Create 1847_x7536110.cpp

QUSTOJ/1847_x7536110.cpp

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+#include <cstdio>
+#include <cstring>
+#include <algorithm>
+using namespace std;
+namespace acm {
+/// count primes between [1..n] (0< n <=1e9)
+/// solution: dp
+/// d(n, i) means that the number of value whose min prime number is bigger than i in [1..n]
+/// d(n, i) = d(n, i-1) if number i is not a prime
+/// d(n, i) = d(n, i-1) - d(n/i, i) + d(i, i-1) if number i is a prime
+/// complex time: O(n^(3/4)), space: O(n^(1/2))
+static const long long maxn = 1e6+11;
+long long dp[maxn];
+struct CountPrime {
+    long long solve(long long n) {
+        if (n < 2) {
+            return 0;
+        }
+        dp[0] = 0;
+        long long sqrtn = 1, length = 0;
+        for (; sqrtn <= n / sqrtn; ++sqrtn) {
+            dp[++length] = sqrtn - 1;
+        }
+        for (long long i = sqrtn - 1; i > 0; --i) {
+            long long val = n / i;
+            if (val != i) {
+                dp[++length] = val - 1;
+            }
+        }
+        for (long long i = 1; i < sqrtn; ++i) {
+            if (dp[i] == dp[i-1]) {
+                continue;
+            }
+            for (long long j=length; j>0; --j) {
+                long long val = j < sqrtn ? j : n / (length - j + 1);
+                if (i > val / i) {
+                    break;
+                }
+                long long pre_statue_pos = val / i;
+                if (pre_statue_pos >= sqrtn) {
+                    pre_statue_pos = length - n / pre_statue_pos + 1;
+                }
+                dp[j] += dp[i-1] - dp[pre_statue_pos];
+            }
+        }
+        return dp[length];
+    }
+};
+} // namespace acm
+int main()
+{
+    //freopen("in", "r", stdin);
+    //freopen("out", "w", stdout);
+    acm::CountPrime cp;
+    //printf("IIII\n");
+    long long n;
+    while (scanf ("%lld", &n) != EOF) {
+        printf ("%lld\n", cp.solve(n));
+    }
+    return 0;
+}