HDU 5301(Buildings-贪心构造)
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Buildings
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 2210 Accepted Submission(s): 624
Problem Description
Your current task is to make a ground plan for a residential building located in HZXJHS. So you must determine a way to split the floor building with walls to make apartments in the shape of a rectangle. Each built wall must be paralled
to the building‘s sides.
The floor is represented in the ground plan as a large rectangle with dimensionsn×m ,
where each apartment is a smaller rectangle with dimensions
a×b
located inside. For each apartment, its dimensions can be different from each other. The numbera
and b
must be integers.
Additionally, the apartments must completely cover the floor without one1×1
square located on (x,y) .
The apartments must not intersect, but they can touch.
For this example, this is a sample ofn=2,m=3,x=2,y=2 .
To prevent darkness indoors, the apartments must have windows. Therefore, each apartment must share its at least one side with the edge of the rectangle representing the floor so it is possible to place a window.
Your boss XXY wants to minimize the maximum areas of all apartments, now it‘s your turn to tell him the answer.
The floor is represented in the ground plan as a large rectangle with dimensions
Additionally, the apartments must completely cover the floor without one
For this example, this is a sample of
To prevent darkness indoors, the apartments must have windows. Therefore, each apartment must share its at least one side with the edge of the rectangle representing the floor so it is possible to place a window.
Your boss XXY wants to minimize the maximum areas of all apartments, now it‘s your turn to tell him the answer.
Input
There are at most 10000
testcases.
For each testcase, only four space-separated integers,n,m,x,y(1≤n,m≤108,n×m>1,1≤x≤n,1≤y≤m) .
For each testcase, only four space-separated integers,
Output
For each testcase, print only one interger, representing the answer.
Sample Input
2 3 2 2 3 3 1 1
Sample Output
1 2HintCase 1 :You can split the floor into five $1 \times 1$ apartments. The answer is 1. Case 2: You can split the floor into three $2 \times 1$ apartments and two $1\times 1$ apartments. The answer is 2. If you want to split the floor into eight $1 \times 1$ apartments, it will be unacceptable because the apartment located on (2,2) can‘t have windows.
Author
XJZX
Source
php?
field=problem&key=2015+Multi-University+Training+Contest+2&source=1&searchmode=source">2015 Multi-University Training Contest 2
Recommend
假设没有坏点 ans=(min(n,m)+1)/2
假设n=m=奇数,x,y在中间 ans‘=(min(n,m)+1)/2-1
否则,x,y用对称性挪到左上角
此时对于宿舍楼要么竖着分max(y,m-y+1)+1
要么横着分 min(x,n-x+1)
#include<cstdio> #include<cstring> #include<cstdlib> #include<algorithm> #include<functional> #include<iostream> #include<cmath> #include<cctype> #include<ctime> using namespace std; #define For(i,n) for(int i=1;i<=n;i++) #define Fork(i,k,n) for(int i=k;i<=n;i++) #define Rep(i,n) for(int i=0;i<n;i++) #define ForD(i,n) for(int i=n;i;i--) #define RepD(i,n) for(int i=n;i>=0;i--) #define Forp(x) for(int p=pre[x];p;p=next[p]) #define Forpiter(x) for(int &p=iter[x];p;p=next[p]) #define Lson (x<<1) #define Rson ((x<<1)+1) #define MEM(a) memset(a,0,sizeof(a)); #define MEMI(a) memset(a,127,sizeof(a)); #define MEMi(a) memset(a,128,sizeof(a)); #define INF (2139062143) #define F (100000007) typedef long long ll; ll mul(ll a,ll b){return (a*b)%F;} ll add(ll a,ll b){return (a+b)%F;} ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;} void upd(ll &a,ll b){a=(a%F+b%F)%F;} int main() { // freopen("B.in","r",stdin); int n,m,x,y; while(scanf("%d%d%d%d",&n,&m,&x,&y)==4) { if (n<m) swap(n,m),swap(x,y); int ans=(min(n,m)+1)/2; if (n==m&&x==y&&n==2*x-1) { cout<<ans-1<<endl; continue; } x=min(x,n-x+1),y=max(y,m-y+1); int ans2=min(x,y-1); cout<<max(ans2,ans)<<endl; } return 0; }
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