C++ - Checking whether two substrings are equal using hashing - c++

Question

I'm taking a coursera course and one of the assignment is to process large number of queries(upto the order of 10^6) to check whether two substrings are equal or not from a single string(maximum length of string is 500000) using polynomial hashing. A single query includes index a and b and length l.
I've implemented a code that pre-computes hashes for the whole string twice(for two seperate modulo-n numbers) and computes two hashes for each substring. This is to reduce the number of collisions.
The code:
class Solver {
string s;
unsigned long long x, m1, m2;
vector<long long> h1, h2;
public:
Solver(string s) : s(s) {
// initialization, precalculation inside constructor
h1.resize(s.size() + 1); //first array to store precomputed hashes
h2.resize(s.size() + 1); //second array
x = 263; // random multiplier for polynomial hash and 0 < x < m1, m2
m1 = 1000000007;
m2 = 1000000009;
h1[0] = 0, h2[0] = 0;
for (size_t i = 1; i <= s.size(); ++i) {
h1[i] = ((x * h1[i - 1]) + s[i - 1]) % m1;
h2[i] = ((x * h2[i - 1]) + s[i - 1]) % m2;
}
}
bool ask(int a, int b, int l) {
if (a + l > s.size() || b + l > s.size())
return false;
long long y = 1, z = 1;
y = (long long)pow(x, l) % m1;
z = (long long)pow(x, l) % m2;
long long H1 = (((h1[a + l] - (y * h1[a])) % m1) + m1) % m1;
long long H2 = (((h1[b + l] - (y * h1[b])) % m1) + m1) % m1;
long long H3 = (((h2[a + l] - (z * h2[a])) % m2) + m2) % m2;
long long H4 = (((h2[b + l] - (z * h2[b])) % m2) + m2) % m2;
return ((H1 == H2) && (H3 == H4));
}
};
int main() {
ios_base::sync_with_stdio(0), cin.tie(0);
string s;
int q;
cin >> s >> q;
Solver solver(s);
for (int i = 0; i < q; i++) {
int a, b, l;
cin >> a >> b >> l;
cout << (solver.ask(a, b, l) ? "Yes\n" : "No\n");
}
}
sample output:
trololo
4 // number of queries
0 0 7 // a b l
2 4 3
3 5 1
1 3 2
yes
yes
yes
no
The code works for the above example. But when input for a is given as 0 and b a random value such that
on paper it's the right answer but the code outputs the wrong one and also for certain trivial strings like "abcabc", the code outputs the wrong answer.
example:
abcabcabc
4
0 3 3
1 7 2
2 8 1
1 4 4
no
no
no
yes
Where am I going wrong when a = 0 and are my trivial inputs like "thethethe" valid?

Answer 1

If the string is 500k in length, then there are hundreds of billions of substrings - far too many to prehash in advance and fit in memory.
Instead of doing that, you should create hashes from every starting point of length 1, 2, 4, 8, 16, ... There should only be on the order of 10 million of those.
And now given two substrings we can compare at least half of each of them with a single lookup. Which makes the comparison take logarithmic time.