HDU1028——Ignatius and the Princess III(背包问题dp)
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Ignatius and the Princess III
活水源头
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 18990 Accepted Submission(s): 13348
Problem Description
"Well, it seems the first problem is too easy. I will let you know how foolish you are later." feng5166 says.
"The second problem is, given an positive integer N, we define an equation like this:
N=a[1]+a[2]+a[3]+...+a[m];
a[i]>0,1<=m<=N;
My question is how many different equations you can find for a given N.
For example, assume N is 4, we can find:
4 = 4;
4 = 3 + 1;
4 = 2 + 2;
4 = 2 + 1 + 1;
4 = 1 + 1 + 1 + 1;
so the result is 5 when N is 4. Note that "4 = 3 + 1" and "4 = 1 + 3" is the same in this problem. Now, you do it!"
Input
The input contains several test cases. Each test case contains a positive integer N(1<=N<=120) which is mentioned above. The input is terminated by the end of file.
Output
For each test case, you have to output a line contains an integer P which indicate the different equations you have found.
Sample Input
41020
Sample Output
542627解题思路:具体看各种背包问题:各种背包等你来拿代码实现:#include <iostream>#include <cstdio>#include <cmath>#include <queue>#include <cstring>#include <algorithm>using namespace std;typedef long long LL;const int maxn = 1000000+10;int n;int dp[150][150];int main(){ while( ~scanf("%d",&n) ) { memset(dp,0,sizeof(dp)); dp[1][1] = 1; for( int j=0; j<=n; j++ ) { dp[0][j] = dp[j][0] = 0; } for( int i=1; i<=n; i++ ) { for( int j=1; j<=n; j++ ) { if(i==j) dp[i][j] = dp[i][j-1] +1; else if(i>j) dp[i][j] = dp[i-j][j] + dp[i][j-1]; else if(i<j) dp[i][j] = dp[i][i]; } } //for( int i=0; i<=n; i++ ) //{ // for( int j=0; j<=n; j++ ) // cout << dp[i][j] << " "; // cout <<endl; //} printf("%d\n",dp[n][n]); } return 0;}
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