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hdu 5517 Triple(二维树状数组)

Triple

Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 388    Accepted Submission(s): 148


Problem Description
Given the finite multi-set A of n pairs of integers, an another finite multi-set B of m triples of integers, we define the product of A and B as a multi-set

C=AB={?a,c,d??a,b?A, ?c,d,e?B and b=e}

For each ?a,b,c?C, its BETTER set is defined as

BETTERC(?a,b,c?)={?u,v,w?C?u,v,w??a,b,c?, ua, vb, wc}

As a \textbf{multi-set} of triples, we define the TOP subset (as a multi-set as well) of C, denoted by TOP(C), as

TOP(C)={?a,b,c?CBETTERC(?a,b,c?)=}

You need to compute the size of TOP(C).
 

 

Input
The input contains several test cases. The first line of the input is a single integer t (1t10) which is the number of test case. Then t test cases follow.

Each test case contains three lines. The first line contains two integers n (1n105) and m (1m105) corresponding to the size of A and B respectively.
The second line contains 2×n nonnegative integers
a1,b1,a2,b2,?,an,bn

which describe the multi-set A, where 1ai,bi105.
The third line contains 3×m nonnegative integers
c1,d1,e1,c2,d2,e3,?,cm,dm,em

corresponding to the m triples of integers in B, where 1ci,di103 and 1ei105.
 

 

Output
For each test case, you should output the size of set TOP(C).
 

 

Sample Input
2
5 9
1 1 2 2 3 3 3 3 4 2
1 4 1 2 2 1 4 1 1 1 3 2 3 2 2 4 1 2 2 4 3 3 2 3 4 1 3
3 4
2 7 2 7 2 7
1 4 7 2 3 7 3 2 7 4 1 7
 
Sample Output
Case #1: 5
Case #2: 12

 

/*hdu 5517 Triple(二维树状数组)problem:给你n个二元组<a,b>, m个三元组<c,d,e>. 如果d = e,那么<a,c,d>会组成一个新的三元组集合G.问G中有多少个三元组在凸点.(没有其它三元组比它大)solve:要注意去重. 因为要求没有其它三元组比它大. 如果同一个b有多个a,那么只需要取最大的即可.然后通过排序可以解决第一位a. 剩下两位c,d则可以通过二维树状数组来维护是否是最大值.三元组G中相同的合并.hhh-2016-08-31 20:06:36*/#pragma comment(linker,"/STACK:124000000,124000000")#include <algorithm>#include <iostream>#include <cstdlib>#include <cstdio>#include <cstring>#include <vector>#include <math.h>#include <queue>#include <set>#include <map>#define lson  i<<1#define rson  i<<1|1#define ll long long#define clr(a,b) memset(a,b,sizeof(a))#define scanfi(a) scanf("%d",&a)#define scanfs(a) scanf("%s",a)#define scanfl(a) scanf("%I64d",&a)#define key_val ch[ch[root][1]][0]#define inf 0x3f3f3f3f3f3f3f3fusing namespace std;const ll mod = 1e9+7;const int maxn = 100010;const int maxx = 1050;int a,b;int to[maxn],have[maxn];struct node{    int a,b,c;    int w;    node(){}    node(int _a,int _b,int _c,int _w):a(_a),b(_b),c(_c),w(_w) {}    bool operator <(const node &t)const    {        if(a!= t.a)            return a < t.a;        else if(b != t.b)            return b < t.b;        else if(c != t.c)            return c < t.c;    }    node operator +(const node &t)const    {        return node(a,b,c,w+t.w);    }    bool operator ==(const node &t)const    {        return !(*this<t || t < *this);    }};ll s[maxx][maxx];int lowbit(int x){    return x&(-x);}void add(int x,int y,ll val){    for(int i = x; i <= 1000; i+=lowbit(i))        for(int j = y; j <= 1000; j+=lowbit(j))        {            s[i][j] += val;        }}ll sum(int x,int y){    ll cnt = 0;    for(int i = x; i > 0; i-=lowbit(i))        for(int j = y; j > 0; j-=lowbit(j))        {            cnt += s[i][j];        }    return cnt;}node tp[maxn];int main(){    int T,cas =1;    int c,d,e;//    freopen("in.txt","r",stdin);    scanfi(T);    while(T--)    {        int n,m;        clr(s,0),clr(to,0);        int Maxy = 0, Maxx = 0,cnt = 0;        scanfi(n),scanfi(m);        for(int i = 0; i < n; i++)        {            scanfi(a),scanfi(b);            if(a > to[b])to[b] = a,have[b] = 1;            else if(a == to[b])have[b] ++;//            cout << a[i] <<" " <<b[i] <<endl;        }        for(int i = 0; i < m; i++)        {            scanfi(c),scanfi(d),scanfi(e);            Maxx = max(Maxx,c);            Maxy = max(Maxy,d);            if(to[e])              tp[cnt++] = node(to[e],c,d,have[e]);        }        sort(tp,tp+cnt);        int tot = 0;        for(int i = 1;i < cnt;i++)        {            if(tp[i] == tp[tot])            {                tp[tot] = tp[tot] + tp[i];            }            else            {                tp[++tot] = tp[i];            }        }        ll ans = 0;        for(int i = tot;i >= 0;i--)        {            node t = tp[i];//            printf("%d%d%d %d\n",t.a,t.b,t.c,t.w);            int x = t.b,y = t.c;            int large = sum(1000,1000)-sum(x-1,1000)-sum(1000,y-1)+sum(x-1,y-1);//            if(t.a != last)//                large -= have;            if(large == 0)                ans = (ll)(ans+t.w);            add(x,y,1);        }        printf("Case #%d: %I64d\n",cas++,ans);    }    return 0;}/*13 42 7 2 7 2 71 4 7 2 3 7 3 2 7 4 1 7*/

  

hdu 5517 Triple(二维树状数组)