HDU-1556(线段树或树状数组)

题目链接： Color the ball

思路

已经写过一次类似前缀和的题解了，这次再写一遍线段树或树状数组的解法。这题是区间更新和单点查询，线段树的单点查询不过是区间查询的特殊形式，代码是一样的。但是树状数组的区间更新和单点查询却不同于区间更新和区间查询。不过此处就不详细说了，树状数组本身就是个神奇的东西。

1.线段树

#include <iostream>
#include <algorithm>
#include <string.h>
#include <stdio.h>
using namespace std;
int addmark[450000],seqtree[450000];
void maketree(int node,int begin,int end)
{
    addmark[node]=0;
    if(begin==end)
    {
        seqtree[node]=0;
        return;
    }
    int mid=(begin+end)/2;
    maketree(2*node,begin,mid);
    maketree(2*node+1,mid+1,end);
    seqtree[node]=seqtree[2*node]+seqtree[2*node+1];
}
void pushdown(int node,int begin,int end)
{
    if(!addmark[node])
        return;
    int mid=(begin+end)/2;
    addmark[2*node]+=addmark[node];
    addmark[2*node+1]+=addmark[node];
    seqtree[2*node]+=(mid-begin+1)*addmark[node];
    seqtree[2*node+1]+=(end-mid)*addmark[node];
    addmark[node]=0;
}
void update(int node,int begin,int end,int left,int right,int k)
{
    int mid=(begin+end)/2;
    if(left>end || right<begin)
        return;
    if(left<=begin && right>=end)
    {
        addmark[node]+=k;
        seqtree[node]+=(end-begin+1)*k;
        return;
    }
    pushdown(node,begin,end);
    update(2*node,begin,mid,left,right,k);
    update(2*node+1,mid+1,end,left,right,k);
    seqtree[node]=seqtree[2*node]+seqtree[2*node+1];
}
int query(int node,int begin,int end,int left,int right)
{
    if(left>end || right<begin)
        return 0;
    if(left<=begin && right>=end)
    {
        return seqtree[node];
    }
    pushdown(node,begin,end);
    int mid=(begin+end)/2,sum=0;
    sum+=query(2*node,begin,mid,left,right);
    sum+=query(2*node+1,mid+1,end,left,right);
    return sum;
}
int main()
{
    int n,i,A,B;
    while(scanf("%d",&n)!=EOF && n)
    {
    memset(seqtree,0,sizeof(seqtree));
    memset(addmark,0,sizeof(addmark));
    maketree(1,1,n);
    for(i=1;i<=n;i++)
    {
        scanf("%d %d",&A,&B);
        update(1,1,n,A,B,1);
    }
    for(i=1;i<=n;i++)
    printf("%d%c",query(1,1,n,i,i),(i==n)?'\n':' ');
    }
}

2.树状数组

#include <bits/stdc++.h>
using namespace std;
int n,tree[100001];
int lowbit(int x)
{
    return (x&(-x));
}
int update(int x,int k)
{
    int sum=0;
    for(int i=x; i<=n ;i=i+lowbit(i))
    {
        tree[i]+=k;
    }
    return sum;
}
int query(int x)
{
    int sum=0;
    for(int i=x;i>0;i=i-lowbit(i))
    {
        sum+=tree[i];
    }
    return sum;
}
int main()
{
    int i,A,B;
    while(cin>>n && n)
    {
    memset(tree,0,sizeof(tree));
    for(i=1;i<=n;i++)
    {
        cin>>A>>B;
        update(A,1);
        update(B+1,-1);
    }
    for(i=1;i<=n;i++)
    {
        if(i==1)
            printf("%d",query(i));
        else
            printf(" %d",query(i));
    }
    cout<<endl;
    }

}