Problem Description
Fleeting time does not blur my memory of you. Can it
really be 4 years since I first saw you? I still remember, vividly, on the
beautiful Zhuhai Campus, 4 years ago, from the moment I saw you smile, as you
were walking out of the classroom and turned your head back, with the soft
sunset glow shining on your rosy cheek, I knew, I knew that I was already drunk
on you. Then, after several months’ observation and prying, your grace and your
wisdom, your attitude to life and your aspiration for future were all strongly
impressed on my memory. You were the glamorous and sunny girl whom I always
dream of to share the rest of my life with. Alas, actually you were far beyond
my wildest dreams and I had no idea about how to bridge that gulf between you
and me. So I schemed nothing but to wait, to wait for an appropriate
opportunity. Till now the arrival of graduation, I realize I am such an idiot
that one should create the opportunity and seize it instead of just
waiting.
These days, having parted with friends, roommates and classmates one after another, I still cannot believe the fact that after waving hands, these familiar faces will soon vanish from our life and become no more than a memory. I will move out from school tomorrow. And you are planning to fly far far away, to pursue your future and fulfill your dreams. Perhaps we will not meet each other any more if without fate and luck. So tonight, I was wandering around your dormitory building hoping to meet you there by chance. But contradictorily, your appearance must quicken my heartbeat and my clumsy tongue might be not able to belch out a word. I cannot remember how many times I have passed your dormitory building both in Zhuhai and Guangzhou, and each time aspired to see you appear in the balcony or your silhouette that cast on the window. I cannot remember how many times this idea comes to my mind: call her out to have dinner or at least a conversation. But each time, thinking of your excellence and my commonness, the predominance of timidity over courage drove me leave silently.
Graduation, means the end of life in university, the end of these glorious, romantic years. Your lovely smile which is my original incentive to work hard and this unrequited love will be both sealed as a memory in the deep of my heart and my mind. Graduation, also means a start of new life, a footprint on the way to bright prospect. I truly hope you will be happy everyday abroad and everything goes well. Meanwhile, I will try to get out from puerility and become more sophisticated. To pursue my own love and happiness here in reality will be my ideal I never desert.
Farewell, my princess!
If someday, somewhere, we have a chance to gather, even as gray-haired man and woman, at that time, I hope we can be good friends to share this memory proudly to relight the youthful and joyful emotions. If this chance never comes, I wish I were the stars in the sky and twinkling in your window, to bless you far away, as friends, to accompany you every night, sharing the sweet dreams or going through the nightmares together.
Here comes the problem: Assume the sky is a flat plane. All the stars lie on it with a location (x, y). for each star, there is a grade ranging from 1 to 100, representing its brightness, where 100 is the brightest and 1 is the weakest. The window is a rectangle whose edges are parallel to the x-axis or y-axis. Your task is to tell where I should put the window in order to maximize the sum of the brightness of the stars within the window. Note, the stars which are right on the edge of the window does not count. The window can be translated but rotation is not allowed.
These days, having parted with friends, roommates and classmates one after another, I still cannot believe the fact that after waving hands, these familiar faces will soon vanish from our life and become no more than a memory. I will move out from school tomorrow. And you are planning to fly far far away, to pursue your future and fulfill your dreams. Perhaps we will not meet each other any more if without fate and luck. So tonight, I was wandering around your dormitory building hoping to meet you there by chance. But contradictorily, your appearance must quicken my heartbeat and my clumsy tongue might be not able to belch out a word. I cannot remember how many times I have passed your dormitory building both in Zhuhai and Guangzhou, and each time aspired to see you appear in the balcony or your silhouette that cast on the window. I cannot remember how many times this idea comes to my mind: call her out to have dinner or at least a conversation. But each time, thinking of your excellence and my commonness, the predominance of timidity over courage drove me leave silently.
Graduation, means the end of life in university, the end of these glorious, romantic years. Your lovely smile which is my original incentive to work hard and this unrequited love will be both sealed as a memory in the deep of my heart and my mind. Graduation, also means a start of new life, a footprint on the way to bright prospect. I truly hope you will be happy everyday abroad and everything goes well. Meanwhile, I will try to get out from puerility and become more sophisticated. To pursue my own love and happiness here in reality will be my ideal I never desert.
Farewell, my princess!
If someday, somewhere, we have a chance to gather, even as gray-haired man and woman, at that time, I hope we can be good friends to share this memory proudly to relight the youthful and joyful emotions. If this chance never comes, I wish I were the stars in the sky and twinkling in your window, to bless you far away, as friends, to accompany you every night, sharing the sweet dreams or going through the nightmares together.
Here comes the problem: Assume the sky is a flat plane. All the stars lie on it with a location (x, y). for each star, there is a grade ranging from 1 to 100, representing its brightness, where 100 is the brightest and 1 is the weakest. The window is a rectangle whose edges are parallel to the x-axis or y-axis. Your task is to tell where I should put the window in order to maximize the sum of the brightness of the stars within the window. Note, the stars which are right on the edge of the window does not count. The window can be translated but rotation is not allowed.
Input
There are several test cases in the input. The first
line of each case contains 3 integers: n, W, H, indicating the number of stars,
the horizontal length and the vertical height of the rectangle-shaped window.
Then n lines follow, with 3 integers each: x, y, c, telling the location (x, y)
and the brightness of each star. No two stars are on the same
point.
There are at least 1 and at most 10000 stars in the sky. 1<=W，H<=1000000, 0<=x，y<2^31.
There are at least 1 and at most 10000 stars in the sky. 1<=W，H<=1000000, 0<=x，y<2^31.
Output
For each test case, output the maximum brightness in
a single line.
Sample Input
3 5 4 1 2 3 2 3 2 6 3 1 3 5 4 1 2 3 2 3 2 5 3 1
Sample Output
5 6
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题意：在一个平面内有N个星星，每个星星都在一个亮度值，用一个W*H的矩形去围这些星星，（边上的不算）
求能得到的最大亮度值。
每个星星所能影响的范围[(x,y),(x+w-1,y+h-1)]且有一权值 它们重合就表示 能被这个矩形框在一起，也就是说，只要求出重合的矩形的权值最大就行。
以x从小到大排序，y值离散化，投影到y轴上，那么对于每个星星的纵坐标，y，y+h-1就是每个星星可以影响到的矩形 然后x，x+w-1就是一个进入事件和一个出去事件，其所带的值互为相反数. node[1].sum 保存当前的最大值 当所有的矩形都遍历一遍 取其中的最大值就是ans
每个星星所能影响的范围[(x,y),(x+w-1,y+h-1)]且有一权值 它们重合就表示 能被这个矩形框在一起，也就是说，只要求出重合的矩形的权值最大就行。
以x从小到大排序，y值离散化，投影到y轴上，那么对于每个星星的纵坐标，y，y+h-1就是每个星星可以影响到的矩形 然后x，x+w-1就是一个进入事件和一个出去事件，其所带的值互为相反数. node[1].sum 保存当前的最大值 当所有的矩形都遍历一遍 取其中的最大值就是ans
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1 #include <iostream> 2 #include <string> 3 #include <cstring> 4 #include <cstdio> 5 #include <algorithm> 6 #define L(rt) rt<<1 7 #define R(rt) rt<<1|1 8 #define lson l,mid,rt<<1 9 #define rson mid+1,r, rt<<1|1 10 #define MAXN 10010 11 using namespace std; 12 13 struct node1//扫描线，以点（x,y1）为线段的下端点 14 { 15 long long x,y1,y2,val; 16 }seg[MAXN<<1]; 17 18 struct node2 19 { 20 long long l,r; 21 long long add,sum; 22 }tree[MAXN<<3]; 23 24 long long y[MAXN<<1];//为了去重 25 bool cmp(node1 a,node1 b) 26 { 27 if(a.x!=b.x) 28 return a.x<b.x; 29 return a.val>b.val; 30 } 31 32 void build(long long l,long long r,int rt) 33 { 34 tree[rt].l=l; 35 tree[rt].r=r; 36 tree[rt].sum=tree[rt].add=0; 37 if(l==r) 38 return; 39 long long mid=(l+r)>>1; 40 build(lson); 41 build(rson); 42 } 43 void push(int rt) 44 { 45 tree[L(rt)].sum+=tree[rt].add; 46 tree[L(rt)].add+=tree[rt].add; 47 tree[R(rt)].sum+=tree[rt].add; 48 tree[R(rt)].add+=tree[rt].add; 49 tree[rt].add=0; 50 } 51 52 void update(long long val,long long l,long long r,int rt) 53 { 54 if(l==y[tree[rt].l]&&r==y[tree[rt].r]) 55 { 56 tree[rt].add+=val; 57 tree[rt].sum+=val; 58 return ; 59 } 60 if(tree[rt].l==tree[rt].r) 61 return; 62 if(tree[rt].add) 63 push(rt); 64 int mid=(tree[rt].l+tree[rt].r)>>1; 65 if(r<=y[mid]) 66 update(val,l,r,L(rt)); 67 else 68 if(l>=y[mid+1]) 69 update(val,l,r,R(rt)); 70 else 71 { 72 update(val,l,y[mid],L(rt)); 73 update(val,y[mid+1],r,R(rt)); 74 } 75 tree[rt].sum=max(tree[L(rt)].sum,tree[R(rt)].sum);//此处应该是最大，而不是和 76 } 77 78 int main() 79 { 80 int n,w,h; 81 while(~scanf("%d%d%d",&n,&w,&h)){ 82 for(int i=0;i<n;i++){ 83 scanf("%I64d%I64d%I64d",&seg[i].x,&seg[i].y1,&seg[i].val); 84 y[i*2+1]=seg[i].y1; 85 y[i*2+2]=seg[i].y1+h-1; 86 seg[i].y2=seg[i].y1+h-1; 87 seg[n+i]=seg[i]; 88 seg[n+i].x=seg[i].x+w-1; 89 seg[n+i].val=-seg[i].val; //出边的val为负，表不在这矩形里 90 } 91 sort(y+1,y+2*n+1); 92 sort(seg,seg+2*n,cmp); 93 int cnt=unique(y+1,y+2*n+1)-y-1; //unique 去重函数 94 build(1,cnt,1); 95 long long ans=0; 96 for(int i=0;i<2*n;i++){ 97 update(seg[i].val,seg[i].y1,seg[i].y2,1); 98 ans=max(ans,tree[1].sum); 99 } 100 printf("%I64d\n",ans); 101 } 102 }