个人觉得非常棒的博客：https://www.cnblogs.com/xenny/p/9739600.html
第一类：单点更新，区间查询
例题：http://acm.hdu.edu.cn/showproblem.php?pid=1166
AC代码：
1 /* */
2 # include <iostream>
3 # include <cstdio>
4 # include <cstring>
5 # include <string>
6 # include <cstdlib>
7 # include <queue>
8 # include <stack>
9 # include <vector>
10 # include <map>
11 # include <set>
12 # include <cmath>
13 # include <bitset>
14 # include <functional>
15 using namespace std;
16
17 int n, m;
18 int a[50005], c[50005];///对应原数组和树状数组
19 int lowbit(int x)
20 {
21 return x&(-x);///当x为0时结果为0,当x为奇数时,结果为1;
22 ///当x为偶数时,结果为x中2的最大次方的因子
23 ///2^k=i&(-i)
24 }
25
26 void updata(int i, int k)///在第i个位置上加上k
27 {
28 while( i<=n )///a[i]包含于c[i+2^k], c[i+2^k+2^k], c[i+2^k+2^k+2^k], ,,,
29 {
30 c[i] += k;
31 i += lowbit(i);
32 }
33 }
34
35 int getsum(int i)
36 {
37 int res=0;
38 while( i>0 )
39 {
40 res += c[i];
41 i -= lowbit(i);
42 }
43 return res;
44 }
45
46 int main()
47 {
48 int t;
49 cin>>t;
50 for(int tot=1; tot<=t; tot++ )
51 {
52 cout<<"Case "<<tot<<":"<<endl;
53 memset(a, 0, sizeof(a));
54 memset(c, 0, sizeof(c));
55 cin>>n;
56 for(int i=1; i<=n; i++ )
57 {
58 cin>>a[i];
59 updata(i, a[i]);
60 }
61
62 string s;
63 int x, y;
64 while( cin>>s && s[0]!=‘E‘ )
65 {
66 cin>>x>>y;
67 if( s[0]==‘Q‘)
68 {
69 int sum=getsum(y)-getsum(x-1);
70 cout<<sum<<endl;
71 }
72 else if( s[0]==‘A‘ )
73 {
74 updata(x, y);
75 }
76 else if( s[0]==‘S‘ )
77 {
78 updata(x, -y);
79 }
80 }
81 }
82 return 0;
83 }
第二类：区间修改，单点查询
例题：http://acm.hdu.edu.cn/showproblem.php?pid=1556
AC代码：
1 /* 一位数状数组：区间修改,单点查询 */
2 # include <iostream>
3 # include <stdio.h>
4 # include <string.h>
5 # include <string>
6 # include <algorithm>
7 # include <cmath>
8 # include <cstdlib>
9 # include <cctype>
10 # include <deque>
11 # include <climits>
12 # include <queue>
13 # include <stack>
14 # include <set>
15 # include <bitset>
16 # include <list>
17 # include <map>
18 using namespace std;
19
20 # define LL long long
21 # define lowbit(x)(x&(-x))
22 # define gcd(a, b) __gcd(a, b)
23 # define INF 0x3f3f3f3f
24 # define N 100010
25
26 int c[N];///树状数组不一定是求和
27
28 void updata(int x, int val)
29 {
30 while( x<=N )
31 {
32 c[x] += val;
33 x += lowbit(x);
34 }
35 }
36
37 int getsum(int x)
38 {
39 int res=0;
40 while( x>0 )
41 {
42 res += c[x];
43 x -= lowbit(x);
44 }
45 return res;
46 }
47
48 int main()
49 {
50 int n, x, y, i;
51 while( ~ scanf("%d", &n) && n )
52 {
53 memset(c, 0, sizeof(c));
54 for(i=0; i<n; i++ )
55 {
56 scanf("%d %d", &x, &y);
57 updata(x, 1);
58 updata(y+1, -1);
59 }
60
61 for(i=1; i<=n-1; i++ )
62 printf("%d ", getsum(i));
63 printf("%d\n", getsum(n));
64 }
65 return 0;
66 }
第三类：区间修改，区间查询
例题：http://poj.org/problem?id=3468
AC代码：
1 #include<cstring>
2 #include<cstdio>
3 #include<iostream>
4 #include<algorithm>
5
6 using namespace std;
7
8 #define maxn 100004
9
10 int n,m;
11 long long c1[maxn],c2[maxn];
12 long long a[maxn];
13
14 inline int lowbit(int x)
15 {
16 return x&-x;
17 }
18
19 inline void update(int index,int x,long long val)
20 {
21 if(index==0) for(int i=x;i<=n;i+=lowbit(i)) c1[i]+=val;
22 else for(int i=x;i<=n;i+=lowbit(i)) c2[i]+=(x-1)*val;
23 }
24
25 inline long long query(int x)
26 {
27 long long sum1=0,sum2=0;
28 for(int i=x;i>0;i-=lowbit(i)) sum1+=c1[i],sum2+=c2[i];
29 return x*sum1-sum2;
30 }
31
32 void init()
33 {
34 a[0]=0;
35 memset(c1,0,sizeof c1);
36 memset(c2,0,sizeof c2);
37 for(int i=1;i<=n;i++)
38 {
39 long long d=a[i]-a[i-1];
40 update(0,i,d);
41 update(1,i,d);
42 }
43 }
44
45 int main()
46 {
47 while(scanf("%d%d",&n,&m)!=EOF)
48 {
49 for(int i=1;i<=n;i++)
50 {
51 scanf("%lld",&a[i]);
52 }
53 init();
54 while(m--)
55 {
56 char op[3];
57 scanf("%s",op);
58 if(op[0]==‘Q‘)
59 {
60 int l,r;
61 scanf("%d%d",&l,&r);
62 long long ans=query(r)-query(l-1);
63 printf("%lld\n",ans);
64 }
65 else
66 {
67 int l,r;
68 long long x;
69 scanf("%d%d%lld",&l,&r,&x);
70 update(0,l,x);
71 update(0,r+1,-x);
72 update(1,l,x);
73 update(1,r+1,-x);
74 }
75 }
76 }
77 return 0;
78 }
原文地址：https://www.cnblogs.com/wsy107316/p/11323605.html
时间： 2024-08-03 16:31:02