noi7219 复杂的整数划分问题

Posted 2020-12-02 wstong

noi7219 复杂的整数划分问题

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 const int maxn = 55;
 4 int dp1[maxn][maxn], dp2[maxn][maxn], dp3[maxn][maxn], dp4[maxn][maxn];
 5 void init() {
 6     for (int n = 1; n <= 50; n++) {
 7         for (int k = 1; k <= 50; k++) {
 8             if (n == k) dp1[n][k] = 1;
 9             else if (n < k) dp1[n][k] = 0;
10             else dp1[n][k] = dp1[n-k][k]+dp1[n-1][k-1];
11         }
12     }
13 
14     for (int n = 1; n <= 50; n++) {
15         dp2[n][1] = n==1 ? 1 : 0;
16         for (int m = 2; m <= 50; m++) {
17             if (n < m) dp2[n][m] = dp2[n][n];
18             else if (n == m) dp2[n][m] = dp2[n][m-1]+1;
19             else dp2[n][m] = dp2[n][m-1]+dp2[n-m][m-1];
20         }
21     }
22 
23     for (int n = 1; n <= 50; n++) {
24         dp3[n][1] = (n%2), dp4[n][1] = (n%2==0);
25         dp3[n][0] = dp3[n][1];
26         for (int m = 2; m <= 50; m++) {
27             if (n < m) dp3[n][m] = dp4[n][m] = 0;
28             else if (n == m) dp3[n][m] = 1, dp4[n][m] = 0;
29             else {
30                 dp3[n][m] = dp3[n-1][m-1]+dp4[n-m][m];
31                 dp4[n][m] = dp3[n-m][m];
32             }
33             dp3[n][0] += dp3[n][m];
34         }
35     }
36 }
37 int main() {
38     init();
39     int n, k;
40     while (cin >> n >> k) {
41         cout << dp1[n][k] << endl;
42         cout << dp2[n][n] << endl;
43         cout << dp3[n][0] << endl;
44     }
45     return 0;
46 }