Combination Sum II

LeetCode 40 | Difficulty: Medium

Medium

Problem 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.

Example 1:

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

Example 2:

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`

Topics: Array, Backtracking

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Approach

Backtracking

Explore all candidates by building solutions incrementally. At each step, choose an option, explore further, then unchoose (backtrack) to try the next option. Prune branches that can't lead to valid solutions.

When to use

Generate all combinations/permutations, or find solutions that satisfy constraints.

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Solutions

Solution 1: C# (Best: 522 ms)

Metric	Value
Runtime	522 ms
Memory	N/A
Date	2018-01-21

Solution

public class Solution {
    public IList<IList<int>> CombinationSum2(int[] candidates, int target) {
      List<IList<int>> dp = new List<System.Collections.Generic.IList<int>>();
    Array.Sort(candidates);
    backtrack2(dp, new List<int>(), candidates, target, 0);
    return dp;
}

public void backtrack2(List<IList<int>> dp, List<int> templist, int[] candidates, int target, int start)
{
    if(target<0) return;
    else if (target == 0)
    {
        dp.Add(templist.ToList());
    }
    else
    {
        for (int i = start; i < candidates.Length; i++)
        {
            if(i>start && candidates[i-1]==candidates[i]) continue;
            templist.Add(candidates[i]);
            backtrack2(dp, templist, candidates, target - candidates[i], i+1);
            templist.RemoveAt(templist.Count-1);
        }
    }
}
}

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Complexity Analysis

Approach	Time	Space
Backtracking	$O(n! or 2^n)$	$O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Identify pruning conditions early to avoid exploring invalid branches.