hdu 5456 Matches Puzzle Game(dp)

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题意：给出n个火柴，要求拼出形如x-y=z的等式，x,y,z都为正数。问情况总数。

做法：用一个数组a[i]代表用了i根火柴拼成数字情况总数，数组b[i]代表用了i根火柴拼成2个数字（相差1）的情况总数。

然后dp[i][0]代表用了i根火柴不借位的情况数，dp[i][1]则代表借位，然后枚举前面放的新的数字是几然后分类讨论即可。

做法比较搓，细节问题多思考量比较大。

AC代码：

#pragma comment(linker, "/STACK:102400000,102400000")#include<cstdio>#include<ctype.h>#include<algorithm>#include<iostream>#include<cstring>#include<vector>#include<cstdlib>#include<stack>#include<queue>#include<set>#include<map>#include<cmath>#include<ctime>#include<string.h>#include<string>#include<sstream>#include<bitset>using namespace std;#define ll __int64#define ull unsigned __int64#define eps 1e-8#define NMAX 200000000#define MOD 530600414#define lson l,mid,rt<<1#define rson mid+1,r,rt<<1|1#define PI acos(-1)template<class T>inline void scan_d(T &ret){    char c;    int flag = 0;    ret=0;    while(((c=getchar())<'0'||c>'9')&&c!='-');    if(c == '-')    {        flag = 1;        c = getchar();    }    while(c>='0'&&c<='9') ret=ret*10+(c-'0'),c=getchar();    if(flag) ret = -ret;}ll a[605],b[1105];int shu[10] = {6,2,5,5,4,5,6,3,7,6};ll dp[605][2];int main(){#ifdef GLQ    freopen("input.txt","r",stdin);//    freopen("o.txt","w",stdout);#endif    int T,cas = 1;    scanf("%d",&T);    while(T--)    {        int n;        ll m;        scanf("%d%I64d",&n,&m);        memset(a,0,sizeof(a));        a[0] = 1;        for(int i = 0; i <= n; i++)        {            int lim = i == 0 ? 1 : 0;            for(int j = lim; j <= 9; j++)                a[i+shu[j]] = (a[i+shu[j]]+a[i])%m;        }        memset(b,0,sizeof(b));        b[2] = 1;        for(int i = 3; i <= n; i++)        {            for(int s1 = 1; s1 <= 9; s1++) if(i >= shu[s1]+shu[s1-1])                {                    int p = i-shu[s1]-shu[s1-1];                    if(((s1 == 1 && p > 0) || s1 != 1) && p%2 == 0)                        b[i] = (b[i]+a[p/2])%m;                }            if(i >= shu[0]+shu[9]) b[i] = (b[i]+b[i-shu[0]-shu[9]])%m;        }        n -= 3;        memset(dp,0,sizeof(dp));        dp[0][0] = 1;        ll ans = 0;        for(int i = 0; i < n; i++)        {            if(dp[i][0])            {                for(int s1 = 0; s1 <= 9; s1++)                    for(int s2 = 0; s2 <= 9; s2++)                    {                        if(s1 > s2)                        {                            int ha = shu[s1]+shu[s2]+shu[s1-s2];                            if(s2)                            {                                int wo = 2, p = n-i-ha;                                if(p == 0) wo = 1;                                if(p >= 0 && p%2 == 0) ans = (ans+a[p/2]*dp[i][0]%m*wo%m)%m;                            }                            else                            {                                int p = n-i-ha;                                if(p > 0 && p%2 == 0) ans = (ans+a[p/2]*dp[i][0]%m)%m;                            }                            dp[i+ha][0] = (dp[i+ha][0]+dp[i][0])%m;                        }                        else if(s1 < s2)                        {                            int ha = shu[s1]+shu[s2]+shu[s1-s2+10];                            if(n-i-ha >= 2)                            {                                int wo = n-i-ha == 2 ? 1 : 2;                                ans = (ans+dp[i][0]*b[n-i-ha]%m*wo%m)%m;                            }                            dp[i+ha][1] = (dp[i+ha][1]+dp[i][0])%m;                        }                        else                        {                            int ha = shu[s1]+shu[s2]+shu[0];                            int p = n-i-ha;                            if(s1 != 0 && p > 0 && p%2 == 0) ans = (ans+a[p/2]*dp[i][0]%m)%m;                            dp[i+ha][0] = (dp[i+ha][0]+dp[i][0])%m;                        }                    }            }            if(dp[i][1])            {                for(int s1 = 0; s1 <= 9; s1++)                    for(int s2 = 0; s2 <= 9; s2++)                    {                        if(s1-1 >= s2)                        {                            int ha = shu[s1]+shu[s2]+shu[s1-1-s2];                            if(s2 != 0 && s1-1-s2 != 0)                            {                                int wo = 2, p = n-i-ha;                                if(p == 0) wo = 1;                                if(p >= 0 && p%2 == 0) ans = (ans+dp[i][1]*a[p/2]%m*wo%m)%m;                            }                            else if((s2 == 0 && s1-1-s2 != 0) || (s2 != 0 && s1-1-s2 == 0))                            {                                int p = n-i-ha;                                if(p > 0 && p%2 == 0) ans = (ans+dp[i][1]*a[p/2]%m)%m;                            }                            dp[i+ha][0] = (dp[i+ha][0]+dp[i][1])%m;                        }                        else                        {                            int ha = shu[s1]+shu[s2]+shu[s1+9-s2];                            if(s2 == 0 || s1+9-s2 == 0)                            {                                int p = n-i-ha;                                if(p > 2) ans = (ans+dp[i][1]*b[p]%m);                            }                            else                            {                                int p = n-i-ha;                                int wo = p == 2 ? 1 : 2;                                if(p >= 2) ans = (ans+dp[i][1]*b[p]%m*wo%m)%m;                            }                            dp[i+ha][1] = (dp[i+ha][1]+dp[i][1])%m;                        }                    }            }        }        printf("Case #%d: %I64d\n",cas++,ans);    }    return 0;}

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