YJJ's Salesman

YJJ's Salesman

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1085    Accepted Submission(s): 371

 

Problem Description

YJJ is a salesman who has traveled through western country. YJJ is always on journey. Either is he at the destination, or on the way to destination.
One day, he is going to travel from city A to southeastern city B. Let us assume that A is (0,0) on the rectangle map and B (109,109). YJJ is so busy so he never turn back or go twice the same way, he will only move to east, south or southeast, which means, if YJJ is at (x,y) now (0≤x≤109,0≤y≤109), he will only forward to (x+1,y), (x,y+1) or (x+1,y+1).
On the rectangle map from (0,0) to (109,109), there are several villages scattering on the map. Villagers will do business deals with salesmen from northwestern, but not northern or western. In mathematical language, this means when there is a village k on (xk,yk) (1≤xk≤109,1≤yk≤109), only the one who was from (xk−1,yk−1) to (xk,yk) will be able to earn vk dollars.(YJJ may get different number of dollars from different village.)
YJJ has no time to plan the path, can you help him to find maximum of dollars YJJ can get.

 

 

Input

The first line of the input contains an integer T (1≤T≤10),which is the number of test cases.

In each case, the first line of the input contains an integer N (1≤N≤105).The following N lines, the k-th line contains 3 integers, xk,yk,vk (0≤vk≤103), which indicate that there is a village on (xk,yk) and he can get vk dollars in that village.
The positions of each village is distinct.

 

 

Output

The maximum of dollars YJJ can get.

 

 

Sample Input

1 3 1 1 1 1 2 2 3 3 1

 

 

Sample Output

3

 

 

Source

2018中国大学生程序设计竞赛 - 网络选拔赛

 

想到了离散化，想到了背包，甚至树状数组也想到了，但就是没做出来。。。。

好烦。。

代码转载自

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn=1e5+5;
int maxx[maxn],pos[maxn];
int lowbit(int x)
{
    return x&(-x);
}
void add(int pos,int val)
{
    for(int i=pos;i<=maxn;i+=lowbit(i))
        maxx[i]=max(maxx[i],val);
}
int query(int pos)
{
    int ans=0;
    for(int i=pos;i>=1;i-=lowbit(i))
        ans=max(ans,maxx[i]);
    return ans;
}
int a[maxn];
struct node
{
    int x,y,v;
    bool operator < (const node& q)const
    {
        if(x==q.x)
            return y>q.y;
        return x<q.x;
    }
}p[maxn];
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        memset(maxx,0,sizeof(maxx));
        int n;
        scanf("%d",&n);
        for(int i=1;i<=n;i++)
            scanf("%d%d%d",&p[i].x,&p[i].y,&p[i].v),a[i]=p[i].y;
        sort(a+1,a+1+n);
        int all=unique(a+1,a+1+n)-(a+1);
        for(int i=1;i<=n;i++)
            p[i].y=lower_bound(a+1,a+1+all,p[i].y)-a;
        sort(p+1,p+1+n);
        for(int i=1;i<=n;i++)
        {
            int val=query(p[i].y-1)+p[i].v;

            add(p[i].y,val);
        }
        printf("%d\n",query(maxn-1));
    }
    return 0;
}