【蓝桥杯】历届试题 公式求值

 1 import java.math.BigInteger;
 2 import java.util.Scanner;
 3 
 4 public class Main {
 5     public static BigInteger lucas(BigInteger n, BigInteger m, BigInteger p) {
 6         if (m.equals(BigInteger.ZERO))
 7             return BigInteger.ONE;
 8         return BigInteger
 9                 .valueOf(f(n.mod(p).longValue(), m.mod(p).longValue()))
10                 .multiply(lucas(n.divide(p), m.divide(p), p)).mod(p);
11     }
12 
13     public static long f(long n, long m) {
14         if (m > n)
15             return 1;
16         if (n == m || m == 0)
17             return 1;
18         if (m > n - m)
19             m = n - m;
20         long tmpi = 1, tmpn = 1, s1 = 1, s2 = 1, ans = 1;
21         for (int i = 1; i <= m; i++) {
22             tmpi = i;
23             tmpn = n - i + 1;
24             s1 = s1 * tmpi % 999101;
25             s2 = s2 * tmpn % 999101;
26         }
27         ans = s2 * pow1(s1, 999099) % 999101;
28         return ans % 999101;
29     }
30 
31     public static long pow1(long x, long n) {
32         if (x == 1)
33             return 1;
34         if (n == 0)
35             return 1;
36         else {
37             while ((n & 1) == 0) {
38                 n >>= 1;
39                 x = (x * x) % 999101;
40             }
41         }
42         long result = x % 999101;
43         n >>= 1;
44         while (n != 0) {
45             x = (x * x) % 999101;
46             ;
47             if ((n & 1) != 0)
48                 result = result * x % 999101;
49             n >>= 1;
50         }
51         return result;
52     }
53 
54     public static void main(String[] args) {
55         Scanner sc = new Scanner(System.in);
56         BigInteger n = new BigInteger(sc.nextLine());
57         BigInteger m = new BigInteger(sc.nextLine());
58         int k = Integer.parseInt(sc.nextLine());
59         BigInteger md = new BigInteger("999101");
60         long Cnm = lucas(n, m, md).longValue() % 999101;
61         long sum = 0;
62         if (Cnm != 0) {
63             int[][] a = new int[k][k];
64             int h = 1;
65             for (int i = 0; i < k; i++) {
66                 for (int j = 0; j < k; j++) {
67                     if (j >= h)
68                         a[i][j] = 0;
69                     else {
70                         if (j == 0 || j == h - 1)
71                             a[i][j] = 1;
72                         else {
73                             a[i][j] = (a[i - 1][j - 1] * (h - j) + a[i - 1][j]) % 999101;
74                         }
75                     }
76                 }
77                 h++;
78             }
79             long m1 = 1, n1 = 1;
80             long x = n.subtract(new BigInteger(k + ""))
81                     .mod(md.subtract(BigInteger.ONE)).longValue();
82             long n3 = pow1(2, x);
83             for (int i = k - 1; i >= 0; i--) {
84                 n1 = n3 * pow1(2, i) % 999101;
85                 m1 = m1
86                         * (n.subtract(new BigInteger((k - 1 - i) + "")).mod(md)
87                                 .longValue()) % 999101;
88                 sum = (sum + m1 * a[k - 1][i] * n1) % 999101;
89             }
90             sum = sum * Cnm % 999101;
91         }
92         System.out.println(sum);
93     }
94 
95 }