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Combinations of K Numbers that Sum to N

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to implement the FindCombinations function, which finds all possible combinations of k numbers that sum to n. The function should return a list of all possible k combinations that add up to n. Numbers can only be used once in each combination.

Example 1
    
  
  • Input: k = 3, n = 7
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  • Output: [[1,2,4]]
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  • Explanation: 
      
      
    • There is only one valid combination: 1 + 2 + 4 = 7
      • 
    
    •
Example 2
    
  
  • Input: k = 3, n = 9
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  • Output: [[1,2,6], [1,3,5], [2,3,4]]
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  • Explanation: 
      
      
    • These are all valid combinations:
      • 
      
    • 1 + 2 + 6 = 9
      • 
      
    • 1 + 3 + 5 = 9
      • 
      
    • 2 + 3 + 4 = 9
      • 
    
    •
Constraints
    
  
  • 1 ≤ k ≤ 9
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  • 1 ≤ n ≤ 60
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  • All numbers used must be positive integers
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  • Each combination should contain exactly k unique numbers
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  • Time Complexity: O(C(9,k) * k) where C(9,k) is the binomial coefficient
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  • Space Complexity: O(k) for the recursion depth
    •
NumberBacktracking AccenturePwC
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Hint
Solution

Solution Hints

    
  
  • Use backtracking to explore all possible combinations
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  • Start with an empty combination and recursively add numbers
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  • Maintain a current sum to avoid unnecessary calculations
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  • Prune branches where the sum exceeds the target
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  • When the combination size reaches k, check if the sum equals n
    •

Steps to solve by this approach:

 Step 1: Create a backtracking function that builds combinations one element at a time
 Step 2: Use parameters to track the current combination, starting point, remaining elements needed (k), and remaining sum
 Step 3: When the combination reaches size k, check if the sum equals the target n
 Step 4: For each recursive call, try adding numbers from the current start position up to 9
 Step 5: Optimize by skipping numbers that would make the sum exceed the target
 Step 6: After exploring with a number added, remove it (backtrack) to try other possibilities
 Step 7: Return all valid combinations found during the process

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