POJ1221 UNIMODAL PALINDROMIC DECOMPOSITIONS

                                                  UNIMODAL PALINDROMIC DECOMPOSITIONS

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 2893		Accepted: 1335

Description

A sequence of positive integers is Palindromic if it reads the same forward and backward. For example:
23 11 15 1 37 37 1 15 11 23
1 1 2 3 4 7 7 10 7 7 4 3 2 1 1
A Palindromic sequence is Unimodal Palindromic if the values do not decrease up to the middle value and then (since the sequence is palindromic) do not increase from the middle to the end For example, the first example sequence above is NOT Unimodal Palindromic while the second example is.
A Unimodal Palindromic sequence is a Unimodal Palindromic Decomposition of an integer N, if the sum of the integers in the sequence is N. For example, all of the Unimodal Palindromic Decompositions of the first few integers are given below:
1: (1)
2: (2), (1 1)
3: (3), (1 1 1)
4: (4), (1 2 1), (2 2), (1 1 1 1)
5: (5), (1 3 1), (1 1 1 1 1)
6: (6), (1 4 1), (2 2 2), (1 1 2 1 1), (3 3),
(1 2 2 1), ( 1 1 1 1 1 1)
7: (7), (1 5 1), (2 3 2), (1 1 3 1 1), (1 1 1 1 1 1 1)
8: (8), (1 6 1), (2 4 2), (1 1 4 1 1), (1 2 2 2 1),
(1 1 1 2 1 1 1), ( 4 4), (1 3 3 1), (2 2 2 2),
(1 1 2 2 1 1), (1 1 1 1 1 1 1 1)

Write a program, which computes the number of Unimodal Palindromic Decompositions of an integer.

Input

Input consists of a sequence of positive integers, one per line ending with a 0 (zero) indicating the end.

Output

For each input value except the last, the output is a line containing the input value followed by a space, then the number of Unimodal Palindromic Decompositions of the input value. See the example on the next page.

Sample Input

2
3
4
5
6
7
8
10
23
24
131
213
92
0

Sample Output

2 2
3 2
4 4
5 3
6 7
7 5
8 11
10 17
23 104
24 199
131 5010688
213 1055852590
92 331143

Source

Greater New York 2002

这个题目我想了很久，开始就认为是DP，后来证实我是对的。通过慢慢地在纸上演算终于找到它的公式

s[i][j]=s[i-2*j][j]+s[i][j+1];

在经过一个小时慢慢地写程序和调试终于将程序搞好了，下面是我的程序：

#include<iostream>
#include<cstring>
using namespace std;
__int64 m[301][301];
int main()
{
    int i,j,n;
    memset(m,0,sizeof(m));
    for(i=1;i<=300;i++)
    {
           for(j=i;j>=0;j--)
               m[i][j]=1;
    }
    for(i=0;i<=300;i++)
         m[0][i]=1;
    for(i=2;i<=300;i++)
    {
           for(j=i/2;j>=1;j--)
           {
               m[i][j]=m[i-2*j][j]+m[i][j+1];
               //cout<<"m["<<i<<"]["<<j<<"]"<<endl;
               //cout<<m[i][j]<<endl;
           }
    }                         
    while(cin>>n&&n!=0)
    {
        cout<<n<<" "<<m[n][1]<<endl;
    }
    return 0;
}