Combination Sum II
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
Solution
The logics for the template are:
start_index
: the start index of the next potential candidate incandidates
.is_leaf
: ifremaining == 0
we have reached our target using elements inpath
.get_edges
: all candidates incandidates[start_index:]
.is_valid
:candidate[i]
is valid if it does not exceed remaining and is not a duplicate.
We will follow the same steps as in Deduplication to validate and avoid a duplicate candidate.
Implementation
1def combinationSum2(self, candidates: List[int], target: int) -> List[List[int]]:
2 def dfs(start_index, path, remaining):
3 if remaining == 0:
4 ans.append(path[:])
5 for i in range(start_index, len(candidates)):
6 if remaining - candidates[i] < 0: # avoid results exceeding target
7 break
8 elif i != start_index and candidates[i] == candidates[i-1]: # avoid duplicates
9 continue
10 path.append(candidates[i])
11 dfs(i+1, path, remaining - candidates[i])
12 path.pop()
13 candidates.sort()
14 ans = []
15 dfs(0, [], target)
16 return ans
What's the relationship between a tree and a graph?
Consider the classic dynamic programming of longest increasing subsequence:
Find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order.
For example, the length of LIS for [50, 3, 10, 7, 40, 80]
is 4
and LIS is
[3, 7, 40, 80]
.
What is the recurrence relation?
Solution Implementation
The three-steps of Depth First Search are:
- Identify states;
- Draw the state-space tree;
- DFS on the state-space tree.
Which algorithm should you use to find a node that is close to the root of the tree?
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