Leetcode 39.组合总和

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39.组合总和

题目

给定一个无重复元素的数组 candidates 和一个目标数 target ，找出 candidates 中所有可以使数字和为 target 的组合。

candidates 中的数字可以无限制重复被选取。

说明：

所有数字（包括 target）都是正整数。
解集不能包含重复的组合。

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示例 1:

输入: candidates = [2,3,6,7], target = 7,
所求解集为:
[
  [7],
  [2,2,3]
]
示例 2:

输入: candidates = [2,3,5], target = 8,
所求解集为:
[
  [2,2,2,2],
  [2,3,3],
  [3,5]
]

方法

方法1：回溯法

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class Solution(object):
    def combinationSum(self, candidates, target):
        """
        :type candidates: List[int]
        :type target: int
        :rtype: List[List[int]]
        """
        res=[]
        self.backtrack(candidates,target,res,[],0)
        return res

    def backtrack(self,candidates,target,res,temp,start):
        if target<0:
            return
        elif target==0:
            res.append(list(temp))
        else:
            for i in range(start,len(candidates)):
                temp.append(candidates[i])
                self.backtrack(candidates,target-candidates[i],res,temp,i)    # 元素可以重复使用，所以此处是i，不是i+1
                temp.pop()
# backtrack([2, 3, 6, 7], 7, [], [], 0)
# backtrack([2, 3, 6, 7], 5, [], [2], 0)
# backtrack([2, 3, 6, 7], 3, [], [2, 2], 0)
# backtrack([2, 3, 6, 7], 1, [], [2, 2, 2], 0)
# backtrack([2, 3, 6, 7], -1, [], [2, 2, 2, 2], 0)
# pop:  2
# --------------------
# backtrack([2, 3, 6, 7], -2, [], [2, 2, 2, 3], 1)
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -5, [], [2, 2, 2, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -6, [], [2, 2, 2, 7], 3)
# pop:  7
# --------------------
# pop:  2
# --------------------
# backtrack([2, 3, 6, 7], 0, [], [2, 2, 3], 1)
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -3, [[2, 2, 3]], [2, 2, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -4, [[2, 2, 3]], [2, 2, 7], 3)
# pop:  7
# --------------------
# pop:  2
# --------------------
# backtrack([2, 3, 6, 7], 2, [[2, 2, 3]], [2, 3], 1)
# backtrack([2, 3, 6, 7], -1, [[2, 2, 3]], [2, 3, 3], 1)
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -4, [[2, 2, 3]], [2, 3, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -5, [[2, 2, 3]], [2, 3, 7], 3)
# pop:  7
# --------------------
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -1, [[2, 2, 3]], [2, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -2, [[2, 2, 3]], [2, 7], 3)
# pop:  7
# --------------------
# pop:  2
# --------------------
# backtrack([2, 3, 6, 7], 4, [[2, 2, 3]], [3], 1)
# backtrack([2, 3, 6, 7], 1, [[2, 2, 3]], [3, 3], 1)
# backtrack([2, 3, 6, 7], -2, [[2, 2, 3]], [3, 3, 3], 1)
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -5, [[2, 2, 3]], [3, 3, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -6, [[2, 2, 3]], [3, 3, 7], 3)
# pop:  7
# --------------------
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], -2, [[2, 2, 3]], [3, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -3, [[2, 2, 3]], [3, 7], 3)
# pop:  7
# --------------------
# pop:  3
# --------------------
# backtrack([2, 3, 6, 7], 1, [[2, 2, 3]], [6], 2)
# backtrack([2, 3, 6, 7], -5, [[2, 2, 3]], [6, 6], 2)
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], -6, [[2, 2, 3]], [6, 7], 3)
# pop:  7
# --------------------
# pop:  6
# --------------------
# backtrack([2, 3, 6, 7], 0, [[2, 2, 3]], [7], 3)
# pop:  7
# --------------------
# [[2, 2, 3], [7]]