HDU 5456 Matches Puzzle Game [数位DP]
Problem Description
As an exciting puzzle game for kids and girlfriends, the Matches Puzzle Game asks the player to find the number of possible equations
A−B=C with exactly
n (5≤n≤500) matches (or sticks).
In these equations, A,B and C are positive integers. The equality sign needs two matches and the sign of subtraction needs just one. Leading zeros are not allowed.
Please answer the number, modulo a given integer m (3≤m≤2×109).
In these equations, A,B and C are positive integers. The equality sign needs two matches and the sign of subtraction needs just one. Leading zeros are not allowed.
Please answer the number, modulo a given integer m (3≤m≤2×109).
Input
The input contains several test cases. The first line of the input is a single integer
t which is the number of test cases. Then
t (1≤t≤30) test cases follow.
Each test case contains one line with two integers n (5≤n≤500) m (3≤m≤2×109).
Each test case contains one line with two integers n (5≤n≤500) m (3≤m≤2×109).
Output
For each test case, you should output the answer modulo
m.
题意：
给出每个数字的火柴拼接数，问用N个火柴棍构恰好造出一个无前导0的A-B=C的方程式的方案数（减号和等号算3个棍子）
解法：
转换为A+B=C，然后数位DP求解，DP[I][J][2][3][3] 分别表示 棒数 位数 进位状态 A的状态，B的状态 ：状态0表示前导为1-9，1表示前导为0,2表示前导为空格
(状态比较丑，A,B的状态其实可以只表示成2种：0：没到最高位，1：已经到过最高位)
可以发现每多一位（即J+1），I都是增加的（除非A,B的前导都是空格），那么J这一维可以省略（这个优化完全想不到，一开始跑了900MS，后来才知道这一维可以优化掉，然后就变成了60MS）
注意取模数最大为20亿，所以加法会暴int，需要定义成unsigned int
代码：
#include
#include
#include
#include
#include
#include
#include
#include