Merge pull request #332 from Rushalverma/main

My contribution for issue number 003

Author: zonedoutdg

Problems/Mathematics/Day-01/sol/Rushalverma/Solution2.cpp

@@ -0,0 +1,94 @@
+/*
+https://codeforces.com/contest/1225/submission/355245357
+
+time complexity: Factorization of each number using seive primes O(log maxA)
+                 total factorization cost - O(nlog maxA)
+                 Each number produces a vector of prime–exponent pairs mod k -> O(log maxA)
+                 total map work - O(nlong maxA)
+                 total complexity = O(nlog maxA)
+                 
+
+
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+using ll = long long;
+
+int main(){
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+    ll k;
+    cin >> n >> k;
+
+    vector<ll> a(n);
+    ll mx = 0;
+    for(int i = 0; i < n; i++){
+        cin >> a[i];
+        mx = max(mx, a[i]);
+    }
+
+
+    ll LIM = sqrt(mx) + 2;
+    vector<int> primes;
+    vector<bool> is_prime(LIM+1, true);
+    is_prime[0] = is_prime[1] = false;
+    for(int i = 2; i <= LIM; i++){
+        if(is_prime[i]){
+            primes.push_back(i);
+            for(ll j = 1LL * i * i; j <= LIM; j += i)
+                is_prime[j] = false;
+        }
+    }
+
+    unordered_map<string, long long> cnt;
+    long long ans = 0;
+
+    for(int idx = 0; idx < n; idx++){
+        ll x = a[idx];
+
+        vector<pair<ll,ll>> v; 
+
+        for(int p: primes){
+            if(1LL * p * p > x) break;
+            if(x % p == 0){
+                ll c = 0;
+                while(x % p == 0){
+                    x /= p;
+                    c++;
+                }
+                c %= k;
+                if(c) v.push_back({p, c});
+            }
+        }
+
+        if(x > 1) v.push_back({x, 1 % k}); 
+
+        string key = "";
+        for(auto &pr: v){
+            key += to_string(pr.first) + "#" + to_string(pr.second) + "|";
+        }
+
+        vector<pair<ll,ll>> u;
+        for(auto &pr: v){
+            ll need = (k - pr.second) % k;
+            if(need) u.push_back({pr.first, need});
+        }
+
+        string key2 = "";
+        for(auto &pr: u){
+            key2 += to_string(pr.first) + "#" + to_string(pr.second) + "|";
+        }
+
+        ans += cnt[key2];
+
+
+        cnt[key]++;
+    }
+
+    cout << ans << "";
+    return 0;
+}