HDOJ 5389 Zero Escape DP

一个数的数字根只和它$mod9$之后的值有关，只要类似背包就能完成人员分配的计算。

具体证明：数字根=\sum_{i=0}^{w}a_i∑​i=0​w​​a​i​​，数字=\sum_{i=0}^{w}10^i*a_i∑​i=0​w​​10​i​​∗a​i​​

数字-数字根=\sum_{i=0}^{w}(10^i-1)*a_i∑​i=0​w​​(10​i​​−1)∗a​i​​，这个数字在$mod$ $9$域下为$0$

Zero Escape

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 730    Accepted Submission(s): 362

Problem Description

Zero Escape, is a visual novel adventure video game directed by Kotaro Uchikoshi (you may hear about ever17?) and developed by Chunsoft.

Stilwell is enjoying the first chapter of this series, and in this chapter digital root is an important factor. 

This is the definition of digital root on Wikipedia:
The digital root of a non-negative integer is the single digit value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
For example, the digital root of 65536 is 7, because 6+5+5+3+6=25 and 2+5=7.

In the game, every player has a special identifier. Maybe two players have the same identifier, but they are different players. If a group of players want to get into a door numbered X(1≤X≤9), the digital root of their identifier sum must be X.
For example, players {1,2,6} can get into the door 9, but players {2,3,3} can't.

There is two doors, numbered A and B. Maybe A=B, but they are two different door.
And there is n players, everyone must get into one of these two doors. Some players will get into the door A, and others will get into the door B.
For example: 
players are {1,2,6}, A=9, B=1
There is only one way to distribute the players: all players get into the door 9. Because there is no player to get into the door 1, the digital root limit of this door will be ignored.

Given the identifier of every player, please calculate how many kinds of methods are there, mod 258280327.

 

Input

The first line of the input contains a single number T, the number of test cases.
For each test case, the first line contains three integers n, A and B.
Next line contains n integers idi, describing the identifier of every player.
T≤100, n≤105, ∑n≤106, 1≤A,B,idi≤9

 

Output

For each test case, output a single integer in a single line, the number of ways that these n players can get into these two doors.

 

Sample Input

43 9 11 2 63 9 12 3 35 2 31 1 1 1 19 9 91 2 3 4 5 6 7 8 9

 

Sample Output

101060

 

Source

2015 Multi-University Training Contest 8

 

/* ***********************************************Author        :CKbossCreated Time  :2015年08月14日 星期五 14时24分21秒File Name     :HDOJ5389.cpp************************************************ */#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <string>#include <cmath>#include <cstdlib>#include <vector>#include <queue>#include <set>#include <map>using namespace std;typedef long long int LL;const int maxn=100100;const LL mod=258280327LL;int n,A,B,sum;int a[maxn];int Calu(int a,int b){int ret=(a+b)%9;if(ret==0) return 9;return ret;}LL dp[maxn][10];int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);int T_T;scanf("%d",&T_T);while(T_T--){scanf("%d%d%d",&n,&A,&B);sum=0;for(int i=1;i<=n;i++) {scanf("%d",a+i);sum=Calu(sum,a[i]);}for(int i=0;i<=9;i++) dp[1][i]=0;dp[1][a[1]]=1;for(int i=2;i<=n;i++){for(int j=1;j<=9;j++) dp[i][j]=dp[i-1][j];dp[i][a[i]]=(dp[i][a[i]]+1)%mod;for(int j=1;j<=9;j++){int c=Calu(j,a[i]);dp[i][c]=(dp[i][c]+dp[i-1][j])%mod;}}LL ans=0;if(Calu(A,B)==sum){ans=dp[n][A];if(A==sum) ans--;}if(A==sum) ans++;if(B==sum) ans++;cout<<ans%mod<<endl;}    return 0;}