study from :
https://www.cnblogs.com/RabbitHu/p/BIT.html
loj
130
https://loj.ac/problem/130
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <string> 6 #include <algorithm> 7 #include <set> 8 #include <map> 9 #include <queue> 10 #include <iostream> 11 using namespace std; 12 13 #define ll long long 14 15 const int maxn=1e6+10; 16 const int inf=1e9; 17 const double eps=1e-8; 18 19 ll f[maxn]; 20 int n; 21 22 void modify(int i,int x) 23 { 24 while (i<=n) 25 { 26 f[i]+=x; 27 i+=i&-i; 28 } 29 } 30 31 ll cal(int i) 32 { 33 ll sum=0; 34 while (i) 35 { 36 sum+=f[i]; 37 i-=i&-i; 38 } 39 return sum; 40 } 41 42 int main() 43 { 44 int q,x,y,z,i; 45 scanf("%d%d",&n,&q); 46 for (i=1;i<=n;i++) 47 { 48 scanf("%d",&x); 49 modify(i,x); 50 } 51 52 while (q--) 53 { 54 scanf("%d%d%d",&x,&y,&z); 55 if (x==1) 56 modify(y,z); 57 else 58 printf("%lld\n",cal(z)-cal(y-1)); 59 } 60 return 0; 61 } 62 /* 63 64 */
131
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <string> 6 #include <algorithm> 7 #include <set> 8 #include <map> 9 #include <queue> 10 #include <iostream> 11 using namespace std; 12 13 #define ll long long 14 15 const int maxn=1e6+10; 16 const int inf=1e9; 17 const double eps=1e-8; 18 19 ll f[maxn]; 20 int n; 21 22 void modify(int i,int x) 23 { 24 while (i<=n) 25 { 26 f[i]+=x; 27 i+=i&-i; 28 } 29 } 30 31 ll cal(int i) 32 { 33 ll sum=0; 34 while (i) 35 { 36 sum+=f[i]; 37 i-=i&-i; 38 } 39 return sum; 40 } 41 42 int main() 43 { 44 int q,x,y,z,r,i; 45 scanf("%d%d",&n,&q); 46 y=0; 47 for (i=1;i<=n;i++) 48 { 49 scanf("%d",&x); 50 modify(i,x-y); 51 y=x; 52 } 53 54 while (q--) 55 { 56 scanf("%d%d",&x,&y); 57 if (x==1) 58 { 59 scanf("%d%d",&z,&r); 60 modify(y,r); 61 modify(z+1,-r); 62 } 63 else 64 printf("%lld\n",cal(y)); 65 } 66 return 0; 67 } 68 /* 69 70 */
132
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <string> 6 #include <algorithm> 7 #include <set> 8 #include <map> 9 #include <queue> 10 #include <iostream> 11 using namespace std; 12 13 #define ll long long 14 15 const int maxn=1e6+10; 16 const int inf=1e9; 17 const double eps=1e-8; 18 19 ll f1[maxn],f2[maxn]; 20 int n; 21 22 void modify(int i,int x) 23 { 24 ll xx=1ll*x*i; 25 while (i<=n) 26 { 27 f1[i]+=x; 28 f2[i]+=xx; 29 i+=i&-i; 30 } 31 } 32 33 ll cal(int i) 34 { 35 int c=i+1; 36 ll sum=0; 37 while (i) 38 { 39 sum+=f1[i]*c-f2[i]; 40 i-=i&-i; 41 } 42 return sum; 43 } 44 45 int main() 46 { 47 int q,x,y,z,r,i; 48 scanf("%d%d",&n,&q); 49 y=0; 50 for (i=1;i<=n;i++) 51 { 52 scanf("%d",&x); 53 modify(i,x-y); 54 y=x; 55 } 56 57 while (q--) 58 { 59 scanf("%d%d%d",&x,&y,&z); 60 if (x==1) 61 { 62 scanf("%d",&r); 63 modify(y,r); 64 modify(z+1,-r); 65 } 66 else 67 printf("%lld\n",cal(z)-cal(y-1)); 68 } 69 return 0; 70 } 71 /* 72 73 */
133
看数组就好。公式推导无法理解。
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <string> 6 #include <algorithm> 7 #include <set> 8 #include <map> 9 #include <queue> 10 #include <iostream> 11 using namespace std; 12 13 #define ll long long 14 15 const int maxn=1e6+10; 16 const int inf=1e9; 17 const double eps=1e-8; 18 19 ll f[1<<12|1][1<<12|1]; 20 int n,m; 21 22 void modify(int i,int j,int x) 23 { 24 int ii=i; 25 while (j<=m) 26 { 27 i=ii; 28 while (i<=n) 29 { 30 f[i][j]+=x; 31 i+=i&-i; 32 } 33 j+=j&-j; 34 } 35 } 36 37 ll cal(int i,int j) 38 { 39 int ii=i; 40 ll sum=0; 41 while (j) 42 { 43 i=ii; 44 while (i) 45 { 46 sum+=f[i][j]; 47 i-=i&-i; 48 } 49 j-=j&-j; 50 } 51 return sum; 52 } 53 54 int main() 55 { 56 int x,y,z,s,t; 57 scanf("%d%d",&n,&m); 58 while (~scanf("%d%d%d%d",&x,&y,&z,&s)) 59 { 60 if (x==1) 61 modify(y,z,s); 62 else 63 { 64 scanf("%d",&t); 65 printf("%lld\n",cal(s,t)-cal(y-1,t)-cal(s,z-1)+cal(y-1,z-1)); 66 } 67 } 68 return 0; 69 } 70 /* 71 72 */
135
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <string> 6 #include <algorithm> 7 #include <set> 8 #include <map> 9 #include <queue> 10 #include <iostream> 11 using namespace std; 12 13 #define ll long long 14 15 const int maxn=1e6+10; 16 const int inf=1e9; 17 const double eps=1e-8; 18 19 ll f1[1<<12|1][1<<12|1],f2[1<<12|1][1<<12|1],f3[1<<12|1][1<<12|1],f4[1<<12|1][1<<12|1]; 20 int n,m; 21 22 void modify(int i,int j,int x) 23 { 24 int ii=i; 25 ll x2=1ll*x*i,x3=1ll*x*j,x4=1ll*x*i*j; 26 while (j<=m) 27 { 28 i=ii; 29 while (i<=n) 30 { 31 f1[i][j]+=x; 32 f2[i][j]+=x2; 33 f3[i][j]+=x3; 34 f4[i][j]+=x4; 35 i+=i&-i; 36 } 37 j+=j&-j; 38 } 39 } 40 41 ll cal(int i,int j) 42 { 43 ll c1=1ll*(i+1)*(j+1),c2=j+1,c3=i+1; 44 int ii=i; 45 ll sum=0; 46 while (j) 47 { 48 i=ii; 49 while (i) 50 { 51 sum+=c1*f1[i][j]-c2*f2[i][j]-c3*f3[i][j]+f4[i][j]; 52 i-=i&-i; 53 } 54 j-=j&-j; 55 } 56 return sum; 57 } 58 59 int main() 60 { 61 int x,y,z,s,t,r; 62 scanf("%d%d",&n,&m); 63 64 while (~scanf("%d%d%d%d%d",&x,&y,&z,&s,&t)) 65 { 66 if (x==1) 67 { 68 scanf("%d",&r); 69 modify(y,z,r); 70 modify(y,t+1,-r); 71 modify(s+1,z,-r); 72 modify(s+1,t+1,r); 73 } 74 else 75 printf("%lld\n",cal(s,t)-cal(y-1,t)-cal(s,z-1)+cal(y-1,z-1)); 76 } 77 return 0; 78 } 79 /* 80 81 */