Hashing using int array or unordered_map in STL? - performance

Question

Which is more efficient in terms of memory and time complexity hashing using int array or unordered_map in STL?
By hashing I mean storing elements formed by the combination of a key value and a mapped value, and fast retrieval of individual elements based on their keys.
Actually I was trying to solve this question.
Here's my solution:-
#include <bits/stdc++.h>
#define MAX 15000005
using namespace std;
/*
* author: vivekcrux
*/
int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
int c[MAX];
int n;
int sieve()
{
bitset<MAX> m;
m.set();
int ans = 0;
for(int i=2;i<MAX;i++)
{
if(m[i])
{
int mans = 0;
for(int j=i;j<MAX;j+=i)
{
m[j]=0;
mans += c[j];
}
if(mans<n)
ans = max(ans,mans);
}
}
return ans;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
int i,j;
cin>>n;
int a[n+1];
for(i=0;i<n;i++)
{
cin>>a[i];
}
int g = a[0];
for(i=1;i<n;i++)
{
g = gcd(g,a[i]);
}
for(i=0;i<n;i++)
{
a[i] /= g;
if(a[i]!=1) c[a[i]]++;
}
int m = sieve();
if(m==0)
cout<<"-1";
else
cout<<n - m<<endl;
return 0;
}
In this code if I use
unordered_map<int,int> c;
instead of
int c[MAX];
I get a Memory limit exceeded verdict.I have found here that unordered_map has a constant average time complexity on average, but no details about space complexity is mentioned here.I wonder why am I getting MLE with unordered_map.

Answer 1

unordered_map uses bucket to store values. A bucket is a slot in the container's internal hash table to which elements are assigned based on the hash value of their key. Lets see the following code in C++17.
#include <bits/stdc++.h>
using namespace std;
int main() {
unordered_map<int,int> mp;
mp[4] = 1;
mp[41] = 5;
mp[67] = 6;
cout<<mp.bucket_count();
}
The output comes out be 7 (depends on compiler). This is the number of buckets used in the above code. But if we use an array of size 67, it will obviously take more memory. Another case would be that if we would had numbers 1, 2 and 3 instead of 4, 41 and 67, the output would have been 7. Here using array was the way to go for saving space. So it depends on the keys you are storing in the hash table. For time complexity, both performs equally same. There is a collision condition in unordered_map which would blow the overall time complexity of the code. Here is the codeforces link of the blog.