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Discrete Logarithm.cpp
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Discrete Logarithm.cpp
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//Finds smallest x such that a^x mod m = b mod m, returns -1 if there is no such x
//Complexity: O(sqrtM * logM)
long long pow(long long a, long long b, long long m)
{
long long ans=1;
while(b)
{
if(b&1)
ans=(ans*a)%m;
b/=2;
a=(a*a)%m;
}
return ans;
}
int discreteLog(int a, int b, int m)
{
a %= m, b %= m;
if(b == 1)
return 0;
int cnt = 0;
long long t = 1;
for(int curg=__gcd(a, m);curg!=1;curg=__gcd(a, m))
{
if(b % curg)
return -1;
b /= curg, m /= curg, t = (t * a / curg) % m;
cnt++;
if(b == t)
return cnt;
}
map<int, int> hash;
int mid = ((int)sqrt(1.0 * m) + 1);
long long base = b;
for(int i=0;i<mid;i++)
{
hash[base] = i;
base = base * a % m;
}
base = pow(a, mid, m);
long long cur = t;
for(int i=1;i<=mid+1;i++)
{
cur = cur * base % m;
if(hash.count(cur))
return i * mid - hash[cur] + cnt;
}
}
------------------------------------------------------------------------------------------------------------------------------------
//Faster Implementation
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define int long long
long long pow(long long a, long long b, long long m)
{
long long ans=1;
while(b)
{
if(b&1)
ans=(ans*a)%m;
b/=2;
a=(a*a)%m;
}
return ans;
}
int discreteLog(int a, int b, int m)
{
a %= m, b %= m;
if(b == 1)
return 0;
int cnt = 0;
long long t = 1;
for(int curg=__gcd(a, m);curg!=1;curg=__gcd(a, m))
{
if(b % curg)
return -1;
b /= curg, m /= curg, t = (t * a / curg) % m;
cnt++;
if(b == t)
return cnt;
}
gp_hash_table<int, int> hash;
int mid = ((int)sqrt(1.0 * m) + 1);
long long base = b;
for(int i=0;i<mid;i++)
{
hash[base] = i;
base = base * a % m;
}
base = pow(a, mid, m);
long long cur = t;
for(int i=1;i<=mid+1;i++)
{
cur = cur * base % m;
auto it = hash.find(cur);
if(it != hash.end())
return i * mid - it->second + cnt;
}
}
//Problem 1: https://codeforces.com/gym/101853/problem/G
//Solution 1: https://codeforces.com/gym/101853/submission/50273547
//Problem 2: https://www.spoj.com/problems/MOD/
//Solution 2: http://p.ip.fi/9xAa