1, ele))) 
          
        # appending last element left 
        res.append(K - idx + ele) 
        break
  
# printing result  
print("The Required elements : " + str(res))

Output

The value of K : 19
The Required elements : [1, 2, 3, 4, 9]

Method #2 : Using combinations() + sum()

In this, we get the elements using combinations(), and check for sum using summation, this doesn’t perform in greedy but random way to get to the required summation.

Python3

# Python3 code to demonstrate working of 
# Distinct Positive Integers Sum to K 
# Using combinations() + sum() 
from itertools import combinations 
  
# initializing K 
K = 19
  
# printing K 
print("The value of K : " + str(K)) 
  
res = [] 
flag = 0
for idx in range(K - 1, 0, -1): 
      
    # forming combinations 
    for sub in combinations(range(1, K), idx): 
        if sum(sub) == K and flag == 0: 
            res.extend(list(sub)) 
            flag = 1
            break
        else: 
            continue
        break
  
# printing result 
print("The Required elements : " + str(res))

Output

The value of K : 19
The Required elements : [1, 2, 3, 4, 9]

Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course.

My Personal Notes

Related Articles

Python3

Python3