信息学集训队作业ural竞赛

1、题目来源Ural 1611. Decimation题目描述读入一个n（0n=10000）位的 01 字符串，至多k 个 1，使得在 10 的倍数位上的 1 的个数最少。算法描述动态规划算法实现这道题目的方程f(i,j)表示前i 位j 个字符的，分以下情况1 当 i+j mod 10=0 则 f(i,j):=max(f(i-1,j)+ord(sti)-48,f(i,j-1)+1)2 当i+j mod 100 则f(i,j):=max(f(i-1,j),f(i,j-1)表示的含义是:当i+j mod 10=0 则将该位置上的 1 的会增加中 1 的个数，f(i-1,j)表示不1 的情况下。f(i,

2、j-1)表示原来的字串中在（i+j）的位置则不用考虑f(i,j-1);再从后往前扫描 如果ai,j=ai,j-1+1 表示在i+j 位置有位置输出即可。一个 1。当j=0 时了一个 1，所源程序var n,k,i,j:long;ans:array1.50of long;a:array0.100000,0.50of long st:ansistring;beginreadln(n,k); readln(st);for i:=0 to k do a0,i:=i div 10; for i:=1 to n dofor j:=0 to k do beginif (i+j) mod 10=0)and(s

3、ti=1)then ai,j:=ai-1,j+1else ai,j:=ai-1,j; if j0 thenif (i+j) mod 10=0then begin if ai,jai,j-1+1 then ai,j:=ai,j-1+1 end else begin if ai,jai,j-1 then ai,j:=ai,j-1; end;end; j:=0;for i:=0 to kf an,jan,i then j:=i; i:=n;wrin(an,j); k:=0;while (i=0)and(j0) do if (i+j) mod 10=0then if ai,j=ai,j-1+1 the

4、n begin inc(k); ansk:=i+j; dec(j); end else dec(i) else if ai,j=ai,j-1 then begin inc(k); ansk:=i+j; dec(j); end else dec(i); write(k); for i:=k downto 1 do write( ,ansi);wrin;end.原题描述：1611. Decimation Time Limit: 0.5 second Memory Limit: 64 MBDecimation was a form of extreme military discipline use

5、d he Roman Army, when every tenth soldier was executed.Do you think fare dodgers fine without because theyit is easy to work as a conductor in a always try to ride free of charge, and remorse not only fare dodgers but also dont cope with their duties.tram? Persistent ticket inspectors tram conductor

6、she course of operation Fare Dodger 2008, which was carried out recently by the Yekaterinburg Assotion of Ticket Inspectors, itturned outt in every tram there waseast one fare dodger at the of Yekaterinburg becamemoment of inspection. Chief Ticket Inspectorfurious and decided to punish conductors. H

7、e a column and to fine every tenth conductor a conductors salary.ordered to line them up insum equalto aageChiere Dodger of Yekaterinburg felt sorry for poor decided to help them, because he knewt some of theconductors and conductors weregood Fare fare everyand coped with their duties. Before conduc

8、tors are fined, ChiefDodger can placeothe column some of his friends, who are alsododgers. Chief TicketInspector doesntthisand will fine10 (the number Dodger towhosenumberhehe column is a multiple ofof the place hiscolumn is 1). Help Chierefriendshe column sot the total numberof fined faredodgers an

9、d good conductors be minimal.InputThelinecontainsegers n (1 n 10000) andspace; they are the number of conductorsk (0 k 50)he columnseparated by a and the numberof Chiere Dodgers friends who are ready to help the line consists of n symbols; the ith symbol ishe column is initially occupied by a goodco

10、nductors. The second“1” if the ith placeconductor, and “0” if the conductor is bad.Outputhe and good dodgers which are separatedline, output the minimal total number of fined faredodgers re egers,he second line, output the number mconductors.t should be their numbers by a space.omplacedhe column, and then outputhe resulting column. The numbersmustbeSlesinput10 2output000000000