Ignatius and the Princess III
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 13171 Accepted Submission(s): 9316
"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!"
#include"stdio.h"
#include"string.h"
int main()
{
int n;
int dp[130][130];
int i,l;
memset(dp,0,sizeof(dp));
dp[1][1]=1;
for(i=1;i<=130;i++)
{
dp[i][1]=1;
dp[1][i]=1;
}
for(i=2;i<=120;i++)
{
for(l=2;l<=120;l++)
{
if(l>i)
dp[i][l]=dp[i][i];
else if(l==i)
dp[i][l]=dp[i][l-1]+1;
else
dp[i][l]=dp[i][l-1]+dp[i-l][l];
}
}
while(scanf("%d",&n)!=EOF)
printf("%d\n",dp[n][n]);
return 0;
}