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hdu5456 Matches Puzzle Game

2015-09-23 12:06 393 查看

题意：给出n个火柴棒，问能摆成多少个a-b=c的等式，其中，a,b,c均为正整数。
做法：dp[i][j][cr][c]，当前用了i个火柴棒，从低位到高位，已经考虑到了第j位，cr代表j-1位是否给j位贡献了一个1，b代表数字b是否已经到了最高位，c代表数字c是否已经到了最高位。有多少种方法到达目标状态。不断枚举在j位的数字进行数位dp即可。由于j肯定是不断在增大的，所以写的时候可以直接舍去这维。

#include<map> #include<string> #include<cstring> #include<cstdio> #include<cstdlib> #include<cmath> #include<queue> #include<vector> #include<iostream> #include<algorithm> #include<bitset> #include<climits> #include<list> #include<iomanip> #include<stack> #include<set> using namespace std; typedef long long ll; int n; int a[10]={6,2,5,5,4,5,6,3,7,6}; ll m; ll dp[510][2][2][2]; ll dfs(int num,int cr,int b,int c) { if(num>n) return 0; if(num+a[1]==n&&cr==1&&b==1&&c==1) return 1; if(num==n) { if(cr==0&&b==1&&c==1) return 1; return 0; } if(dp[num][cr][b][c]!=-1) return dp[num][cr][b][c]; dp[num][cr][b][c]=0; if(b==0) { if(c==0) { for(int i=0;i<10;i++) for(int j=0;j<10;j++) { int t=a[i]+a[j]+a[(i+j+cr)%10]; dp[num][cr][b][c]+=dfs(num+t,(i+j+cr)/10,0,0); if(i!=0) dp[num][cr][b][c]+=dfs(num+t,(i+j+cr)/10,1,0); if(j!=0) dp[num][cr][b][c]+=dfs(num+t,(i+j+cr)/10,0,1); if(i!=0&&j!=0) dp[num][cr][b][c]+=dfs(num+t,(i+j+cr)/10,1,1); dp[num][cr][b][c]%=m; } } else { for(int i=0;i<10;i++) { int t=a[i]+a[(i+cr)%10]; dp[num][cr][b][c]+=dfs(num+t,(i+cr)/10,0,1); if(i!=0) dp[num][cr][b][c]+=dfs(num+t,(i+cr)/10,1,1); } } } else { if(c==0) { for(int i=0;i<10;i++) { int t=a[i]+a[(i+cr)%10]; dp[num][cr][b][c]+=dfs(num+t,(i+cr)/10,1,0); if(i!=0) dp[num][cr][b][c]+=dfs(num+t,(i+cr)/10,1,1); } } } return dp[num][cr][b][c]%=m; } int main() { int T; scanf("%d",&T); for(int cs=1;cs<=T;cs++) { cin>>n>>m; n-=3; memset(dp,-1,sizeof(dp)); printf("Case #%d: %d\n",cs,int(dfs(0,0,0,0))); } }

[b]Time Limit: 3000/2000 MS (Java/Others) Memory Limit: 65535/102400 K (Java/Others)

Total Submission(s): 107 Accepted Submission(s): 70

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).

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) and m (3≤m≤2×109).

Output

For each test case, you should output the answer modulo m.

Sample Input

4
12 1000000007
17 1000000007
20 1000000007
147 1000000007

Sample Output

Case #1: 1
Case #2: 5
Case #3: 38
Case #4: 815630825

Source

2015 ACM/ICPC Asia Regional Shenyang Online

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