{"id":261,"date":"2012-11-14T10:55:00","date_gmt":"2012-11-14T02:55:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/166"},"modified":"2012-11-14T10:55:00","modified_gmt":"2012-11-14T02:55:00","slug":"poj_3468_updated_into_segments","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=261","title":{"rendered":"POJ 3468(\u6210\u6bb5\u66f4\u65b0\uff09"},"content":{"rendered":"\n\n\n
\n
Language:\n\n\n\n\n
Time Limit:<\/strong> 5000MS<\/td>\n <\/td>\nMemory Limit:<\/strong> 131072K<\/td>\n<\/tr>\n
Total Submissions:<\/strong> 38010<\/td>\n <\/td>\nAccepted:<\/strong> 11017<\/td>\n<\/tr>\n
Case Time Limit:<\/strong> 2000MS<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Description<\/p>\n

\n

\u5bf9\u4e8e\u6570\u5217 A<\/em>1<\/sub>, A<\/em>2<\/sub>, ... , AN<\/sub><\/em>. \u4f60\u8981\u8fdb\u884c2\u4e2a\u64cd\u4f5c\uff1a\u5c06\u4e00\u4e2a\u533a\u95f4\u7684\u6570\u540c\u52a0\u4e0a\u67d0\u4e2a\u6570\uff0c\u8f93\u51fa\u4e00\u6bb5\u533a\u95f4\u7684\u548c\u3002<\/p>\n<\/div>\n

Input<\/p>\n

\n

\u7b2c\u4e00\u884c2\u4e2a\u6574\u6570\u8868\u793a\u6570\u5217\u957f\u5ea6\u548c\u64cd\u4f5c\u6b21\u6570. 1 \u2264 N<\/em>,Q<\/em> \u2264 100000.
\n\u7b2c\u4e8c\u884c\u4e3a\u6570\u5217 A<\/em>1<\/sub>, A<\/em>2<\/sub>, ... , AN<\/sub><\/em>. -1000000000 \u2264 Ai<\/sub><\/em> \u2264 1000000000.
\n\u63a5\u4e0b\u6765\u7684Q\u884c\u64cd\u4f5c\uff1a
\n"C a b c<\/em>" \u8868\u793a\u5c06 Aa<\/sub><\/em>, Aa<\/sub><\/em>+1<\/sub>, ... , Ab<\/sub><\/em>.\u52a0\u4e0ac. -10000 \u2264 c<\/em> \u2264 10000.
\n"Q a b<\/em>" \u8f93\u51fa\u533a\u95f4[a,b]\u7684\u548c\u3002<\/p>\n<\/div>\n

Output<\/p>\n

\n

\u8f93\u51fa\u6240\u6709\u8be2\u95ee\u7684\u7b54\u6848\uff0c\u6bcf\u884c1\u4e2a\u3002<\/p>\n<\/div>\n

Sample Input<\/p>\n

10 5\n1 2 3 4 5 6 7 8 9 10\nQ 4 4\nQ 1 10\nQ 2 4\nC 3 6 3\nQ 2 4\n<\/pre>\n
Sample Output<\/p>\n
4\n55\n9\n15<\/pre>\n
Hint<\/p>\n
\nlongint\u4f1a\u7206\u7684\u3002<\/div>\n
Source<\/p>\n
\nPOJ Monthly--2007.11.25<\/a>, Yang Yi<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\n<\/span><\/p>\n

\n<\/span><\/p>\n
\u663e\u7136\u8fd9\u9898\u662f\u7ebf\u6bb5\u6811\u3002<\/span><\/p>\n
\u4f46\u662f\u6211\u4e4b\u524d\u4e60\u60ef\u7684nowl\u548cnowr似\u4e4e\u592a\u8d39\u89e3\u4e86\uff08\u4ee5\u81f4\u4e8e\u6211\u81ea\u5df1\u90fd\u8981\u60f3\u534a\u5929\uff09<\/span><\/p>\n
\u56de\u53bb\u770b\u770b\u5176\u5b83\u4eba\u548b\u5199\u2026\u2026<\/span><\/p>\n

\n<\/span><\/p>\n
<\/span><\/p>\n
Program poj3468;\nconst\n   maxn=100000;\n   maxq=100000;\nvar\n   n,m,i,j,k:longint;\n   lazy,t:array[1..maxn*8] of int64;\n   c:char;\nProcedure pushup(root:longint);\nbegin\n   t[root]:=t[root*2]+t[root*2+1];\nend;\nProcedure build(l,r,root:longint);\nvar\n   m:longint;\nbegin\n   if (l=r) then\n   begin\n      read(t[root]);\n      exit;\n   end;\n   m:=(l+r) shr 1;\n   build(l,m,root*2);\n   build(m+1,r,root*2+1);\n   pushup(root);\nend;\nProcedure Pushdown(l,r,root:longint);\nvar\n   m:longint;\nbegin\n   m:=(l+r) shr 1;\n   if (lazy[root]=0) then exit;\n   inc(lazy[root shl 1],lazy[root]);\n   inc(lazy[root shl 1+1],lazy[root]);\n   inc(t[root shl 1],lazy[root]*(m-l+1));\n   inc(t[root shl 1+1],lazy[root]*(r-(m+1)+1));\n\n   lazy[root]:=0;\nend;\nProcedure update(l,r,nowl,nowr,root,cost:longint);\nvar\n   m:longint;\nbegin\n   if (l<=nowl) and (nowr<=r) then\n   begin\n      inc(lazy[root],cost);\n      inc(t[root],(nowr-nowl+1)*cost);\n      exit;\n   end;\n   pushdown(nowl,nowr,root);\n   m:=(nowl+nowr) shr 1;\n   if (l<=m) then update(l,r,nowl,m,root*2,cost);\n   if (m+1<=r) then update(l,r,m+1,nowr,root*2+1,cost);\n   pushup(root);\nend;\nfunction query(l,r,nowl,nowr,root:longint):int64;\nvar\n   m:longint;\n   res:int64;\nbegin\n   if (l<=nowl) and (nowr<=r) then\n   begin\n      exit(t[root]);\n   end;\n   pushdown(nowl,nowr,root);\n   m:=(nowl+nowr) shr 1;\n   res:=0;\n   if (l<=m) then res:=res+query(l,r,nowl,m,root*2);\n   if (m+1<=r) then res:=res+query(l,r,m+1,nowr,root*2+1);\n   exit(res);\nend;\n\n\nbegin\n   readln(n,m);\n   fillchar(lazy,sizeof(lazy),0);\n   build(1,n,1);\n   readln;\n   while (m>0) do\n   begin\n      read(c);\n      if c='Q' then\n      begin\n         readln(i,j);\n         writeln(query(i,j,1,n,1));\n      end\n      else\n      begin\n         readln(i,j,k);\n         update(i,j,1,n,1,k);\n      end;\n\n\n\n      dec(m);\n   end;\nend.\n<\/pre>\n
<\/p>\n
\u63a5\u4e0b\u6765\u518d\u6765\u8bf4\u8bf4zkw\u7ebf\u6bb5\u6811\u7684\u89e3\u6cd5\uff1a<\/p>\n
\u8fd9\u6d89\u53ca\u5230\u539f\u6570\u7ec4A\uff0c\u5dee\u5206\u6570\u7ec4A\u2018\uff0c\u5dee\u5206\u6570\u7ec4\u524d\u7f00\u524d\u7f00\u548cA''\uff1a<\/h2>\n
\u9996\u5148\uff0c\u5b83\u4eec3\u8005\u6ee1\u8db3\u5982\u4e0b\u5173\u7cfb\uff1a<\/span><\/div>\n
\n<\/div>\n
1.\u5dee\u5206\u6570\u7ec4\u7684\u524d\u7f00\u548cSA[i]'\u4e3a\u539f\u6570\u7ec4A[i](\u5b9a\u4e49)\u3002<\/span><\/div>\n
2.\u539f\u6570\u7ec4\u7684\u524d\u7f00\u548cSA[I]\u4e3a\u5dee\u5206\u6570\u7ec4\u7684\u524d\u7f00\u524d\u7f00\u548cA''[i];<\/span><\/div>\n
\"\"
\n<\/span><\/div>\n

\n<\/span><\/div>\n
\u63a5\u4e0b\u6765\u6211\u4eec\u5206\u522b\u5efa\u7acbA\u2018\u548c(i*A')\u7684{\u5355\u70b9\u4fee\u6539\uff0c\u533a\u95f4\u6c42\u548c}\u7ebf\u6bb5\u6811<\/span><\/div>\n
\u663e\u7136\u8981\u60f3\u77e5\u9053<\/span><\/div>\n

\n<\/span><\/div>\n
<\/span>A[i]+A[i+1]+....A[ j ]<\/span><\/div>\n
     =SA[ j ]-SA[ i -1]<\/span><\/div>\n
     =A''[ j  ] - A'' [ i-1 ]<\/span><\/div>\n
     =(SA'[1] +SA'[2]+...SA''[ j ] )- (SA'[1] +SA'[2]+...SA''[ i-1 ] )<\/span><\/span><\/div>\n
     ={ j *A'[1] +(j-1)'A'[2]+....A'[ j ]}-{ (i-1) *A'[1] +(i-2)'A'[2]+....A'[ i-1 ]  }<\/span><\/span><\/span><\/div>\n
     ={  (j+1)*(A'[1]+A'[2]+...A'[ j ] )-(1*A'[1]+2*A'[2]+...j*A'[ j ]  }  -  {   i*(A'[1]+A'[2]+...A'[ i-1 ] )-(1*A'[1]+2*A'[2]+...(i-1)*A'[ i-1 ]  }<\/span><\/span><\/div>\n

\n<\/span><\/div>\n
\u8fd9\u4e2a\u65b9\u7a0b\u5982\u679c\u770b\u8d77\u6765\u4e71\u7684\u8bdd\u5c31\u76f4\u63a5\u770b\u4e0a\u9762\u7684\u56feA''(\u76f8\u5f53\u4e8e\u539f\u6570\u7ec4\u524d\u7f00\u548cSA-\u8bf7\u60f3\u529e\u6cd5\u8868\u793a\u6210A\u2018\u7684\u7d2f\u52a0\u5f62\u5f0f\uff09<\/span><\/div>\n

\n<\/span><\/div>\n
\u663e\u7136\u5982\u679c\u5c06\u4e00\u4e2a\u533a\u95f4[A,B]+V,\u5bf93\u4e2a\u6570\u7ec4\u5f71\u54cd\u5982\u4e0b\uff1a<\/span><\/div>\n

\n<\/span><\/div>\n
\"\"
\n<\/span><\/div>\n
\u5e78\u8fd0\u7684\u662f\uff0c\u6211\u4eec\u53ea\u8981\u7ef4\u62a4A\u2018\u548c{i*A\u2019}<\/span><\/div>\n
A\u548cA\u2018\u2019\u90fd\u8981\u6298\u817e\u4e00\u6bb5\u533a\u95f4\uff0c\u53ea\u6709A'\u53ea\u8981\u4fee\u6539\u5934\u548c(\u5c3e+1)\uff08\u5982\u679c\u5b58\u5728\uff09<\/span><\/div>\n

\n<\/span><\/div>\n
\u90a3\u4e48{i*A\u2018} \u7684 \u7ef4\u62a4 \u4e5f\u53ea\u8981\u4fee\u65392\u4e2a\u8282\u70b9 \uff08\u8bf7\u6ce8\u610f\u6bcf\u4e2aA\u2018 \u5b9e\u9645\u4e0a\u662f\u72ec\u7acb\u7684\uff09\uff0c\u540c\u4e0a\uff1a<\/span><\/div>\n

\n<\/span><\/div>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<cmath>\n#include<cctype>\n#include<iostream>\n#include<functional>\n#include<algorithm>\nusing namespace std;\n#define MAXN (100000+10)\n#define MAXAi (1000000000)\n#define MAXCi (10000)\n__int64 a[MAXN];\nint n,q;\nchar c[10];\nclass SegMentTree\n{\npublic:\n\tint M;\n\t__int64 t[MAXN*10];\n\tvoid fillchar()\n\t{\n\t\tM=1;while (M-2<n) M<<=1;\n\t\tmemset(t,0,sizeof(t));\n\t}\n\t__int64 h(__int64 x,__int64 y)\n\t{\n\t\treturn x+y;\n\t}\n\tvoid update(int x,__int64 c)\n\t{\n\t\tfor (x>>=1;x;x>>=1) t[x]=t[x]+c;\n\t}\n\tvoid insert(int x,__int64 c)\n\t{\n\t\tx+=M;\n\t\tt[x]+=c;\n\t\tupdate(x,c);\n\t}\n\t__int64 find(int l,int r)\n\t{\n\t\tl=l-1+M;r=r+1+M;\n\t\t__int64 ans=0;\n\t\twhile (l^r^1)\n\t\t{\n\t\t\tif (~l&1) {ans+=t[l+1];\/* cout<<l+1<<' ';*\/}\n\t\t\tif (r&1)  {ans+=t[r-1];\/* cout<<r-1<<' ';*\/}\n\t\t\tl>>=1;r>>=1;\n\t\t}\n\/\/\t\tcout<<ans<<' ';\n\t\treturn ans;\n\t}\n\t\/*\n\tvoid print()\n\t{\n\t\tfor (int i=1;i<=M*2;i++) if (t[i]!=0) cout<<i<<':'<<t[i]<<' ';\n\t\tcout<<endl;\n\t}\n\t*\/\n\n}t_ai,t_iai;\nint main()\n{\n\/\/\tfreopen("Poj3468.in","r",stdin);\n\tscanf("%d%d",&n,&q);t_ai.fillchar();t_iai.fillchar();\n\ta[0]=0;for (int i=1;i<=n;i++) scanf("%I64d",&a[i]);\n\tfor (int i=1;i<=n;i++)\n\t{\n\t\tt_ai.insert(i,a[i]-a[i-1]);\n\t\tt_iai.insert(i,i*(a[i]-a[i-1]));\n\t}\n\tfor (int i=1;i<=q;i++)\n\t{\n\t\tscanf("%s",c);\n\t\tif (c[0]=='Q')\n\t\t{\n\t\t\tint p1,p2;\n\t\t\tscanf("%d%d",&p1,&p2);p1--;\n\t\t\t__int64 ans1=(p1>0)?(__int64)(t_ai.find(1,p1)*(__int64)((__int64)p1+1)-(__int64)t_iai.find(1,p1)):0;\/\/cout<<ans1<<endl;\n\t\t\t__int64 ans2=(__int64)t_ai.find(1,p2)*(__int64)(p2+1)-(__int64)t_iai.find(1,p2);\/\/cout<<ans2<<endl;\n\t\t\tcout<<(__int64)(ans2-ans1)<<endl;\n\t\t}\n\t\telse\n\t\t{\n\t\t\tint l,r;\n\t\t\t__int64 c;\n\t\t\tscanf("%d%d%I64d",&l,&r,&c);\n\t\t\tt_ai.insert(l,(__int64)c);\n\t\t\tt_iai.insert(l,(__int64)c*l);\n\t\t\tif (r<n)\n\t\t\t{\n\t\t\t\tt_ai.insert(r+1,-(__int64)c);\n\t\t\t\tt_iai.insert(r+1,-(__int64)c*(__int64)(r+1));\n\t\t\t}\n\t\t}\n\/\/\t\tt_ai.print();\n\/\/\t\tt_iai.print();\n\t}\n\n\n\treturn 0;\n}\n<\/pre>\n<\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n

\n<\/span><\/div>\n","protected":false},"excerpt":{"rendered":"
Language: Default \u7ebf\u6bb5\u6811\u7684\u6210\u6bb5\u66f4\u65b0 Time Limit: 5000MS &nbs […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[52,109],"class_list":["post-261","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-the_zkw_segment_tree","tag-segment_tree"],"yoast_head":"\nPOJ 3468(\u6210\u6bb5\u66f4\u65b0\uff09 - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=261\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"POJ 3468(\u6210\u6bb5\u66f4\u65b0\uff09 - 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