[kuangbin带你飞]专题七 线段树

Posted 2022-07-02 wangzhebufangqi

https://vjudge.net/contest/66989

A、敌兵布阵

单点修改、区间查询、维护区间和

  1 //CSDN:https://blog.csdn.net/qq_40889820
  2 #include<iostream>
  3 #include<sstream>
  4 #include<fstream>
  5 #include<algorithm>
  6 #include<cstring>
  7 #include<iomanip>
  8 #include<cstdlib>
  9 #include<cctype>
 10 #include<vector>
 11 #include<string>
 12 #include<cmath>
 13 #include<ctime>
 14 #include<stack>
 15 #include<queue>
 16 #include<map>
 17 #include<set>
 18 #define mem(a,b) memset(a,b,sizeof(a))
 19 #define random(a,b) (rand()%(b-a+1)+a)
 20 #define ll long long
 21 #define ull unsigned long long
 22 #define e 2.71828182
 23 #define Pi acos(-1.0)
 24 #define ls(rt) (rt<<1)
 25 #define rs(rt) (rt<<1|1)
 26 #define lowbit(x) (x&(-x))
 27 using namespace std;
 28 const int MAXN=5e4+5;
 29 int a[MAXN];
 30 struct node
 31 
 32     int sum;
 33 T[MAXN<<2];
 34 int read()
 35 
 36     int s=1,x=0;
 37     char ch=getchar();
 38     while(!isdigit(ch)) if(ch==‘-‘) s=-1;ch=getchar();
 39     while(isdigit(ch)) x=10*x+ch-‘0‘;ch=getchar();
 40     return x*s;
 41 
 42 void push_up(int p,int l,int r)
 43 
 44     T[p].sum=T[ls(p)].sum+T[rs(p)].sum;
 45 
 46 void build(int p,int l,int r)
 47 
 48     if(l==r)
 49     
 50         T[p].sum=a[l];
 51         return;
 52     
 53     int mid=(l+r)>>1;
 54     build(ls(p),l,mid);
 55     build(rs(p),mid+1,r);
 56     push_up(p,l,r);
 57 
 58 void update(int p,int l,int r,int lr,int k)
 59 
 60     if(l==r)
 61     
 62         T[p].sum+=k;
 63         return;
 64     
 65     int mid=(l+r)>>1;
 66     if(lr<=mid) update(ls(p),l,mid,lr,k);
 67     else update(rs(p),mid+1,r,lr,k);
 68     push_up(p,l,r);
 69 
 70 int query(int p,int l,int r,int nl,int nr)
 71 
 72     if(nl<=l&&nr>=r)  return T[p].sum;
 73     int mid=(l+r)>>1,ans=0;
 74     if(nl<=mid) ans+=query(ls(p),l,mid,nl,nr);
 75     if(nr>mid) ans+=query(rs(p),mid+1,r,nl,nr);
 76     return ans;
 77 
 78 int main()
 79 
 80     int t=read(),nl,nr,n;
 81     string ord;
 82     for(int cas=1;cas<=t;++cas)
 83     
 84         cout<<"Case "<<cas<<":\n";
 85         n=read();
 86         for(int i=1;i<=n;++i)
 87         a[i]=read();
 88         build(1,1,n);
 89         while(true)
 90         
 91             cin>>ord;
 92             if(ord=="End") break;
 93             else if(ord=="Query")
 94             
 95                 nl=read(),nr=read();
 96                 cout<<query(1,1,n,nl,nr)<<endl;    
 97                 
 98             else if(ord=="Add")
 99             
100                 nl=read(),nr=read();
101                 update(1,1,n,nl,nr);
102             
103             else 
104             
105                 nl=read(),nr=read();
106                 update(1,1,n,nl,-nr);
107             
108          
109     
110     return 0;
111 

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B、I Hate It

单点修改、区间查询、维护区间最大值

 1 //CSDN:https://blog.csdn.net/qq_40889820
 2 #include<iostream>
 3 #include<sstream>
 4 #include<fstream>
 5 #include<algorithm>
 6 #include<cstring>
 7 #include<iomanip>
 8 #include<cstdlib>
 9 #include<cctype>
10 #include<vector>
11 #include<string>
12 #include<cmath>
13 #include<ctime>
14 #include<stack>
15 #include<queue>
16 #include<map>
17 #include<set>
18 #define mem(a,b) memset(a,b,sizeof(a))
19 #define random(a,b) (rand()%(b-a+1)+a)
20 #define ll long long
21 #define ull unsigned long long
22 #define e 2.71828182
23 #define Pi acos(-1.0)
24 #define ls(rt) (rt<<1)
25 #define rs(rt) (rt<<1|1)
26 #define lowbit(x) (x&(-x))
27 using namespace std;
28 const int MAXN=2e5+5;
29 int a[MAXN];
30 struct node
31 
32     int maxx;
33 T[MAXN<<2];
34 int read()
35 
36     int s=1,x=0;
37     char ch=getchar();
38     while(!isdigit(ch)) if(ch==‘-‘) s=-1;ch=getchar();
39     while(isdigit(ch)) x=10*x+ch-‘0‘;ch=getchar();
40     return x*s;
41 
42 void push_up(int p,int l,int r)
43 
44     T[p].maxx=max(T[ls(p)].maxx,T[rs(p)].maxx);
45 
46 void build(int p,int l,int r)
47 
48     if(l==r)
49     
50         T[p].maxx=a[l];
51         return;
52     
53     int mid=(l+r)>>1;
54     build(ls(p),l,mid);
55     build(rs(p),mid+1,r);
56     push_up(p,l,r);
57 
58 void update(int p,int l,int r,int lr,int k)
59 
60     if(l==r)
61     
62         T[p].maxx=k;
63         return;
64     
65     int mid=(l+r)>>1;
66     if(lr<=mid) update(ls(p),l,mid,lr,k);
67     else update(rs(p),mid+1,r,lr,k);
68     push_up(p,l,r);
69 
70 int query(int p,int l,int r,int nl,int nr)
71 
72     if(nl<=l&&nr>=r)  return T[p].maxx;
73     int mid=(l+r)>>1,ans=0;
74     if(nl<=mid) ans=max(query(ls(p),l,mid,nl,nr),ans);
75     if(nr>mid) ans=max(query(rs(p),mid+1,r,nl,nr),ans);
76     return ans;
77 
78 int main()
79 
80     int n,m;
81     while(~scanf("%d%d",&n,&m))
82     
83         for(int i=1;i<=n;++i)
84         a[i]=read();
85         build(1,1,n);
86         char ord;
87         int A,B;
88         while(m--)
89         
90             cin>>ord;
91             A=read(),B=read();
92             if(ord==‘Q‘)
93             cout<<query(1,1,n,A,B)<<endl;
94             else 
95             update(1,1,n,A,B);
96         
97     
98     return 0;
99 

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C、A Simple Problem with Integers

区间修改、区间查询、维护区间和、延迟标记

  1 //CSDN:https://blog.csdn.net/qq_40889820
  2 #include<iostream>
  3 #include<sstream>
  4 #include<fstream>
  5 #include<algorithm>
  6 #include<cstring>
  7 #include<iomanip>
  8 #include<cstdlib>
  9 #include<cctype>
 10 #include<vector>
 11 #include<string>
 12 #include<cmath>
 13 #include<ctime>
 14 #include<stack>
 15 #include<queue>
 16 #include<map>
 17 #include<set>
 18 #define mem(a,b) memset(a,b,sizeof(a))
 19 #define random(a,b) (rand()%(b-a+1)+a)
 20 #define ll long long
 21 #define ull unsigned long long
 22 #define e 2.71828182
 23 #define Pi acos(-1.0)
 24 #define ls(rt) (rt<<1)
 25 #define rs(rt) (rt<<1|1)
 26 #define lowbit(x) (x&(-x))
 27 using namespace std;
 28 const int MAXN=1e5+5;
 29 ll a[MAXN];
 30 struct node
 31 
 32     ll sum,tag;
 33 T[MAXN<<2];
 34 ll read()
 35 
 36     ll s=1,x=0;
 37     char ch=getchar();
 38     while(!isdigit(ch)) if(ch==‘-‘) s=-1;ch=getchar();
 39     while(isdigit(ch)) x=10*x+ch-‘0‘;ch=getchar();
 40     return x*s;
 41 
 42 void push_up(int p,int l,int r)
 43 
 44     T[p].sum=T[ls(p)].sum+T[rs(p)].sum;
 45 
 46 void build(int p,int l,int r)
 47 
 48     if(l==r)
 49     
 50         T[p].sum=a[l];
 51         return;
 52     
 53     T[p].tag=0;
 54     int mid=(l+r)>>1;
 55     build(ls(p),l,mid);
 56     build(rs(p),mid+1,r);
 57     push_up(p,l,r);
 58 
 59 void push_down(int p,int l,int r)
 60 
 61     if(!T[p].tag) return;
 62     T[ls(p)].tag+=T[p].tag,T[rs(p)].tag+=T[p].tag;
 63     int mid=(l+r)>>1;
 64     T[ls(p)].sum+=T[p].tag*(mid-l+1);
 65     T[rs(p)].sum+=T[p].tag*(r-mid);
 66     T[p].tag=0;
 67 
 68 void update(int p,int l,int r,int nl,int nr,ll k)
 69 
 70     if(nl<=l&&nr>=r) 
 71     
 72         T[p].sum+=k*(r-l+1);
 73         T[p].tag+=k;
 74         return ;
 75     
 76     push_down(p,l,r);
 77     int mid=(l+r)>>1;
 78     if(nl<=mid) update(ls(p),l,mid,nl,nr,k);
 79     if(nr>mid) update(rs(p),mid+1,r,nl,nr,k);
 80     push_up(p,l,r);
 81 
 82 ll query(int p,int l,int r,int nl,int nr)
 83 
 84     if(nl<=l&&nr>=r)  return T[p].sum;
 85     push_down(p,l,r);
 86     int mid=(l+r)>>1;
 87     ll ans=0;
 88     if(nl<=mid) ans+=query(ls(p),l,mid,nl,nr);
 89     if(nr>mid) ans+=query(rs(p),mid+1,r,nl,nr);
 90     return ans;
 91 
 92 int main()
 93 
 94     int n=read(),m=read();
 95     for(int i=1;i<=n;++i)
 96     a[i]=read();
 97     build(1,1,n);
 98     char ord;
 99     int A,B;
100     ll C;
101     while(m--)
102     
103         cin>>ord;
104         A=read(),B=read();
105         if(ord==‘Q‘)
106         cout<<query(1,1,n,A,B)<<endl;
107         else 
108         
109             C=read();
110             update(1,1,n,A,B,C);
111             
112     
113     return 0;
114 

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D、Mayor‘s posters