I got AC sorting a vector in problem 479C, but I have no ideia why my solution fails when using a map (C++) instead. Any insights?

#	User	Rating
1	tourist	3985
2	jiangly	3814
3	jqdai0815	3682
4	Benq	3529
5	orzdevinwang	3526
6	ksun48	3517
7	Radewoosh	3410
8	hos.lyric	3399
9	ecnerwala	3392
9	Um_nik	3392

#	User	Contrib.
1	cry	169
2	maomao90	162
2	Um_nik	162
4	atcoder_official	160
5	djm03178	158
6	-is-this-fft-	157
7	adamant	155
8	Dominater069	154
8	awoo	154
10	luogu_official	151

Problem link:↵
http://mirror.codeforces.com/contest/479/problem/C↵
↵
AC submission (~~using map~~sorting a vector): ↵
http://mirror.codeforces.com/contest/479/submission/16772060↵
↵
WA submission (~~sorting a vector~~using map):↵
http://mirror.codeforces.com/contest/479/submission/16772083↵
↵
I used a greedy approach in the WA submission.↵
It's possible to take any exam scheduled to the day A before day A.↵
Suppose that the in the final solution for the problem all the exams scheduled to the day A are taken before A.↵
If this is true, the last exam will be completed in the greatest number B, such that B is smaller than A, within all elements in the set of exams scheduled to the day A.↵
This greedy step translates to code like this:↵
↵
~~~~~↵
auto at = mp.find(a);↵
if(at != mp.end()) {↵
at->second = max(at->second, b);↵
}↵
else {↵
mp[a] = b;↵
}↵
~~~~~↵
↵
If this step is not possible, consider the first element C > A such that mp[C] < mp[A], so I cant take exam C in the day mp[C]. So the next minimum value available is C. This step is done in nom-increasing order of A.↵
But I got WA with this solution and have no ideia why.↵
↵