HDU - 4472 Count
Prof. Tigris is the head of an archaeological team who is currently in charge of an excavation in a site of ancient relics.
This site contains relics of a village where civilization once flourished. One night, examining a writing record, you find some text meaningful to you. It reads as follows.
“Our village is of glory and harmony. Our relationships are constructed in such a way that everyone except the village headman has exactly one direct boss and nobody will be the boss of himself, the boss of boss of himself, etc. Everyone expect the headman is considered as his boss’s subordinate. We call it relationship configuration. The village headman is at level 0, his subordinates are at level 1, and his subordinates’ subordinates are at level 2, etc. Our relationship configuration is harmonious because all people at same level have the same number of subordinates. Therefore our relationship is …”
The record ends here. Prof. Tigris now wonder how many different harmonious relationship configurations can exist. He only cares about the holistic shape of configuration, so two configurations are considered identical if and only if there’s a bijection of n people that transforms one configuration into another one.
Please see the illustrations below for explanation when n = 2 and n = 4.
The result might be very large, so you should take module operation with modules 10 9 +7 before print your answer.
This site contains relics of a village where civilization once flourished. One night, examining a writing record, you find some text meaningful to you. It reads as follows.
“Our village is of glory and harmony. Our relationships are constructed in such a way that everyone except the village headman has exactly one direct boss and nobody will be the boss of himself, the boss of boss of himself, etc. Everyone expect the headman is considered as his boss’s subordinate. We call it relationship configuration. The village headman is at level 0, his subordinates are at level 1, and his subordinates’ subordinates are at level 2, etc. Our relationship configuration is harmonious because all people at same level have the same number of subordinates. Therefore our relationship is …”
The record ends here. Prof. Tigris now wonder how many different harmonious relationship configurations can exist. He only cares about the holistic shape of configuration, so two configurations are considered identical if and only if there’s a bijection of n people that transforms one configuration into another one.
Please see the illustrations below for explanation when n = 2 and n = 4.
The result might be very large, so you should take module operation with modules 10 9 +7 before print your answer.
InputThere are several test cases.
For each test case there is a single line containing only one integer n (1 ≤ n ≤ 1000).
Input is terminated by EOF.OutputFor each test case, output one line “Case X: Y” where X is the test case number (starting from 1) and Y is the desired answer.Sample Input
1 2 3 40 50 600 700
Sample Output
Case 1: 1 Case 2: 1 Case 3: 2 Case 4: 924 Case 5: 1998 Case 6: 315478277 Case 7: 825219749
说实话，这个全场题我知道是dp，但是毫无思路。
可见我的思维有多僵硬，不过也算是回忆一下起树的构造过程了。
思维题都这样，想到了的觉得好简单，没想到的觉得这怎么可能想到。还是要多刷题，刷尽量多的题型，给自己尽量多的思路。
题意：构造一个所有节点的子节点数目都相同的树。
解题思路：从最基础的开始往上递推，想到树的构造过程这题就会很简单。
ac代码：
1 #include <cstdio> 2 #include <cstring> 3 #include <algorithm> 4 #include <string> 5 #include <iostream> 6 using namespace std; 7 typedef long long ll; 8 const int maxn = 1111; 9 const ll mod = 1e9+7; 10 ll dp[maxn]={0,1,1,2,3}; 11 int main() 12 { 13 int n; 14 for(int i=5;i<=1000;++i) 15 { 16 for(int j=1;j<i;++j) 17 { 18 if((i-1)%j==0) 19 { 20 dp[i]=(dp[i]%mod+dp[j]%mod)%mod; 21 } 22 } 23 } 24 int cas=1; 25 while(cin>>n) 26 { 27 cout<<"Case "<<cas++<<": "<<dp[n]<<endl; 28 } 29 }
