线段树

今天写了线段树,

把以前不会的补了回来,

现在OK了,

一会附上线段树大模板,

各种操作都全了,

先简介一下,

总结出了几个道理：

1 区间加,区间替换的lazy下放不一样,

区间加对于tree[ i ]中的全部元素都 +=

区间替换就是直接赋值

2：lazy的含义是对于一个区间,这个区间完成一个操作,而该区间子区间没有进行该操作,

子区间所有元素 (包括最大值,最小值),都要加入lazy标记,

OK啦

下面是三个模板,最全啦,

操作格子1,是单点替换,区间查询区间和,最大值,最小值,

操作格子2,加上了区间替换为一个数,

操作格子3,加上了区间加一个数,

话不多说,

上代码, ( 代码里有注释,但不能直接提交,要弄明白 )

ps : 305行大代码,累死了

#include <cstdio>
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;

#define ls (t<<1)
#define rs ((t<<1)|1)


#define mk make_pair
#define pb push_back
#define fi first
#define se second

#define MAXN 500001

struct tree{
    int l,r;
    ll sum,add,minn,maxx;
    //可以统计 区间和,区间加,区间最大/小
    #define l(x) t[x].l
    #define r(x) t[x].r
    #define sum(x) t[x].sum
    #define add(x) t[x].add
    #define maxx(x) t[x].maxx
    #define minn(x) t[x].minn
    tree() {
        l=r=0;
        sum=add=minn=maxx=0;
    }
}t[MAXN*4];

int a[MAXN];

void build(int p,int l,int r) {
    l(p)=l;
    r(p)=r;
    add(p)=0;
    if (l==r) {
        sum(p)=a[l];
        maxx(p)=a[l];
        minn(p)=a[l];
        return;
    }
    int mid=(l+r)/2;
    build(p*2,l,mid);
    build(p*2+1,mid+1,r);
    sum(p)=sum(p*2)+sum(p*2+1);
    maxx(p)=max(maxx(p*2),maxx(p*2+1));
    minn(p)=min(minn(p*2),minn(p*2+1));
}

void spread1(int p) {
    //lazy标记下放与清除 
    //这里lazy用于区间加一个数 
    if (add(p)) {
        sum(p*2)+=add(p)*(r(p*2)-l(p*2)+1);
        maxx(p*2)+=add(p);
        minn(p*2)+=add(p);
        //更新左节点 
        sum(p*2+1)+=add(p)*(r(p*2+1)-l(p*2+1)+1);
        maxx(p*2+1)+=add(p);
        minn(p*2+1)+=add(p);
        //更新右节点 
        add(p*2)+=add(p);
        //左节点下放lazy 
        add(p*2+1)+=add(p);
        //右节点下放lazy 
        add(p)=0;
        //lazy清空 
    }
}
void spread2(int p) {
    //lazy标记下放与清除 
    //这里lazy用于区间替换为一个数 
    if (add(p)) {
        sum(p*2)=add(p)*(r(p*2)-l(p*2)+1);
        maxx(p*2)=add(p);
        minn(p*2)=add(p);
        //更新左节点 
        sum(p*2+1)=add(p)*(r(p*2+1)-l(p*2+1)+1);
        maxx(p*2+1)=add(p);
        minn(p*2+1)=add(p);
        //更新右节点 
        add(p*2)=add(p);
        //左节点下放lazy 
        add(p*2+1)=add(p);
        //右节点下放lazy 
        add(p)=0;
        //lazy清空 
    }
}

void change1(int p,int l,int r,int d) {
    //l 到 r 均 +d 
    if (l<=l(p)&&r>=r(p)) {
        add(p)+=d;
        sum(p)+=(long long)d*(r(p)-l(p)+1);
        maxx(p)+=d;
        minn(p)+=d;
        return;
    }
    spread1(p);
    //spread2(p);
    int mid=(l(p)+r(p))/2;
    if (l<=mid) change1(p*2,l,r,d);
    if (r>mid) change1(p*2+1,l,r,d);
    sum(p)=sum(p*2)+sum(p*2+1);
    maxx(p)=max(maxx(p*2),maxx(p*2+1));
    minn(p)=min(minn(p*2),minn(p*2+1));
}

void change3(int p,int l,int r,int d) {
    // l~r 均替换为 d
    if (l<=l(p)&&r>=r(p)) {
        add(p)=d;
        sum(p)=(long long)d*(r(p)-l(p)+1);
        maxx(p)=d;
        minn(p)=d;
        return;
    }
    //spread1(p);
    spread2(p);
    int mid=(l(p)+r(p))/2;
    if (l<=mid) change3(p*2,l,r,d);
    if (r>mid) change3(p*2+1,l,r,d);
    sum(p)=sum(p*2)+sum(p*2+1);
    maxx(p)=max(maxx(p*2),maxx(p*2+1));
    minn(p)=min(minn(p*2),minn(p*2+1)); 
}

void change2(int p,int x,int v) {
    //把 a[x] 值改为 v
    if (l(p)==r(p)) {
        //叶子节点直接赋值 
        sum(p)=v;
        maxx(p)=v;
        minn(p)=v;
        return;
    } 
    spread1(p);
    //spread2(p);
    int mid=(l(p)+r(p))/2;
    if (x<=mid) change2(p*2,x,v);
    else change2(p*2+1,x,v);
    sum(p)=sum(p*2)+sum(p*2+1);
    maxx(p)=max(maxx(p*2),maxx(p*2+1));
    minn(p)=min(minn(p*2),minn(p*2+1));
}


ll asksum(int p,int l,int r) {
    //查询 l~r 的和 
    if (l<=l(p)&&r>=r(p)) return sum(p);
    //spread1(p);
    spread2(p);
    int mid=(l(p)+r(p))/2;
    ll val=0;
    if (l<=mid) val+=asksum(p*2,l,r);
    if (r>mid) val+=asksum(p*2+1,l,r);
    return val;
}

ll askmax(int p,int l,int r) {
    //查询 l~r 的最大
    if (l<=l(p)&&r>=r(p)) return maxx(p);
    //spread1(p);
    spread2(p);
    int mid=(l(p)+r(p))/2;
    ll val=-(1<<30);
    if (l<=mid) val=max(val,askmax(p*2,l,r));
    if (r>mid) val=max(val,askmax(p*2+1,l,r));
    return val;
}

ll askmin(int p,int l,int r) {
    //查询 l~r 的最小
    if (l<=l(p)&&r>=r(p)) return minn(p);
    //spread(p);
    spread2(p);
    int mid=(l(p)+r(p))/2;
    ll val=(1<<30);
    if (l<=mid) val=min(val,askmin(p*2,l,r));
    if (r>mid) val=min(val,askmin(p*2+1,l,r));
    return val;
}

/*
int n,m;
char c;
//操作格子1 
int main() {
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++) {
        scanf("%d",&a[i]);
    }
    build(1,1,n);
    for (int i=1,x,y;i<=m;i++) {
        cin>>c;
        scanf("%d%d",&x,&y);
        if (c=='Q') {
            ll ansmax=0;
            ll ansmin=0;
            ll anssum=0;
            ansmax=askmax(1,x,y);
            ansmin=askmin(1,x,y);
            anssum=asksum(1,x,y);
            printf("%lld %lld %lld
",ansmax,ansmin,anssum);
        }
        if (c=='U') {
            change2(1,x,y);
        }
    }

    return 0;
}
*/

/*
int n,m;
char op[6];
//操作格子3 
int main () {
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++) {
        scanf("%d",&a[i]);
    }
    build(1,1,n);
    for (int i=1;i<=m;i++) {
        cin>>op;
        if (op[0]=='S') {
            int x,y;
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=asksum(1,x,y);
            printf("%lld
",ans);
        }
        if (op[0]=='A') {
            int x,y,z;
            scanf("%d%d%d",&x,&y,&z);
            change1(1,x,y,z);
        }
        if (op[0]=='M'&&op[1]=='A') {
            int x,y;
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=askmax(1,x,y);
            printf("%lld
",ans);
        }
        if (op[0]=='M'&&op[1]=='I') {
            int x,y;
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=askmin(1,x,y);
            printf("%lld
",ans);
        }
    }
    
    return 0;
}
*/

/*
int n,m;
char op[10];
int main () {
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++) {
        scanf("%d",&a[i]);
    }
    build(1,1,n);
    for (int i=1,x,y,z;i<=m;i++) {
        cin>>op;
        if (op[0]=='S') {
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=asksum(1,x,y);
            printf("%lld
",ans);
        }
        if (op[0]=='U') {
            scanf("%d%d%d",&x,&y,&z);
            change3(1,x,y,z);
        }
        if (op[0]=='M'&&op[1]=='A') {
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=askmax(1,x,y);
            printf("%lld
",ans);
        }
        if (op[0]=='M'&&op[1]=='I') {
            scanf("%d%d",&x,&y);
            ll ans=0;
            ans=askmin(1,x,y);
            printf("%lld
",ans);
        }
    }
    return 0;
}
*/

int main () {
    return 0;
}