Codeforces 544C Writing Code【二维完全背包】
2017-06-14 14:39
417 查看
C. Writing Code
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Programmers working on a large project have just received a task to write exactly
m lines of code. There are
n programmers working on a project, the i-th of them makes exactly
ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a
plan, if v1 + v2 + ... + vn = m. The programmers follow
the plan like that: in the beginning the first programmer writes the first
v1 lines of the given task, then the second programmer writes
v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan
good, if all the written lines of the task contain at most
b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer
mod.
Input
The first line contains four integers n,
m, b,
mod (1 ≤ n, m ≤ 500,
0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively
and the modulo you should use when printing the answer.
The next line contains n space-separated integers
a1, a2, ..., an (0 ≤ ai ≤ 500) —
the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo
mod.
Examples
Input
Output
Input
Output
Input
Output
题目大意:
现在一共有N个程序员,一个程序员(编号为i)写一行代码会有Ai个bug.目的是完成一个M行的程序。
第i个程序员会写Vi行代码,对应就会出现Vi*Ai个Bug.
问将这个M行的程序写完之后,Bug数量不超过b个的分配方案数。
思路:
题目读懂之后,很显然的一个完全背包。
设定dp【i】【j】表示一共写了i行代码,一共写出来了j个Bug的方案数。
那么很简单的递推方程:dp【i】【j】=dp【i-1】【j-Ai】;
那么ans=Σdp【m】【i】(0<=i<=b)
Ac代码:
#include<stdio.h>
#include<string.h>
using namespace std;
int dp[505][500*4];
int main()
{
int n,m,b,mod;
while(~scanf("%d%d%d%d",&n,&m,&b,&mod))
{
memset(dp,0,sizeof(dp));
dp[0][0]=1;
for(int z=0;z<n;z++)
{
int x;
scanf("%d",&x);
for(int i=1;i<=m;i++)
{
for(int j=x;j<=b;j++)
{
dp[i][j]+=dp[i-1][j-x];
dp[i][j]%=mod;
}
}
}
int ans=0;
for(int i=0;i<=b;i++)
{
ans+=dp[m][i];
ans%=mod;
}
printf("%d\n",ans);
}
}
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Programmers working on a large project have just received a task to write exactly
m lines of code. There are
n programmers working on a project, the i-th of them makes exactly
ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a
plan, if v1 + v2 + ... + vn = m. The programmers follow
the plan like that: in the beginning the first programmer writes the first
v1 lines of the given task, then the second programmer writes
v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan
good, if all the written lines of the task contain at most
b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer
mod.
Input
The first line contains four integers n,
m, b,
mod (1 ≤ n, m ≤ 500,
0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively
and the modulo you should use when printing the answer.
The next line contains n space-separated integers
a1, a2, ..., an (0 ≤ ai ≤ 500) —
the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo
mod.
Examples
Input
3 3 3 100 1 1 1
Output
10
Input
3 6 5 1000000007 1 2 3
Output
0
Input
3 5 6 11 1 2 1
Output
0
题目大意:
现在一共有N个程序员,一个程序员(编号为i)写一行代码会有Ai个bug.目的是完成一个M行的程序。
第i个程序员会写Vi行代码,对应就会出现Vi*Ai个Bug.
问将这个M行的程序写完之后,Bug数量不超过b个的分配方案数。
思路:
题目读懂之后,很显然的一个完全背包。
设定dp【i】【j】表示一共写了i行代码,一共写出来了j个Bug的方案数。
那么很简单的递推方程:dp【i】【j】=dp【i-1】【j-Ai】;
那么ans=Σdp【m】【i】(0<=i<=b)
Ac代码:
#include<stdio.h>
#include<string.h>
using namespace std;
int dp[505][500*4];
int main()
{
int n,m,b,mod;
while(~scanf("%d%d%d%d",&n,&m,&b,&mod))
{
memset(dp,0,sizeof(dp));
dp[0][0]=1;
for(int z=0;z<n;z++)
{
int x;
scanf("%d",&x);
for(int i=1;i<=m;i++)
{
for(int j=x;j<=b;j++)
{
dp[i][j]+=dp[i-1][j-x];
dp[i][j]%=mod;
}
}
}
int ans=0;
for(int i=0;i<=b;i++)
{
ans+=dp[m][i];
ans%=mod;
}
printf("%d\n",ans);
}
}
相关文章推荐
- codeforces 543A A. Writing Code(完全背包优化dp )
- CodeForces 543A - Writing Code DP 完全背包
- 0-1背包,完全背包,多重背包, 二维费用背包模板
- CodeForces 632E Thief in a Shop(DP|完全背包)
- hdu2159FATE【二维完全背包】
- HDU-2159-FATE(二维完全背包)
- Codeforces 284E Coin Troubles【思维+拓扑排序+完全背包】好题!
- hdu 2159 fate 二维完全背包
- 【背包专题】B - FATE hdu2159【二维完全背包】
- hdu 2159 FATE (完全背包-二维)
- UVa 10306 e-Coins(二维完全背包)
- 第五讲 二维费用的背包问题 HD FATE(二维完全背包)
- FATE(二维完全背包)
- 【二维费用之完全背包】HDU3127-WHUgirls
- HDU2159(二维完全背包)
- CF544C:Writing Code(二维完全背包)
- hdu2159 FATE (二维完全背包)
- UVA 10306 e-Coins(完全背包: 二维限制条件)
- HDU 2159 FATE 二维完全背包 dp
- HDU3127 二维完全背包 DP