P4446 [AHOI2018初中组]根式化简

https://www.luogu.com.cn/record/94275503

Luogu/P4446/P4446.cpp

@@ -0,0 +1,68 @@
+#include <iostream>
+#include <cmath>
+#include <unordered_map>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+
+int t, p, primes[N];
+bool not_prime[N];
+std::unordered_map<long long, int> map;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    for (int i = 2; i < N; i++) {
+        if (!not_prime[i]) primes[++p] = i;
+
+        for (int j = 1; j <= p && primes[j] * i < N; j++) {
+            not_prime[primes[j] * i] = true;
+
+            if (i % primes[j] == 0) break;
+        }
+    }
+
+    for (int i = 1; i <= p; i++) {
+        long long x = primes[i];
+        map[x * x * x] = primes[i];
+    }
+
+    cin >> t;
+
+    while (t--) {
+        long long n, ans = 1;
+
+        cin >> n;
+
+        int m = std::sqrt(std::sqrt(n));
+
+        if (map.count(n)) {
+            cout << map[n] << endl;
+
+            continue;
+        }
+
+        for (int i = 1, x = primes[i]; i <= p && x <= m && static_cast<long long>(x) * x * x <= n; x = primes[++i]) {
+            long long y = static_cast<long long>(x) * x * x;
+
+            while (n % y == 0) {
+                ans *= x;
+                n /= y;
+            }
+
+            while (n % x == 0) {
+                n /= x;
+            }
+        }
+
+        if (map.count(n)) ans *= map[n];
+
+        cout << ans << endl;
+    }
+
+    return 0;
+}