'commit'

TangDou/Topic/Mobius/P4318.cpp

@@ -1,29 +1,43 @@
 #include <bits/stdc++.h>
 using namespace std;
-int t, k, z[100005], p[100005], mu[100005];
-long long check(long long g) {
-    long long res = 0;
-    for (int i = 1; i * i <= g; i++)
-        res = res + mu[i] * (g / i / i);
+const int N = 100010;
 
-    return res;
-}
-int main() {
+// 筛法求莫比乌斯函数(枚举约数)
+int mu[N], sum[N]; // sum[N]:梅滕斯函数,也就是莫比乌斯函数的前缀和
+int primes[N], cnt;
+bool st[N];
+void get_mobius(int n) {
     mu[1] = 1;
-    for (int i = 2; i <= 100000; i++) {
-        if (!z[i]) {
-            p[++p[0]] = i;
+    for (int i = 2; i <= n; i++) {
+        if (!st[i]) {
+            primes[cnt++] = i;
             mu[i] = -1;
         }
-        for (int j = 1; j <= p[0] && i * p[j] <= 100000; j++) {
-            z[i * p[j]] = 1;
-            if (i % p[j] == 0) {
-                mu[i * p[j]] = 0;
+        for (int j = 0; primes[j] <= n / i; j++) {
+            int t = primes[j] * i;
+            st[t] = true;
+            if (i % primes[j] == 0) {
+                mu[t] = 0;
                 break;
             }
-            mu[i * p[j]] = -mu[i];
+            mu[t] = -mu[i];
         }
     }
+    // 维护u(x)前缀和:梅滕斯函数
+    for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + mu[i];
+}
+long long check(long long g) {
+    long long res = 0;
+    for (int i = 1; i * i <= g; i++)
+        res = res + mu[i] * (g / i / i);
+
+    return res;
+}
+
+int main() {
+    get_mobius(N - 1);
+
+    int t, k;
     cin >> t;
     while (t--) {
         cin >> k;