poj 2482 Stars in Your Window 线段树

题意:平面上有n个星星，给出每个星星的位置和亮度 求一个W*H的矩形（不包括边界）使得矩形内的星星亮度之和最大。

思路：每个点(x,y,brightness) 存两个点(x,y,brightness)和(x,y+H,-brightness)
先离散化
从左到右两根间距为W的扫描线，左开右闭。依次把点加进线段树，下标是y，权值是brightness，题目所求的就是前i个点的和的最大值。

线段树存当前范围内的sum，maxsum
其中 maxsum[i]=max(maxsum[2*i],sum[2*i]+maxsum[2*i+1]);

ans=max(maxsum[i])

#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
#define MAXN 20002
struct node
{
int sum,maxsum;
int left,right;
};
struct star
{
long long x,y;
int degree;
int id;
};
node tree[MAXN*4];
star a[MAXN];
int home[MAXN];
int width,high;
int n;
void buildtree(int i)
{
tree[i].sum=tree[i].maxsum=0;
if(tree[i].left==tree[i].right)
return ;
int mid=(tree[i].left+tree[i].right)/2;
tree[2*i].left=tree[i].left; tree[2*i].right=mid;
tree[2*i+1].left=mid+1; tree[2*i+1].right=tree[i].right;
buildtree(2*i); buildtree(2*i+1);
}
bool cmp1(const star &x,const star &y)
{
if(x.y<y.y) return 1;
if(x.y==y.y&&x.x<y.x) return 1;
return 0;
}
bool cmp2(const star &x,const star &y)
{
return x.x<y.x;
}
void insert(int i,int x,int add)
{
if(tree[i].left==tree[i].right)
{
tree[i].maxsum=tree[i].sum=tree[i].sum+add;
return ;
}
int mid=(tree[i].left+tree[i].right)/2;
if(x<=mid) insert(2*i,x,add);
else insert(2*i+1,x,add);
tree[i].sum+=add;
tree[i].maxsum=max(tree[2*i].sum+tree[2*i+1].maxsum,tree[2*i].maxsum);
}
int main()
{
while(scanf("%d%d%d",&n,&width,&high)!=EOF)
{
int i,j,k;

int x,y,z;
for(i=1;i<=n;i++)
{
scanf("%lld%lld%d",&a[i].x,&a[i].y,&a[i].degree);
a[i].id=i; a[i+n].id=i+n;
a[i+n].x=a[i].x; a[i+n].y=a[i].y+high; a[i+n].degree=-a[i].degree;
}
n=2*n;
sort(a+1,a+n+1,cmp1);
j=0;
a[j].x=-1; a[j].y=-1;
for(i=1;i<=n;i++)
{
if(a[i].y==a[j].y&&a[i].x==a[j].x)
{
a[j].degree+=a[i].degree;
}
else
{
j++; a[j].x=a[i].x; a[j].y=a[i].y; a[j].id=a[i].id; a[j].degree=a[i].degree;
home[a[j].id]=j;
}
}
n=j;
tree[1].left=1; tree[1].right=n;
buildtree(1);
sort(a+1,a+n+1,cmp2);
long long l1,l2;
l1=a[1].x; l2=l1+width;
i=1; j=0;
int ans=0;
while(j<n)
{
if(a[i].x-l1<=a[j+1].x-l2)//必须是小于等于 左开右闭
{
l1=a[i].x;
while(a[i].x==l1)//每次一定要把线上的所有点都处理了
{
insert(1,home[a[i].id],-a[i].degree); i++;
}
l2=l1+width;
}
else
{
l2=a[j+1].x;
while(a[j+1].x==l2)
{
j++; insert(1,home[a[j].id],a[j].degree);
}
l1=l2-width;
}
if(tree[1].maxsum>ans) ans=tree[1].maxsum;
}
printf("%d\n",ans);
}
return 0;
}