HDU 4417 Super Mario

Posted 2020-08-27 神犇(shenben)

Super Mario

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6018    Accepted Submission(s): 2620


　

Problem Description

Mario is world-famous plumber. His “burly” figure and amazing jumping ability reminded in our memory. Now the poor princess is in trouble again and Mario needs to save his lover. We regard the road to the boss’s castle as a line (the length is n), on every integer point i there is a brick on height hi. Now the question is how many bricks in [L, R] Mario can hit if the maximal height he can jump is H.

 

　

Input

The first line follows an integer T, the number of test data.
For each test data:
The first line contains two integers n, m (1 <= n <=10^5, 1 <= m <= 10^5), n is the length of the road, m is the number of queries.
Next line contains n integers, the height of each brick, the range is [0, 1000000000].
Next m lines, each line contains three integers L, R,H.( 0 <= L <= R < n 0 <= H <= 1000000000.)

 

　

Output

For each case, output "Case X: " (X is the case number starting from 1) followed by m lines, each line contains an integer. The ith integer is the number of bricks Mario can hit for the ith query.
　

 

　

Sample Input

1 10 10 0 5 2 7 5 4 3 8 7 7 2 8 6 3 5 0 1 3 1 1 9 4 0 1 0 3 5 5 5 5 1 4 6 3 1 5 7 5 7 3

 

　

Sample Output

Case 1: 4 0 0 3 1 2 0 1 5 1

 

　

Source

2012 ACM/ICPC Asia Regional Hangzhou Online

题意：给一些数，数中有重复的。还有一些询问，问的是[L,R] 区间内有多少个数小于h,有多次询问。

思路：普通方法的话肯定会超时，题目问[L,R]区间内小于h的数有多少个，则可以算出cal(R) 和 cal(L - 1), 两者相减就是答案。这类问题和求逆序数的问题非常类似，即求一个数前面有几个数比它小。求逆序数的问题可以用树状数组解决。

    然而我不想用树状数组写。据说是主席树的裸题，

    然后就这样了

//自己写的没调出来的WA代码 
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<map>
#define m(s) memset(s,0,sizeof s)
using namespace std;
const int N=1e5+10;
const int M=N*20;
int n,m,T,sum[M],ls[M],rs[M];
int root[N],a[N],b[N],sz;
map<int,int>ys;
void build(int &k,int l,int r){
    k=++sz;
    sum[k]=0;
    if(l==r) return ;
    int mid=l+r>>1;
    build(ls[k],l,mid);
    build(rs[k],mid+1,r);
}
void insert(int &k,int last,int l,int r,int pos,int val){
    k=++sz;
    ls[k]=ls[last];
    rs[k]=rs[last];
    sum[k]=sum[last]+val;
    if(l==r) return ;
    int mid=l+r>>1;
    if(pos<=mid) insert(ls[k],ls[last],l,mid,pos,val);
    else insert(rs[k],rs[last],mid+1,r,pos,val);
}
int query(int x,int y,int l,int r,int pos){
    int mid=l+r>>1;
    if(l==r) return sum[y]-sum[x];
    else if(pos<=mid) return query(ls[x],ls[y],l,mid,pos);
    else return sum[ls[y]]-sum[ls[x]]+query(rs[x],rs[y],mid+1,r,pos);
}
void Cl(){
    sz=0;m(root);m(ls);m(rs);m(sum);m(a);m(b);
}
int main(){
    int T,cas=1;
    for(scanf("%d",&T);cas<=T;cas++){
        scanf("%d%d",&n,&m);printf("Case %d:\n",cas);
        for(int i=1;i<=n;i++) scanf("%d",&a[i]),b[i]=a[i];
        sort(b+1,b+n+1);
        int cnt=unique(b+1,b+n+1)-(b+1);
        for(int i=1;i<=cnt;i++) ys[b[i]]=i;
        Cl();build(root[0],1,cnt);
        for(int i=1;i<=n;i++) insert(root[i],root[i-1],1,cnt,ys[a[i]],1);
        for(int i=1,l,r,h;i<=m;i++){
            scanf("%d%d%d",&l,&r,&h);l++;r++;
            int k=upper_bound(b+1,b+cnt+1,h)-(b+1);
            if(k) printf("%d\n",query(root[l-1],root[r],1,cnt,k));
            else puts("0");
        }
    }     
    return 0;
}

//面向STD的源码 
#include<bits/stdc++.h>
using namespace std;
const int N=100010;
int n,m,a[N],b[N];
map<int,int>ys;
struct Tree{
    int ls,rs,sum;
}tree[N*20];
int root[N],sz;
int build(int l,int r){
    int o=++sz;
    tree[o].sum=0;
    if(l == r)  return o;
    int mid=(l+r)>>1;
    tree[o].ls=build(l,mid);
    tree[o].rs=build(mid+1,r);
    return o;
}
int insert(int x,int l,int r,int lt,int v){
    int o=++sz;
    tree[o]=tree[lt];
    tree[o].sum+=v;
    if(l==r) return o;
    int mid=(l+r)>>1;
    if(x<=mid) tree[o].ls=insert(x,l,mid,tree[lt].ls,v);
    else tree[o].rs=insert(x,mid+1,r,tree[lt].rs,v);
    return o;
}
int query(int i,int j,int x,int l,int r){
    if(l==r)  return tree[i].sum-tree[j].sum;
    int mid=(l+r)>>1,ret=0;
    if(x <= mid) ret+=query(tree[i].ls,tree[j].ls,x,l,mid);
    else{
        ret+=tree[tree[i].ls].sum-tree[tree[j].ls].sum;
        ret+=query(tree[i].rs,tree[j].rs,x,mid+1,r);
    }
    return ret;
}
int main(){
    int T,tCase=0;scanf("%d",&T);
    while(T--){
        printf("Case %d:\n",++tCase);
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;i++) scanf("%d",&a[i]),b[i]=a[i];
        sort(b+1,b+n+1);
        int cnt=unique(b+1,b+n+1)-b-1;
        for(int i=1;i<=cnt;i++) ys[b[i]]=i;
        sz=0;root[0]=build(1,cnt);
        for(int i=1;i<=n;i++) root[i]=insert(ys[a[i]],1,cnt,root[i-1],1);
        for(int i=1,l,r,h;i<=m;i++){
            scanf("%d%d%d",&l,&r,&h);r++;l++;
            int k=upper_bound(b+1,b+cnt+1,h)-b-1;
            if(k)  printf("%d\n",query(root[r],root[l-1],k,1,cnt));
            else   printf("0\n");
        }
    }
    return 0;
}