leetcode:Permutation Sequence

The set [1,2,3,…,n] contains a total of n! unique permutations.

By listing and labeling all of the permutations in order,
We get the following sequence (ie, for n = 3):

1. "123"
2. "132"
3. "213"
4. "231"
5. "312"
6. "321"

Given n and k, return the kth permutation sequence.

Note: Given n will be between 1 and 9 inclusive.

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class Solution {
    
private:
    unsigned int hashTable[9];
    
    unsigned int getPai(int n) {

        if (n == 0)
            return 1; 

        if (hashTable[n] != 0)
            return hashTable[n];
        
        if (n==1)
        {
            hashTable[1] = 1;
            return 1;
        }
        
        unsigned int ret = n*getPai(n-1);
        hashTable[n] = ret;
        
        return ret;
    }
    
    string getPermutationHelper(vector<char> &model, int k) {
        
        int n = model.size();
        if (n == 0)
            return "";
        
        int numIdx = (k-1) / getPai(n-1); // (k-1) 这里很关键
        int remain = k - numIdx*getPai(n-1); // remain = k-numIdx*getPai(n-1)也很关键
        
        char targetChar = model[numIdx];
        vector<char> next;
        
        for (int i=0; i<model.size(); i++)
        {
            if (i != numIdx)
                next.push_back(model[i]);
        }
        
        return model[numIdx] + getPermutationHelper(next, remain);
    }
    
public:
    string getPermutation(int n, int k) {
        
        vector<char> model(n);
        for (int i=1; i<=n; i++)
        {
            model[i-1] = i+'0';
        }
        
        return getPermutationHelper(model, k);
    }
};