Leetcode解题-Combinations

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描述

Given two integers n and k, return all possible combinations of k numbers out of 1 … n.

For example,
If n = 4 and k = 2, a solution is:

[
[2,4],
[3,4],
[2,3],
[1,2],
[1,3],
[1,4],
]

分析

典型的回溯法。时间O(n!)，空间O(n)。注意组合数和排列数不同，[1, 2] 和[2, 1]是同一个组合，不要加重了。

代码

递归

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class Solution(object):
    def dfs(self, n, k, path, rs):
        if len(path) == k:
            rs.append(path[:])
            return
        for i in xrange(1, n + 1):
            if not path or path[-1] < i:
                path.append(i)
                self.dfs(n, k, path, rs)
                path.pop()

    def combine(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: List[List[int]]
        """
        path = []
        rs = []
        self.dfs(n, k, path, rs)
        return rs

递归（稍作优化）

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class Solution(object):
    def dfs(self, n, k, path, rs):
        if len(path) == k:
            rs.append(path[:])
            return
        start = path[-1] + 1 if path else 1
        for i in xrange(start, n + 1):
            path.append(i)
            self.dfs(n, k, path, rs)
            path.pop()

    def combine(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: List[List[int]]
        """
        path = []
        rs = []
        self.dfs(n, k, path, rs)
        return rs

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