BZOJ4176 Lucas的数论

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 template <class _T> inline void read(_T &_x) {
 4     int _t; bool flag = false;
 5     while ((_t = getchar()) != ‘-‘ && (_t < ‘0‘ || _t > ‘9‘)) ;
 6     if (_t == ‘-‘) _t = getchar(), flag = true; _x = _t - ‘0‘;
 7     while ((_t = getchar()) >= ‘0‘ && _t <= ‘9‘) _x = _x * 10 + _t - ‘0‘;
 8     if (flag) _x = -_x;
 9 }
10 typedef long long LL;
11 const int maxn = 2e6;
12 const int mod = 1000000007;
13 int mu[maxn], prime[maxn], pcnt;
14 bool vis[maxn];
15 inline int mul(int a, int b) {return (int)((LL)a * b % mod); }
16 inline void add(int &a, int b) {a += b; if (a < 0) a += mod; if (a >= mod) a -= mod; }
17 inline void init() {
18     mu[0] = 0, mu[1] = 1;
19     for (register int i = 2; i < maxn; ++i) {
20         if (!vis[i]) {
21             prime[++pcnt] = i;
22             mu[i] = -1;
23         }
24         for (register int j = 1, tmp; j <= pcnt && (tmp = prime[j] * i) < maxn; ++j) {
25             vis[tmp] = true;
26             if (i % prime[j] == 0) {
27                 mu[tmp] = 0;
28                 break;
29             }
30             mu[tmp] = -mu[i];
31         }
32     }
33     for (register int i = 2; i < maxn; ++i) mu[i] += mu[i - 1];
34 }
35 map<int, int> Mmu;
36 int Mu(int n) {
37     if (n < maxn) return mu[n];
38     if (Mmu.find(n) != Mmu.end()) return Mmu[n];
39     int ret = 1;
40     for (int i = 2, j, t; i <= n; i = j + 1) {
41         t = n / i, j = n / t;
42         add(ret, -mul(Mu(t), j - i + 1));
43     }
44     Mmu[n] = ret;
45     return ret;
46 }
47 inline int F_2(int n) {
48     int ret = 0;
49     for (register int i = 1, j, t; i <= n; i = j + 1) {
50         t = n / i, j = n / t;
51         add(ret, mul(t, (j - i + 1)));
52     }
53     return mul(ret, ret);
54 }
55 inline int calc(int n) {
56     int ret = 0;
57     for (int i = 1, j, t; i <= n; i = j + 1) {
58         t = n / i, j = n / t;
59         add(ret, mul(Mu(j) - Mu(i - 1), F_2(t)));
60     }
61     return ret;
62 }
63 int main() {
64     //freopen(".in", "r", stdin);
65     //freopen(".out", "w", stdout);
66     init();
67     int n; read(n);
68     cout << calc(n) << endl;
69     return 0;
70 }