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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=A∗B={?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?, u≥a, v≥b, w≥c}
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?∈C∣BETTERC(?a,b,c?)=∅}
You need to compute the size of TOP(C).
C=A∗B={?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?, u≥a, v≥b, w≥c}
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?∈C∣BETTERC(?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 (1≤t≤10) 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 (1≤n≤105) and m (1≤m≤105) corresponding to the size of A and B respectively.
The second line contains 2×n nonnegative integers
which describe the multi-set A, where 1≤ai,bi≤105.
The third line contains 3×m nonnegative integers
corresponding to the m triples of integers in B, where 1≤ci,di≤103 and 1≤ei≤105.
Each test case contains three lines. The first line contains two integers n (1≤n≤105) and m (1≤m≤105) 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 1≤ai,bi≤105.
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 1≤ci,di≤103 and 1≤ei≤105.
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)
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