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C++代码实现区间更新与查询算法

最新推荐文章于 2018-07-20 11:21:55 发布

原创最新推荐文章于 2018-07-20 11:21:55 发布 · 503 阅读

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#离散化 #区间更新

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本文介绍了一种使用C++实现的区间更新与查询算法，通过构建树状数组来高效处理区间操作，包括区间修改和区间求和查询。详细解释了算法原理、数据结构设计以及代码实现步骤。

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;

const int N = 100010;
bool poster[N];

struct Interval{
    int l,r;
}intervals[N];

struct point{
    int num,id;
}points[N<<1];

struct node{
    int l,r,setv;
}tree[N<<2];

bool cmp(const point &a,const point &b){
    return a.num < b.num;
}

void build(int id,int l,int r){
    tree[id].l = l;
    tree[id].r = r;
    tree[id].setv = 0;
    if(l == r)
        return;
    int mid = (l+r)>>1;
    build(id<<1,l,mid);
    build(id<<1|1,mid+1,r);
}

void pushdown(int id){
    if(tree[id].setv){
        tree[id<<1].setv = tree[id].setv;
        tree[id<<1|1].setv = tree[id].setv;
        tree[id].setv = 0;
    }
}

void update(int id,int l,int r,int val){
    if(tree[id].l >= l && tree[id].r <= r){
        tree[id].setv = val;
        return;
    }
    pushdown(id);
    int mid = (tree[id].l+tree[id].r)>>1;
    if(l <= mid)
        update(id<<1,l,r,val);
    if(mid < r)
        update(id<<1|1,l,r,val);
}

void query(int id,int l,int r){
    if (tree[id].setv){
		poster[tree[id].setv] = true;
		return;
	}
    if(tree[id].l < tree[id].r){
        int mid = (tree[id].l + tree[id].r)>>1;
        if(l <= mid)
            query(id<<1,l,r);
        if(mid < r)
            query(id<<1|1,l,r);
    }
}

int main(){
    int n,l,x;
    scanf("%d%d",&n,&l);
    for(int i = 1; i <= n; i++)
        poster[i] = false;
    for(int i = 1; i <= 2*n; i++){
        scanf("%d",&x);
        points[i].id = i;
        points[i].num = x;
    }
    sort(points+1,points+2*n+1,cmp);
    int number = -1;
    int index = 0;
    for(int i = 1; i <= 2*n; i++){
        if(points[i].num != number){
            number = points[i].num;
            index++;
        }
        if(points[i].id%2)
            intervals[(points[i].id+1)/2].l = index;
        else
            intervals[(points[i].id+1)/2].r = index-1;
    }
    build(1,1,index-1);
    for(int i = 1; i <= n; i++)
        update(1,intervals[i].l,intervals[i].r,i);
    query(1,1,index-1);
    int sum = 0;
    for(int i = 1; i <= n; i++){
        if(poster[i])
            sum++;
    }
    printf("%d\n",sum);
    return 0;
}