自定义比较器以分离偶数和奇数给定 TLE

Question

I am trying to implement the solution for this leetcode problem: https://leetcode.com/problems/sort-array-by-parity/ . (ie segregate even and odd elements in an array)

I wrote the below solution using custom comparator in C++:

bool custom_cmp(int &l, int &r){
    return l%2 == 0;
}

class Solution {
public:
    vector<int> sortArrayByParity(vector<int>& nums) {
        sort(nums.begin(), nums.end(), custom_cmp);
        return nums;
    }
};

However, the above solution gives me TLE and is apparently taking more than O(n*logn) time.

Next, I changed the custom comparator in the above code as follows:

bool custom_cmp(int &l, int &r){
    return (l%2 < r%2);
}

The above solution works perfectly fine and is not giving me TLE. Both of the solutions seem to use the same sorting algorithm and the results of the two comparator class also seem the same.

Can you help me explain what is the difference between the above two implementations and why the second one works while the first one fails?

Answer 1

Your first comparator does not meet the requirements defined by Compare since it doesn't take r 's value into account (ie it does not properly establish a "strict weak ordering").

For example, one requirement that the first comparator violates is:

For all a , comp(a,a)==false

Which we can easily break with custom_cmp(0, 0) .

As an experiment I tried using the same comparator in Compiler Explorer , and interestingly it actually ends up invoking Undefined Behavior because of the unsatisfied contract.