BNU 13064 Dice (I) prefix and optimized DP

Dice (I)

You have N dices; Each of the them have K faces numbered from 1 to K. Now there are arranged the N dices in a line. You can rotate/flip any dice if you want. How many ways can set the top faces such so the summation of all the top faces equals S?

Now is given N, K, S; Calculate the total number of ways.

Input

Input starts with an integer T (≤25), denoting the number of test cases.

Each case contains three integers: N (1≤n≤1000), K (1≤k≤1000) and S (0≤s≤15000).

Output

For each case print, the case number and the result modulo 100000007.

Sample Input

Sample Input	Output for Sample Input
5 1 6 3 2 9 8 500 6 1000 800 800 10000 2 100 10	Case 1:1 Case 2:7 Case 3:57,286,574 Case 4:72,413,502 Case 5:9

Sourcejane Alam Jan Test Instructions: Give you n a dice, each dice have 1-k a score, ask you how many ways and is s Solving: First Dp[i][j] represents the first I dice, and the number of programs for S so Dp[i][j]=dp[i-1][j-1]+............+dp[i-1][j-k]; For i is completely by the state of the i-1, we can use Sum[j] to represent a prefix of dp[i-1][1 to J] and, using I to represent the now state to be computed, last represents the state of i-1 so that we can get dp[now][j]=sum[j-1]-sum[    J-K-1]; The final answer is Dp[now][s];

///1085422276#include <iostream>#include<cstdio>#include<cstring>#include<string>#include<algorithm>#include<queue>#include<cmath>#include<map>#include<bitset>#include<Set>#include<vector>using namespacestd; typedefLong Longll;#defineMem (a) memset (A,0,sizeof (a))#defineMeminf (a) memset (A,127,sizeof (a));#defineMemfy (a) memset (A,-1,sizeof (a));#defineTS printf ("111111\n");#definefor (I,A,B) for (int i=a;i<=b;i++)#defineForj (I,A,B) for (int i=a;i>=b;i--)#defineREAD (a,b,c) scanf ("%d%d%d", &a,&b,&c)#defineMoD 100000007#defineINF 100000000inline ll read () {ll x=0, f=1; CharCh=GetChar ();  while(ch<'0'|| Ch>'9')    {        if(ch=='-') f=-1; CH=GetChar (); }     while(ch>='0'&&ch<='9') {x=x*Ten+ch-'0'; CH=GetChar (); }    returnx*F;}//****************************************#defineMAXN 15000+5ll dp[2][MAXN],SUM[MAXN];intn,k,s;intMain () {intt=read (); intoo=1;  while(t--) {scanf ("%d%d%d",&n,&k,&s); intlast=0, now=1;          MEM (DP); dp[now][0]=1;  for(intI=1; i<=n;i++) {swap (last,now);            MEM (Dp[now]); sum[0]=dp[last][0];  for(intj=1; j<=s;j++) {Sum[j]= (sum[j-1]+DP[LAST][J])%MoD; }             for(intj=1; j<=s;j++)            {                if(j<=k) dp[now][j]= (sum[j-1])%MoD; ElseDp[now][j]= (sum[j-1]-sum[j-k-1]+MOD)%MoD; }} printf ("Case %d:", oo++); cout<<dp[now][s]<<Endl;; }    return 0;}

Code

BNU 13064 Dice (I) prefix and optimized DP