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Problem: Combination Sum II

Difficulty: Medium

Description:

Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sum to target. Each number in candidates may only be used once in the combination. Note: The solution set must not contain duplicate combinations.

Examples:

Input: candidates = [10,1,2,7,6,1,5], target = 8
Output: 
[
[1,1,6],
[1,2,5],
[1,7],
[2,6]
]
Input: candidates = [2,5,2,1,2], target = 5
Output: 
[
[1,2,2],
[5]
]

Constraints:

1 <= candidates.length <= 100
1 <= candidates[i] <= 50
1 <= target <= 30

Solutions:

For the DP approach we create an array of size target+1 where each element i is a set of all candadiates where sum is equal to i. The time complexity of this solution is O(N * M^2) and the space complexity is O(M) where N is the length of candidates and M is the target.

def combinationSum(candidates, target):
    """
    :type candidates: List[int]
    :type target: int
    :rtype: List[List[int]]
    :Time Complexity: O(N * M)
    :Space Complexity: O(M)
    """
    candidates.sort(reverse=False)
    dp = [set() for _ in range(target + 1)]
    dp[0].add(())

    for c in candidates:
        for i in reversed(range(c, target + 1)):
            if i - c >= 0:
                for prev in dp[i - c]:
                    dp[i].add(prev + (c,))

    return dp[-1]