摔电脑摔电脑！JZP业界毒瘤！
400题纪念~哇终于上400了的说！！！好不容易欸！
题解什么的还是Orz iwtwiioi
我求组合数的方法明明是O(n)的，为什么这么慢！！！令人报警！
喂，话说这题的重点不在求组合数上面吧。。。
1 /**************************************************************
2 Problem: 3434
3 User: rausen
4 Language: C++
5 Result: Accepted
6 Time:6888 ms
7 Memory:140824 kb
8 ****************************************************************/
9
10 #include <cstdio>
11 #include <cstring>
12 #include <algorithm>
13
14 using namespace std;
15 const int N = 100005;
16 const int mod = 10007;
17 const int Tt = 1005;
18
19 int g[21][N], f[21][15][N];
20 int a[15], p[N], cnt, u[N], mx, mn;
21 int n[Tt], c[Tt], m[Tt][15];
22 int C[N][20];
23 int ans;
24 bool vis[N];
25
26 inline int read() {
27 int x = 0, sgn = 1;
28 char ch = getchar();
29 while (ch < ‘0‘ || ‘9‘ < ch) {
30 if (ch == ‘-‘) sgn = -1;
31 ch = getchar();
32 }
33 while (‘0‘ <= ch && ch <= ‘9‘) {
34 x = x * 10 + ch - ‘0‘;
35 ch = getchar();
36 }
37 return sgn * x;
38 }
39
40 int pow(int x, int y) {
41 int res = 1;
42 while (y) {
43 if (y & 1) (res *= x) %= mod;
44 (x *= x) %= mod;
45 y >>= 1;
46 }
47 return res;
48 }
49
50 void get_f(int N) {
51 int i, j, k, l;
52 for (u[1] = 1, i = 2; i <= N; ++i) {
53 if (!vis[i])
54 p[++cnt] = i, u[i] = -1;
55 for (j = 1; j <= cnt; ++j) {
56 if ((k = i * p[j]) > N) break;
57 vis[k] = 1;
58 if (i % p[j] == 0) {
59 u[k] = 0;
60 break;
61 }
62 u[k] = -u[i];
63 }
64 }
65 for (C[0][0] = i = 1; i <= N; ++i)
66 for (C[i][0] = j = 1; j < 19; ++j)
67 C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
68
69 for (l = 2; l <= 20; ++l)
70 for (i = 1; i <= N; ++i)
71 for (j = i, k = 1; j <= N; j += i, ++k)
72 (g[l][j] += C[i - 1][l - 2] * u[k]) %= mod;
73 for (i = 1; i <= N; ++i)
74 for (l = 2; l <= 20; ++l) {
75 k = 1;
76 for (j = 1; j <= 12; ++j) {
77 f[l][j][i] = (f[l][j][i - 1] + k * g[l][i]) % mod;
78 (k *= i) %= mod;
79 }
80 }
81 }
82
83 void calc(int i, int x) {
84 memset(a, 0, sizeof(a));
85 a[1] = 1;
86 int d1, d2, t, j, k;
87 for (k = 1; k <= n[i]; ++k) {
88 t = m[i][k] / x;
89 d1 = (1ll * t * m[i][k]) % mod;
90 d2 = (1ll * t * (t + 1) >> 1) % mod;
91 for (j = n[i] + 1; j > 1; --j)
92 a[j] =(a[j] * d1 - a[j - 1] * d2) % mod;
93 (a[1] *= d1) %= mod;
94 }
95 }
96
97 int main() {
98 int i, j, k, l, T;
99 T = read();
100 for (i = 1; i <= T; ++i) {
101 n[i] = read(), c[i] = read();
102 for (j = 1; j <= n[i]; ++j)
103 m[i][j] = read(), mx = max(mx, m[i][j]);
104 }
105 get_f(mx);
106
107 for (i = 1; i <= T; ++i) {
108 ans = 0;
109 for (mn = m[i][1], j = 2; j <= n[i]; ++j)
110 mn = min(mn, m[i][j]);
111 for (j = 1; j <= mn; j = k + 1) {
112 k = mn + 1;
113 for (l = 1; l <= n[i]; ++l)
114 k = min(k, m[i][l] / (m[i][l] / j));
115 calc(i, j);
116 for (l = 1; l <= n[i] + 1; ++l)
117 (ans += a[l] * (f[c[i]][l][k] - f[c[i]][l][j - 1])) %= mod;
118 }
119 ans %= mod;
120 printf("%d\n", (ans += mod) %= mod);
121 }
122 return 0;
123 }
(递推求组合数)
1 /**************************************************************
2 Problem: 3434
3 User: rausen
4 Language: C++
5 Result: Accepted
6 Time:9596 ms
7 Memory:134184 kb
8 ****************************************************************/
9
10 #include <cstdio>
11 #include <cstring>
12 #include <algorithm>
13
14 using namespace std;
15 const int N = 100005;
16 const int mod = 10007;
17 const int Tt = 1005;
18
19 int g[21][N], f[21][15][N];
20 int a[15], p[N], cnt, u[N], mx, mn;
21 int n[Tt], c[Tt], m[Tt][15];
22 int fac[N], faci[N], sum[N];
23 int ans;
24 bool vis[N];
25
26 inline int read() {
27 int x = 0, sgn = 1;
28 char ch = getchar();
29 while (ch < ‘0‘ || ‘9‘ < ch) {
30 if (ch == ‘-‘) sgn = -1;
31 ch = getchar();
32 }
33 while (‘0‘ <= ch && ch <= ‘9‘) {
34 x = x * 10 + ch - ‘0‘;
35 ch = getchar();
36 }
37 return sgn * x;
38 }
39
40 int pow(int x, int y) {
41 int res = 1;
42 while (y) {
43 if (y & 1) (res *= x) %= mod;
44 (x *= x) %= mod;
45 y >>= 1;
46 }
47 return res;
48 }
49
50 inline int C(int x, int y) {
51 if (y == 0) return 1;
52 if (x < y) return 0;
53 if (sum[x] != sum[y] + sum[x - y]) return 0;
54 return fac[x] * faci[y] % mod * faci[x - y] % mod;
55 }
56
57 void get_f(int N) {
58 int i, j, k, l;
59 for (u[1] = 1, i = 2; i <= N; ++i) {
60 if (!vis[i])
61 p[++cnt] = i, u[i] = -1;
62 for (j = 1; j <= cnt; ++j) {
63 if ((k = i * p[j]) > N) break;
64 vis[k] = 1;
65 if (i % p[j] == 0) {
66 u[k] = 0;
67 break;
68 }
69 u[k] = -u[i];
70 }
71 }
72 fac[0] = faci[0] = 1;
73 for (fac[1] = 1, i = 2; i <= N; ++i)
74 if (i % mod == 0) {
75 sum[i] = sum[i - 1] + 1;
76 fac[i] = fac[i - 1] * (i / mod) % mod;
77 } else {
78 sum[i] = sum[i - 1];
79 fac[i] = fac[i - 1] * i % mod;
80 }
81 for (faci[N] = pow(fac[N], mod - 2),i = N - 1; i; --i)
82 if ((i + 1) % mod == 0)
83 faci[i] = faci[i + 1] * ((i + 1) / mod) % mod;
84 else faci[i] = faci[i + 1] * (i + 1) % mod;
85
86 for (l = 2; l <= 20; ++l)
87 for (i = 1; i <= N; ++i)
88 for (j = i, k = 1; j <= N; j += i, ++k)
89 (g[l][j] += C(i - 1, l - 2) * u[k]) %= mod;
90 for (i = 1; i <= N; ++i)
91 for (l = 2; l <= 20; ++l) {
92 k = 1;
93 for (j = 1; j <= 12; ++j) {
94 f[l][j][i] = (f[l][j][i - 1] + k * g[l][i]) % mod;
95 (k *= i) %= mod;
96 }
97 }
98 }
99
100 void calc(int i, int x) {
101 memset(a, 0, sizeof(a));
102 a[1] = 1;
103 int d1, d2, t, j, k;
104 for (k = 1; k <= n[i]; ++k) {
105 t = m[i][k] / x;
106 d1 = (1ll * t * m[i][k]) % mod;
107 d2 = (1ll * t * (t + 1) >> 1) % mod;
108 for (j = n[i] + 1; j > 1; --j)
109 a[j] =(a[j] * d1 - a[j - 1] * d2) % mod;
110 (a[1] *= d1) %= mod;
111 }
112 }
113
114 int main() {
115 int i, j, k, l, T;
116 T = read();
117 for (i = 1; i <= T; ++i) {
118 n[i] = read(), c[i] = read();
119 for (j = 1; j <= n[i]; ++j)
120 m[i][j] = read(), mx = max(mx, m[i][j]);
121 }
122 get_f(mx);
123
124 for (i = 1; i <= T; ++i) {
125 ans = 0;
126 for (mn = m[i][1], j = 2; j <= n[i]; ++j)
127 mn = min(mn, m[i][j]);
128 for (j = 1; j <= mn; j = k + 1) {
129 k = mn + 1;
130 for (l = 1; l <= n[i]; ++l)
131 k = min(k, m[i][l] / (m[i][l] / j));
132 calc(i, j);
133 for (l = 1; l <= n[i] + 1; ++l)
134 (ans += a[l] * (f[c[i]][l][k] - f[c[i]][l][j - 1])) %= mod;
135 }
136 ans %= mod;
137 printf("%d\n", (ans += mod) %= mod);
138 }
139 return 0;
140 }
(奇怪的组合数求法)
(p.s. 关于那种空间较小的求组合数的方法为什么慢了3秒我也是无言以对。。。)
时间： 2024-10-24 14:58:04