[leetcode] Permutation Sequence

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1. 题目：https://leetcode.com/problems/permutation-sequence/
2. 分析：康托编码
3. code：

// LeetCode, Permutation Sequence
// 康托编码，时间复杂度 O(n)，空间复杂度 O(1)
class Solution
{
public:
    string getPermutation(int n, int k)
    {
        string s(n, ‘0‘);
        string result;
        for (int i = 0; i < n; ++i)
            s[i] += i + 1;
        return kth_permutation(s, k);
    }
private:
    int factorial(int n)
    {
        int result = 1;
        for (int i = 1; i <= n; ++i)
            result *= i;
        return result;
    }
// seq 已排好序，是第一个排列
    template<typename Sequence>
    Sequence kth_permutation(const Sequence &seq, int k)
    {
        const int n = seq.size();
        Sequence S(seq);
        Sequence result;
        int base = factorial(n - 1);
        --k; // 康托编码从 0 开始
        for (int i = n - 1; i > 0; k %= base, base /= i, --i)
            {
                auto a = next(S.begin(), k / base);
                result.push_back(*a);
                S.erase(a);
            }
        result.push_back(S[0]); // 最后一个
        return result;
    }
};

参考：https://github.com/soulmachine/leetcode

[leetcode] Permutation Sequence

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原文地址：http://www.cnblogs.com/panweishadow/p/4776944.html