{"id":343,"date":"2013-03-02T13:23:00","date_gmt":"2013-03-02T05:23:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/247"},"modified":"2013-03-02T13:23:00","modified_gmt":"2013-03-02T05:23:00","slug":"fzu_1040_gene_sequence_similarity-clcs","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=343","title":{"rendered":"FZU 1040(\u57fa\u56e0\u5e8f\u5217\u76f8\u4f3c\u6027\u95ee\u9898-CLCS)"},"content":{"rendered":"
Problem 1040 \u57fa\u56e0\u5e8f\u5217\u76f8似\u6027\u95ee\u9898 <\/strong><\/div>\n
\n

Accept: 59    Submit: 548
\nTime Limit: 1000 mSec    Memory Limit : 32768 KB<\/h3>\n<\/div>\n
\n

\"\" Problem Description<\/h2>\n
\n

Genotype \u662f\u4e00\u4e2a\u6709\u9650\u7684\u57fa\u56e0\u5e8f\u5217\u96c6\u3002\u5b83\u7684\u6bcf\u4e2a\u6210\u5458\u90fd\u662f\u7531\u5927\u5199\u7684\u82f1\u6587\u5b57\u6bcdA-Z\u7ec4\u6210\uff0c\u4e0d\u540c\u7684\u5b57\u6bcd\u8868\u793a\u4e0d\u540c\u79cd\u7c7b\u7684\u57fa\u56e0\u3002\u4e00\u4e2a\u57fa\u56e0\u79cd\u7c7b\u53ef\u4ee5\u5206\u5316\u6210\u4e3a\u82e5\u5e72\u65b0\u7684\u57fa\u56e0\u79cd\u7c7b\u3002\u8fd9\u79cd\u5206\u5316\u4e00\u822c\u5448\u6811\u72b6\u7ed3\u6784\u3002\u6811\u6839\u5904\u7684\u57fa\u56e0\u5e8f\u5217\u79f0\u4e3a\u6bcd\u5e8f\u5217\u3002\u57fa\u56e0\u5e8f\u5217\u4e2d\u542b\u6709\u6bcd\u5e8f\u5217\u7684\u57fa\u56e0\u5b50\u5e8f\u5217\u79f0\u4e3a\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\u3002\u751f\u7269\u4fe1\u606f\u5b66\u5bb6\u4eec\u5728\u7814\u7a76Genotype \u57fa\u56e0\u5e8f\u5217\u65f6\uff0c\u9700\u8981\u7814\u7a76\u540c\u4e00\u79cd\u7c7b\u57fa\u56e0\u5e8f\u5217\u7684\u76f8似\u6027\u3002\u5bf9\u4e8e\u540c\u4e00\u79cd\u7c7b\u76842\u4e2a\u57fa\u56e0\u5e8f\u5217X\u548cY\uff0c\u5df2\u77e5\u5b83\u4eec\u7684\u6bcd\u5e8f\u5217P\uff0c\u57fa\u56e0\u5e8f\u5217X\u548cY\u7684\u6700\u957f\u516c\u5171\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\u7ed9\u51fa\u5176\u76f8似\u6027\u7684\u51c6\u786e\u523b\u753b\u3002\u4e3a\u4e86\u6709\u6548\u5730\u5206\u6790\u57fa\u56e0\u5e8f\u5217\u7684\u76f8似\u6027\uff0c\u79d1\u5b66\u5bb6\u4eec\u5e0c\u671b\u8bbe\u8ba1\u51fa\u4e00\u4e2a\u9ad8\u6548\u7684\u8ba1\u7b97\u7a0b\u5e8f\uff0c\u80fd\u5bf9\u7ed9\u5b9a\u7684\u57fa\u56e0\u5e8f\u5217X\uff0cY\u548c\u5b83\u4eec\u7684\u6bcd\u5e8f\u5217P\uff0c\u5feb\u901f\u8ba1\u7b97\u51fa\u57fa\u56e0\u5e8f\u5217X\u548cY\u7684\u6700\u957f\u516c\u5171\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002<\/p>\n

\u7f16\u7a0b\u4efb\u52a1:
\n\u7ed9\u5b9a\u57fa\u56e0\u5e8f\u5217X\uff0cY\u548c\u6bcd\u5e8f\u5217P\uff0c\u8ba1\u7b97\u51fa\u57fa\u56e0\u5e8f\u5217X\u548cY\u7684\u6700\u957f\u516c\u5171\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002 <\/p>\n<\/div>\n

\"\" Input<\/h2>\n
\u8f93\u5165\u6570\u636e\u7684\u524d3\u884c\u4e2d\u6bcf\u884c\u6709\u4e00\u4e2a\u6b63\u6574\u6570\uff0c\u5206\u522b\u8868\u793a\u5e8f\u5217X\uff0cY\u548cP\u7684\u957f\u5ea6m\uff0cn\u548cr\uff081\u2264m,n,r\u22641000\uff09\u3002\u63a5\u4e0b\u6765\u76843\u884c\u7ed9\u51fa\u5e8f\u5217X\uff0cY\u548cP\u3002<\/div>\n

\"\" Output<\/h2>\n
\u5728\u5c4f\u5e55\u4e0a\u8f93\u51fa\u57fa\u56e0\u5e8f\u5217X\u548cY\u7684\u6700\u957f\u516c\u5171\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002\u5982\u679c\u57fa\u56e0\u5e8f\u5217X\u548cY\u6ca1\u6709\u4ee5P\u4e3a\u6bcd\u5e8f\u5217\u7684\u516c\u5171\u672c\u8d28\u57fa\u56e0\u5b50\u5e8f\u5217\uff0c\u5219\u8f93\u51fa0\u3002<\/div>\n

\"\" Sample Input<\/h2>\n
331ABCBCAA<\/div>\n

\"\" Sample Output<\/h2>\n
1<\/div>\n<\/div>\n

\n<\/p>\n

\u8fd9\u9898\u662f\u4e3a\u4e86\u627e\u7701\u9009\u9898\u65e0\u610f\u53d1\u73b0\u7684\uff0c\u539f\u95ee\u9898\u7684\u52a0\u5f3a\u7248\u3002<\/span><\/p>\n

\u89e3\u6cd5\uff1a<\/span><\/p>\n

\u9996\u5148\u6211\u6709\u4e00\u4e2a\u7528i\u6eda\u52a8\u7684\u505a\u6cd5\uff0c\u53cd\u6b63\u662fT\u4e86\uff0c\u6b63\u8bef\u4e0d\u660e\u3002\u3002\u3002<\/span><\/p>\n<\/p>\n

#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<functional>\n#include<iostream>\n#include<cstdlib>\nusing namespace std;\n#define MAXN (1000+10)\nint f[2][MAXN][MAXN];\nchar a[MAXN],b[MAXN],c[MAXN];\nint n,m,p;\nint main()\n{\n\tfreopen("fzu1040.out","r",stdin);\n\twhile (scanf("%d%d%d",&n,&m,&p)==3)\n\t{\n\t\tscanf("%s%s%s",a+1,b+1,c+1);\n\t\tmemset(f,0,sizeof(f));\n\t\tfor (int i=1;i<=n;i++)\n\t\t{\n\t\t\tfor (int j=1;j<=m;j++)\n\t\t\t\tfor (int k=0;k<=min(i,j);k++)\n\t\t\t\t{\n\t\t\t\t\tf[i%2][j][k]=max(f[i%2][j-1][k],f[(i-1)%2][j][k]);\n\t\t\t\t\tif (k&&(a[i]==b[j]&&b[j]==c[k])&&(f[(i-1)%2][j-1][k-1]||k==1)) f[i%2][j][k]=max(f[(i-1)%2][j-1][k-1]+1,f[i%2][j][k]);\n\t\t\t\t\tif ((a[i]==b[j])&&(f[(i-1)%2][j-1][k]||k==0)) f[i%2][j][k]=max(f[(i-1)%2][j-1][k]+1,f[i%2][j][k]);\n\t\t\t\t}\n\t\t\tfor(int j=1;j<=m;j++)\n\t\t\t\tfor (int k=1;k<=p;k++)\n\t\t\t\t\tf[(i+1)%2][j][k]=0;\n\t\t}\n\tif (f[n%2][m][p]<p) cout<<"0"<<endl;\n\telse cout<<f[n%2][m][p]<<endl;\n\t}\n\treturn 0;\n}<\/pre>\n
\n\u627e\u5230\u53cd\u4f8b\u8bf7\u56de\u590d\u6211.<\/p>\n

\n<\/span><\/p>\n
\u518d\u6765\u8bf4\u8bf4\u6b63\u89e3(\u8f93\u51fa\u65f6\u8bb0\u5f97\u8f93\u7684\u662ff[p%2][n][m]\u4e0d\u662ff[k%2][n][m]\uff0c\u53d8\u91cf\u540d\u4e71\u8bbe\u5bb3\u6b7b\u4eba\uff09<\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<functional>\n#include<iostream>\n#include<cstdlib>\nusing namespace std;\n#define MAXN (1000+10)\nint f[2][MAXN][MAXN];\nchar a[MAXN],b[MAXN],c[MAXN];\nint n,m,p;\nint main()\n{\n\/\/\tfreopen("fzu1040.out","r",stdin);\n\twhile (scanf("%d%d%d",&n,&m,&p)!=EOF)\n\t{\n\t\tscanf("%s%s%s",a+1,b+1,c+1);\n\t\tmemset(f,0,sizeof(f));\n\t\tint k=0;\n\t\tfor (int i=1;i<=n;i++)\n\t\t\tfor (int j=1;j<=m;j++)\n\t\t\t{\n\t\t\t\tif (a[i]==b[j]) f[k][i][j]=f[k][i-1][j-1]+1;\n\t\t\t\telse f[k][i][j]=max(f[k][i][j-1],f[k][i-1][j]);\n\t\t\t}\n\t\tbool flag=1;\n\t\tint ta=MAXN,tb=MAXN,mina=1,minb=1;\n\t\tfor (int k=1;k<=p&&flag;k++)\n\t\t{\n\t\t\tflag=0;\n\t\t\tfor (int i=mina-1;i<=n;i++)\n\t\t\t\tfor (int j=minb-1;j<=m;j++)\n\t\t\t\t\tf[k%2][i][j]=0;\n\t\t\tfor (int i=mina;i<=n;i++)\n\t\t\t\tfor (int j=minb;j<=m;j++)\n\t\t\t\t{\n\t\t\t\t\tf[k%2][i][j]=0;\n\t\t\t\t\tif ((a[i]==b[j]&&b[j]==c[k])&&(f[(k%2)^1][i-1][j-1]||k==1))\n\t\t\t\t\t{\n\t\t\t\t\t\tf[k%2][i][j]=f[(k%2)^1][i-1][j-1]+1;\n\t\t\t\t\t\tflag=1;ta=min(ta,i);tb=min(tb,j);\n\t\t\t\t\t}\n\t\t\t\t\telse if (a[i]==b[j]&&b[j]==c[k]) continue;\n\t\t\t\t\telse if ((a[i]==b[j])&&(f[k%2][i-1][j-1])) f[k%2][i][j]=max(f[k%2][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t\telse if (a[i]==b[j]) continue;\n\t\t\t\t\telse f[k%2][i][j]=max(f[k%2][i][j-1],f[k%2][i-1][j]);\n\t\t\t\t}\n\t\t\tmina=ta;minb=tb;\n\t\t\tta=tb=MAXN;\n\t\t}\n\t\t\/*\n\t\tif (!flag)\n\t\t{\n\t\t\tif (f[k%2][n][m]>=k) while (1);\n\t\t}\n\t\t*\/\n\t\tif (!flag) printf("0n");\n\t\telse printf("%dn",f[p%2][n][m]);\n\t}\n\treturn 0;\n}<\/pre>\n
\n\u5f88\u76f4\u89c2\u7684Dp\u3002\u3002<\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<functional>\n#include<iostream>\n#include<cstdlib>\nusing namespace std;\n#define MAXN (1000+10)\nint f[2][MAXN][MAXN];\nchar a[MAXN],b[MAXN],c[MAXN];\nint n,m,p;\nint main()\n{\n\/\/\tfreopen("fzu1040.out","r",stdin);\n\twhile (scanf("%d%d%d",&n,&m,&p)!=EOF)\n\t{\n\t\tscanf("%s%s%s",a+1,b+1,c+1);\n\t\tmemset(f,0,sizeof(f));\n\t\tint k=0;\n\t\tfor (int i=1;i<=n;i++)\n\t\t\tfor (int j=1;j<=m;j++)\n\t\t\t{\n\t\t\t\tif (a[i]==b[j]) f[k][i][j]=f[k][i-1][j-1]+1;\n\t\t\t\telse f[k][i][j]=max(f[k][i][j-1],f[k][i-1][j]);\n\t\t\t}\n\t\tbool flag=1;\n\t\tint ta=MAXN,tb=MAXN,mina=1,minb=1;\n\t\tfor (int k=1;k<=p&&flag;k++)\n\t\t{\n\t\t\tflag=0;\n\t\t\tfor (int i=mina-1;i<=n;i++)\n\t\t\t\tfor (int j=minb-1;j<=m;j++)\n\t\t\t\t\tf[k%2][i][j]=0;\n\t\t\tfor (int i=mina;i<=n;i++)\n\t\t\t\tfor (int j=minb;j<=m;j++)\n\t\t\t\t{\n\n\t\t\t\t\tf[k%2][i][j]=max(f[k%2][i][j-1],f[k%2][i-1][j]);\n\t\t\t\t\tif (k&&(a[i]==b[j]&&b[j]==c[k])&&(f[(k%2)^1][i-1][j-1]||k==1))\n\t\t\t\t\t{\n\t\t\t\t\t\tf[k%2][i][j]=max(f[(k%2)^1][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t\t\tflag=1;ta=min(ta,i);tb=min(tb,j);\n\t\t\t\t\t}\n\t\t\t\t\tif ((a[i]==b[j])&&(f[k%2][i-1][j-1])) f[k%2][i][j]=max(f[k%2][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t}\n\t\t\tmina=ta;minb=tb;\n\t\t\tta=tb=MAXN;\n\t\t}\n\t\t\/*\n\t\tif (!flag)\n\t\t{\n\t\t\tif (f[k%2][n][m]>=k) while (1);\n\t\t}\n\t\t*\/\n\t\tif (!flag) printf("0n");\n\t\telse printf("%dn",f[p%2][n][m]);\n\t}\n\treturn 0;\n}<\/pre>\n
\n\u8981\u8003\u8651\u4ecef[k-1][i-1][j-1],f[k][i-1][j-1],f[k][i-1][j],f[k][i][j-1]\u8f6c\u79fb\u7684\u60c5\u51b5,\u8f93\u51fa\u8bb0\u5f97\u6e050.<\/p>\n
\u4e8b\u5b9e\u4e0a\uff0c\u5173\u4e8e\u6570\u7ec4\u6e050\u90e8\u5206\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u505a\u5f97\u66f4\u597d<\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<functional>\n#include<iostream>\n#include<cstdlib>\nusing namespace std;\n#define MAXN (1000+10)\nint f[2][MAXN][MAXN];\nchar a[MAXN],b[MAXN],c[MAXN];\nint n,m,p;\nint main()\n{\n\/\/\tfreopen("fzu1040.out","r",stdin);\n\twhile (scanf("%d%d%d",&n,&m,&p)!=EOF)\n\t{\n\t\tscanf("%s%s%s",a+1,b+1,c+1);\n\t\tmemset(f,0,sizeof(f));\n\t\tint k=0;\n\t\tfor (int i=1;i<=n;i++)\n\t\t\tfor (int j=1;j<=m;j++)\n\t\t\t{\n\t\t\t\tif (a[i]==b[j]) f[k][i][j]=f[k][i-1][j-1]+1;\n\t\t\t\telse f[k][i][j]=max(f[k][i][j-1],f[k][i-1][j]);\n\t\t\t}\n\t\tbool flag=1;\n\t\tint ta=MAXN,tb=MAXN,mina=1,minb=1;\n\t\tfor (int k=1;k<=p&&flag;k++)\n\t\t{\n\t\t\tflag=0;\n\t\t\tfor (int i=mina-1;i<=n;i++)\n\t\t\t\tf[k%2][i][minb-1]=0;\n\t\t\tfor (int j=minb-1;j<=m;j++)\n\t\t\t\tf[k%2][mina-1][j]=0; \/\/\u53ea\u8981\u628a\u8fb9\u754c\u60c5\u51b5\u8d4b0\n\t\t\tfor (int i=mina;i<=n;i++)\n\t\t\t\tfor (int j=minb;j<=m;j++)\n\t\t\t\t{\n\n\t\t\t\t\tf[k%2][i][j]=max(f[k%2][i][j-1],f[k%2][i-1][j]);\n\t\t\t\t\tif (k&&(a[i]==b[j]&&b[j]==c[k])&&(f[(k%2)^1][i-1][j-1]||k==1))\n\t\t\t\t\t{\n\t\t\t\t\t\tf[k%2][i][j]=max(f[(k%2)^1][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t\t\tflag=1;ta=min(ta,i);tb=min(tb,j);\n\t\t\t\t\t}\n\t\t\t\t\tif ((a[i]==b[j])&&(f[k%2][i-1][j-1])) f[k%2][i][j]=max(f[k%2][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t}\n\t\t\tmina=ta;minb=tb;\n\t\t\tta=tb=MAXN;\n\t\t}\n\t\tif (!flag) printf("0n");\n\t\telse printf("%dn",f[p%2][n][m]);\n\t}\n\treturn 0;\n}<\/pre>\n
\n\u4e0d\u59a8\u628a\u5bf9k=0\u7684\u7279\u5224\u5199\u5728\u4e00\u8d77<\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<functional>\n#include<iostream>\n#include<cstdlib>\nusing namespace std;\n#define MAXN (1000+10)\nint f[2][MAXN][MAXN];\nchar a[MAXN],b[MAXN],c[MAXN];\nint n,m,p;\nint main()\n{\n\/\/\tfreopen("fzu1040.out","r",stdin);\n\tc[0]=' ';\n\twhile (scanf("%d%d%d",&n,&m,&p)!=EOF)\n\t{\n\t\tscanf("%s%s%s",a+1,b+1,c+1);\n\t\tbool flag=1;\n\t\tint ta=MAXN,tb=MAXN,mina=1,minb=1;\n\t\tfor (int k=0;k<=p&&flag;k++)\n\t\t{\n\t\t\tflag=0;\n\t\t\tfor (int i=mina-1;i<=n;i++)\n\t\t\t\tf[k%2][i][minb-1]=0;\n\t\t\tfor (int j=minb-1;j<=m;j++)\n\t\t\t\tf[k%2][mina-1][j]=0;\n\t\t\tfor (int i=mina;i<=n;i++)\n\t\t\t\tfor (int j=minb;j<=m;j++)\n\t\t\t\t{\n\t\t\t\t\tf[k%2][i][j]=max(f[k%2][i][j-1],f[k%2][i-1][j]);\n\t\t\t\t\tif (k&&(a[i]==b[j]&&b[j]==c[k])&&(f[(k%2)^1][i-1][j-1]||k==1))\n\t\t\t\t\t{\n\t\t\t\t\t\tf[k%2][i][j]=max(f[(k%2)^1][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t\t\tflag=1;ta=min(ta,i);tb=min(tb,j);\n\t\t\t\t\t}\n\t\t\t\t\tif ((a[i]==b[j])&&(f[k%2][i-1][j-1]||k==0)) f[k%2][i][j]=max(f[k%2][i-1][j-1]+1,f[k%2][i][j]);\n\t\t\t\t}\n\t\t\tmina=ta;minb=tb;\n\t\t\tta=tb=MAXN;\n\t\t\tif (!k)\n\t\t\t{\n\t\t\t\tflag=1;mina=minb=1;\n\t\t\t}\n\t\t}\n\t\tif (!flag) printf("0n");\n\t\telse printf("%dn",f[p%2][n][m]);\n\t}\n\treturn 0;\n}<\/pre>\n<\/p>\n

\n<\/span><\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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