Partition
Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 880 Accepted Submission(s): 502
Problem Description
How many ways can the numbers 1 to 15 be added together to make 15? The technical term for what you are asking is the "number of partition" which is often called P(n). A partition of n is a collection of positive integers (not necessarily distinct) whose sum
equals n.
equals n.
Now, I will give you a number n, and please tell me P(n) mod 1000000007.
Input
The first line contains a number T(1 ≤ T ≤ 100), which is the number of the case number. The next T lines, each line contains a number n(1 ≤ n ≤ 105) you need to consider.
Output
For each n, output P(n) in a single line.
Sample Input
4 5 11 15 19
Sample Output
7 56 176 490
Source
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ac代码
#include<stdio.h>
#include<string.h>
#define mod 1000000007
__int64 p[100005];
void fun()
{
int a,b,i,flag=1,j;
p[0]=p[1]=1;
p[2]=2;
p[3]=3;
for(i=4;i<100005;i++)
{
p[i]=0;
flag=1;
for(j=1;;j++)
{
a=(j*j*3+j)/2;
b=(j*j*3-j)/2;
if(a>i&&b>i)
break;
if(a<=i)
p[i]=(p[i]+p[i-a]*flag+mod)%mod;
if(b<=i)
p[i]=(p[i]+p[i-b]*flag+mod)%mod;
flag=-flag;
}
}
}
int main()
{
int t;
fun();
scanf("%d",&t);
while(t--)
{
int n;
scanf("%d",&n);
printf("%I64d\n",p[n]);
}
}