POJ-2346 Lucky tickets（线性DP）

Lucky tickets Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 3298 Accepted: 2174 Description

The public transport administration of Ekaterinburg is anxious about the fact that passengers don’t like to pay for passage doing their best to avoid the fee. All the measures that had been taken (hard currency premiums for all of the chiefs, increase in conductors’ salaries, reduction of number of buses) were in vain. An advisor especially invited from the Ural State University says that personally he doesn’t buy tickets because he rarely comes across the lucky ones (a ticket is lucky if the sum of the first three digits in its number equals to the sum of the last three ones). So, the way out is found — of course, tickets must be numbered in sequence, but the number of digits on a ticket may be changed. Say, if there were only two digits, there would have been ten lucky tickets (with numbers 00, 11, …, 99). Maybe under the circumstances the ratio of the lucky tickets to the common ones is greater? And what if we take four digits? A huge work has brought the long-awaited result: in this case there will be 670 lucky tickets. But what to do if there are six or more digits? So you are to save public transport of our city. Write a program that determines a number of lucky tickets for the given number of digits. By the way, there can’t be more than 10 digits on one ticket. Input

Input contains a positive even integer N not greater than 10. It’s an amount of digits in a ticket number. Output

Output should contain a number of tickets such that the sum of the first N/2 digits is equal to the sum of the second half of digits. Sample Input

4 Sample Output

670

动态规划，求一个N位数是否是幸运数字，那么可以枚举前N/2可以组成的所有数字的个数，答案就是每个数字的个数的平方和。dp[i][k]表示i位组成k的个数，用线性dp，递推就好了

#include <iostream>
#include <string.h>
#include <math.h>
#include <algorithm>
#include <stdlib.h>

using namespace std;
int dp[6][46];
int main()
{
    memset(dp,0,sizeof(dp));
    dp[0][0]=1;
    for(int i=1;i<6;i++)
    {
    //j表示当前这个位上的数字
        for(int j=0;j<=9;j++)
        {
            for(int k=9*i;k>=j;k--)
            {
                dp[i][k]+=dp[i-1][k-j];
            }
        }
    }
    int n,ans;
    while(scanf("%d",&n)!=EOF)
    {
        n/=2;
        ans=0;
        for(int i=0;i<=45;i++)
            ans+=dp[n][i]*dp[n][i];
        printf("%d\n",ans);
    }
    return 0;

}