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LC_Combinational_Sum_3.py
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LC_Combinational_Sum_3.py
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"""
216. Combination Sum III
Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.
Note:
All numbers will be positive integers.
The solution set must not contain duplicate combinations.
Example 1:
Input: k = 3, n = 7
Output: [[1,2,4]]
Example 2:
Input: k = 3, n = 9
Output: [[1,2,6], [1,3,5], [2,3,4]]
"""
class Solution(object):
"""
Approach:
=========
Add element to arraylist if it fits.. and call recruisively.. do a depth based search.
Do a depth first based search...
1) loop through all integers from 1 to 9, if arraylist is empty or Arraylist[-1]+1 to 9:
2) if (i<n) add that to the arraylist and call for n = n-i and k = k-1
3) When k is zero. n is zero add the arraylist to answer.
n = 7 and k=3
1-->2-->3 notpossible
1-->2-->4 -- add to answer
1-->2-->5 break
1-->3
1-->4
1-->5
1-->6
"""
def combinationSum3(self, k, n):
"""
:type k: int
:type n: int
:rtype: List[List[int]]
"""
def rec_traverse (ArrayList, n , k, Ans):
# If a n value run
if (n == -1):
return
if (k == 0) and (n == 0):
Ans.append(list(ArrayList))
for i in range(ArrayList[-1]+1,10):
if (i <= n):
Alist = list(ArrayList)
Alist.append(i)
rec_traverse(tuple(Alist),n-i,k-1,Ans)
return
Ans = []
for i in range(1,9):
if (i < n):
Alist = []
Alist.append(i)
rec_traverse(tuple(Alist),n-i, k-1,Ans)
return (Ans)
mysol = Solution()
print (mysol.combinationSum3(2,18))
print (mysol.combinationSum3(3,9))
print (mysol.combinationSum3(3,7))