[LintCode] Permuation Index

Given a permutation which contains no repeated number, find its index in all the permutations of these numbers, which are ordered in lexicographical order. The index begins at 1.

Example

Given [1,2,4], return 1.

class Solution {
public:
    /**
     * @param A an integer array
     * @return a long integer
     */
    long long permutationIndex(vector<int>& A) {
        long long len = A.size();
        if(len < ) return len;

        vector<long long> factorial(len, );
        for(long long i = len - ;i >= ;--i)
            factorial[i] = factorial[i + ] * (len -  - i);

        long long res = ;
        for(long long i = ;i < len;++i){
            long long num = ;
            for(long long j = i + ;j < len;++j)
                if(A[j] < A[i]) ++num;
            res += num * factorial[i];
        }
        return res;
    }
};