86-区间线段树-模板

/*
 * 线段树模板
 * 区间修改 区间查询
 * 版本一：当前区间值正确，tag未下传
 */
#include<iostream>
#include<cstdio>
#include<queue>
#include<algorithm>
#include<cstring>
using namespace std;
typedef long long LL;
const int MAXN=1e6+5;
const LL INF=2e18;
//const int INF=0x3f3f3f3f;//根据是否超long long修改
LL a[MAXN];

//线段树节点结构体
struct Node{
    int left,right;//左右边界
    LL mi,ma;//最小值 最大值
    LL sum;//和
    LL add;//增减标记
    int set;//重置标记
}tree[MAXN*4];//空间开四倍

//向上更新
void PushUp(int rt){
    int lson=rt<<1,rson=rt<<1|1;   //rt << 1 | 1 等价与 rt * 2 + 1 
    tree[rt].mi=min(tree[lson].mi,tree[rson].mi);
    tree[rt].ma=max(tree[lson].ma,tree[rson].ma);
    tree[rt].sum=tree[lson].sum+tree[rson].sum;
}

//向下传递标记
void PushDown(int rt){
    if(tree[rt].left<tree[rt].right){//如果不是叶子
        int lson=rt<<1,rson=rt<<1|1;
        if(tree[rt].set!=-1){//set初始为一个不会重置到的数，这里是-1
            tree[lson].set=tree[rt].set;tree[rson].set=tree[rt].set;
            tree[lson].add=tree[rson].add=0;//add失效
            tree[lson].mi=tree[rson].mi=tree[rt].set;
            tree[lson].ma=tree[rson].ma=tree[rt].set;
            tree[lson].sum=(LL)tree[rt].set*(tree[lson].right-tree[lson].left+1);
            tree[rson].sum=(LL)tree[rt].set*(tree[rson].right-tree[rson].left+1);
            tree[rt].set=-1;
        }
        if(tree[rt].add){
            tree[lson].add+=tree[rt].add; tree[rson].add+=tree[rt].add;
            tree[lson].mi+=tree[rt].add;  tree[rson].mi+=tree[rt].add;
            tree[lson].ma+=tree[rt].add;  tree[rson].ma+=tree[rt].add;
            tree[lson].sum+=(LL)tree[rt].add*(tree[lson].right-tree[lson].left+1);
            tree[rson].sum+=(LL)tree[rt].add*(tree[rson].right-tree[rson].left+1);
            tree[rt].add=0;
        }
    }
}

//建立函数
void Build(int rt,int L,int R){
    tree[rt].left=L;tree[rt].right=R;tree[rt].add=0;tree[rt].set=-1;
    if(L==R) {
		tree[rt].sum=tree[rt].mi=tree[rt].ma=a[L]; 
		return;
	}
    int mid=(tree[rt].left+tree[rt].right)>>1;
    Build(rt<<1,L,mid);//只有Build时LR才会变
    Build(rt<<1|1,mid+1,R);
    PushUp(rt);
}

LL QuerySum(int rt,int L,int R){
    if(R<tree[rt].left||L>tree[rt].right) return  0;
    if(L<=tree[rt].left&&tree[rt].right<=R)  
		return tree[rt].sum;
    PushDown(rt);
    int mid=(tree[rt].left+tree[rt].right)>>1;
    LL res=0;
    if(L<=mid)  res+=QuerySum(rt<<1,L,R);
    if(R>mid)   res+=QuerySum(rt<<1|1,L,R);
    PushUp(rt);
    return  res;
}

LL QueryMin(int rt,int L,int R){
    if(L<=tree[rt].left&&tree[rt].right<=R) return tree[rt].mi;
    PushDown(rt);
    int mid=(tree[rt].left+tree[rt].right)>>1;
    LL res=INF;
    if(L<=mid) res=min(res,QueryMin(rt<<1,L,R));
    if(R>mid) res=min(res,QueryMin(rt<<1|1,L,R));
    PushUp(rt);
    return  res;
}

LL QueryMax(int rt,int L,int R){
    if(L<=tree[rt].left&&tree[rt].right<=R) return  tree[rt].ma;//完全包含才产生贡献
    PushDown(rt);
    int mid=(tree[rt].left+tree[rt].right)>>1;
    LL res=-INF;
    if(L<=mid) res=max(res,QueryMax(rt<<1,L,R));
    if(R>mid) res=max(res,QueryMax(rt<<1|1,L,R));
    PushUp(rt);
    return  res;
}

void UpdateAdd(int rt,int L,int R,int x){//把区间[L,R]加上x
    if(L<=tree[rt].left&&tree[rt].right<=R){
        tree[rt].add+=x;
        tree[rt].sum+=(LL)x*(tree[rt].right-tree[rt].left+1);
        tree[rt].mi+=x;tree[rt].ma+=x;
        return;
    }
    PushDown(rt);
    int mid=(tree[rt].left+tree[rt].right)>>1;
    if(L<=mid) UpdateAdd(rt<<1,L,R,x);
    if(R>mid) UpdateAdd(rt<<1|1,L,R,x);
    PushUp(rt);
}

void Display(int rt){
    cout<<"-------------"<<endl;
    cout<<"id: "<<rt<<endl;
    cout<<"["<<tree[rt].left<<","<<tree[rt].right<<"]"<<endl;
    cout<<"mi: "<<tree[rt].mi<<endl;
    cout<<"ma: "<<tree[rt].ma<<endl;
    cout<<"sum: "<<tree[rt].sum<<endl;
    cout<<"add: "<<tree[rt].add<<endl;
    cout<<"set: "<<tree[rt].set<<endl;
}

void bfs(int rt){
    queue<int> q;
    while(!q.empty()) q.pop();
    q.push(rt);
    while(!q.empty()){
        int fst=q.front();
        q.pop();
        Display(fst);
        if(tree[fst].right>tree[fst].left){
            q.push(fst<<1);
            q.push(fst<<1|1);
        }
    }
}

void UpdateSet(int rt,int L,int R,int x){//把区间[x,y]置为x
    if(L<=tree[rt].left&&tree[rt].right<=R){
        tree[rt].set=x;
        tree[rt].sum=(LL)x*(tree[rt].right-tree[rt].left+1);
        tree[rt].mi=x;tree[rt].ma=x;
        tree[rt].add=0;
        return;
    }
    PushDown(rt);
    int mid=(tree[rt].left+tree[rt].right)>>1;
    if(L<=mid) UpdateSet(rt<<1,L,R,x);
    if(R>mid){
        UpdateSet(rt<<1|1,L,R,x);
    }
    PushUp(rt);
}

int main(){
    int n,m;//n个数 m次询问
    while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
        Build(1,1,n);//建立线段树
        int op,x,y,z;
        for(int i=1;i<=m;i++){
            scanf("%d%d%d",&op,&x,&y);
            if(op==1){//询问[x,y]的和，求平均值可以直接求和然后处以总个数 
                printf("Case #%d:
",i);
                printf("%lld
",QuerySum(1,x,y)); 
            }else if(op==2){//询问[x,y]的最大值
                printf("Case #%d:
",i);
                printf("%lld
",QueryMax(1,x,y));
            }else if(op==3){//询问[x,y]的最小值
                printf("Case #%d:
",i);
                printf("%lld
",QueryMin(1,x,y));
            }else if(op==4){//在[x,y]区间加上z
                scanf("%d",&z);
                UpdateAdd(1,x,y,z);
            }else{//把[x,y]重置为z
                scanf("%d",&z);
                UpdateSet(1,x,y,z);
            }
        }
    }
    return 0;
}