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TOJ 4105 Lines Counting(离线树状数组)
Time Limit: 2.0 Seconds Memory Limit: 150000K
Total Runs: 152 Accepted Runs: 47
On the number axis, there are N lines. The two endpoints L and R of each line are integer. Give you M queries, each query contains two intervals: [L1,R1] and [L2,R2], can you count how many lines satisfy this property: L1≤L≤R1 and L2≤R≤R2?
Input
First line will be a positive integer N (1≤N≤100000) indicating the number of lines. Following the coordinates of the N lines‘ endpoints L and R will be given (1≤L≤R≤100000). Next will be a positive integer M (1≤M≤100000) indicating the number of queries. Following the four numbers L1,R1,L2 and R2 of the M queries will be given (1≤L1≤R1≤L2≤R2≤100000).
Output
For each query output the corresponding answer.
Sample Input
31 32 43 521 2 3 41 4 5 6
Sample Output
21
题目链接:TOJ 4105
题意就是在给你N条在X轴上的线段,求左端点在L1~R1且右端点在L2~R2的线段条数,其实这题跟NBUT上一道题很像,问你在区间L1~R1中,值在L2~R2中有几个数,只是这题在起点计数回退时可能多退几个位子,因为线段的起点和终点坐标可能有重复的,都不能算进去,因此要用while语句来操作。离线树状数组是什么个意思呢?就是满足区间减法这样原理的话就可以这样计数:在遇到起点时减去起点到询问区间起点-1的count1,在遇到计数终点时加上询问起点~询问终点的count2,这样可以发现count1其实是count2的子集,一加一减一定会把count1抵消掉,只留下刚好符合询问区间的答案了。
代码:
#include <stdio.h>#include <bits/stdc++.h>using namespace std;#define INF 0x3f3f3f3f#define LC(x) (x<<1)#define RC(x) ((x<<1)+1)#define MID(x,y) ((x+y)>>1)#define CLR(arr,val) memset(arr,val,sizeof(arr))#define FAST_IO ios::sync_with_stdio(false);cin.tie(0);typedef pair<int, int> pii;typedef long long LL;const double PI = acos(-1.0);const int N=100010;struct Line{ int l,r; bool operator<(const Line &rhs)const { if(l!=rhs.l) return l<rhs.l; return r<rhs.r; }};struct query{ int k,r1,r2,flag,id; query(int _k=0,int _r1=0,int _r2=0,int _flag=0,int _id=0):k(_k),r1(_r1),r2(_r2),flag(_flag),id(_id){} bool operator<(const query &rhs)const { return k<rhs.k; }};Line line[N];query Q[N<<1];int T[N],ans[N];void init(){ CLR(T,0); CLR(ans,0);}void add(int k,int v){ while (k<N) { T[k]+=v; k+=(k&-k); }}int getsum(int k){ int ret=0; while (k) { ret+=T[k]; k-=(k&-k); } return ret;}int main(void){ int n,m,i; while (~scanf("%d",&n)) { init(); for (i=0; i<n; ++i) scanf("%d%d",&line[i].l,&line[i].r); sort(line,line+n); scanf("%d",&m); int qcnt=0; for (i=0; i<m; ++i) { int l1,r1,l2,r2; scanf("%d%d%d%d",&l1,&r1,&l2,&r2); Q[qcnt++]=query(l1,l2,r2,0,i); Q[qcnt++]=query(r1,l2,r2,1,i); } sort(Q,Q+qcnt); int x=0; for (i=0; i<qcnt; ++i) { while (line[x].l<=Q[i].k&&x<n) add(line[x++].r,1); if(Q[i].flag) ans[Q[i].id]+=getsum(Q[i].r2)-getsum(Q[i].r1-1); else { while (line[x-1].l>=Q[i].k&&x-1>=0) { add(line[x-1].r,-1); --x; } ans[Q[i].id]-=getsum(Q[i].r2)-getsum(Q[i].r1-1); while (line[x].l<=Q[i].k&&x<n) { add(line[x].r,1); ++x; } } } for (i=0; i<m; ++i) printf("%d\n",ans[i]); } return 0;}
TOJ 4105 Lines Counting(离线树状数组)