solved q2

Author: arnavsingh010

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

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+#include <bits/stdc++.h>
+using namespace std;
+
+static const int maxi = 100000;
+int spf[maxi + 1];
+int k;
+
+/*sieve*/
+void buildSPF() {
+    for (int i = 1; i <= maxi; i++)
+        spf[i] = i;
+
+    for (int i = 2; i * i <= maxi; i++) {
+        if (spf[i] == i) {
+            for (int j = i * i; j <= maxi; j += i) {
+                if (spf[j] == j)
+                    spf[j] = i;
+            }
+        }
+    }
+}
+
+/*factorise*/
+vector<pair<int,int>> getSignature(int x) {
+    map<int,int> factors;
+
+    while (x > 1) {
+        int p = spf[x];
+        factors[p]++;
+        x /= p;
+    }
+
+    vector<pair<int,int>> sig;
+    for (auto &it : factors) {
+        int exp = it.second % k;
+        if (exp != 0)
+            sig.push_back({it.first, exp});
+    }
+    return sig;
+}
+
+/*how many needed*/
+vector<pair<int,int>> getComplement(const vector<pair<int,int>> &sig) {
+    vector<pair<int,int>> comp;
+    for (auto &p : sig) {
+        comp.push_back({p.first, (k - p.second) % k});
+    }
+    return comp;
+}
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+    cin >> n >> k;
+
+    vector<int> a(n);
+    for (int i = 0; i < n; i++)
+        cin >> a[i];
+
+    buildSPF();
+
+    map<vector<pair<int,int>>, long long> freq;
+    long long ans = 0;
+
+    for (int i = 0; i < n; i++) {
+        vector<pair<int,int>> sig = getSignature(a[i]);
+        vector<pair<int,int>> need = getComplement(sig);
+        ans += freq[need];
+        freq[sig]++;
+    }
+    cout << ans << "\n";
+    return 0;
+}
+//https://codeforces.com/problemset/submission/1225/355302622
+//time  complexity O(nlognlog(10^5))