[NDK 数字游戏]

[题目来源]：NOIP2003普及组

[关键字]：动态规划

[题目大意]：将一个n个数字组成的环分成m份，使每份之和对10取模后相乘的积最大或最小。

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[分析]：类似于石子合并的动态规划，解法比较暴力（n<=50 m<=9）。枚举每一个点，以此为起点将环断开，然后f[i,j]为以枚举断链的点开始前i个分成j组的最大（最小值），f[i,j]=f[k,j-1]*sum[k+1,i]，具体i，j，k所代表的含义有点不同，结合代码再仔细看吧。

[代码]：

View Code

 1 var
 2   n, m, ansa, ansi: longint;
 3   max, min: array[0..50,0..10] of longint;
 4   sum: array[0..50,0..50] of longint;
 5   a: array[0..50] of longint;
 6   
 7 function gmax(x, y: longint):longint;
 8 begin
 9   if x > y then exit(x) else exit(y);
10 end;
11 
12 function gmin(x, y: longint):longint;
13 begin
14   if x < y then exit(x) else exit(y);
15 end;
16 
17 procedure init;
18 var
19   i, j, st, ed, mid: longint;
20 begin
21   readln(n,m);
22   for i := 1 to n do read(a[i]);
23   for i := 1 to n do
24     for j := i to i+n-1 do
25       begin
26         st := i;
27         if j > n then ed := j-n else ed := j;
28         if ed-1 < 1 then mid := ed-1+n else mid := ed-1;
29         sum[st,ed] := sum[st,mid]+a[ed];
30         sum[st,ed] := sum[st,ed] mod 10;
31         if sum[st,ed] < 0 then inc(sum[st,ed],10);
32       end;
33   {for i := 1 to n do
34     for j := 1 to n do writeln(i,' ',j,' ',sum[i,j]);}
35 end;
36 
37 procedure work;
38 var
39   st, i, mid, j, k, mid2: longint;
40 begin
41   ansa := 0;
42   ansi := maxlongint;
43   for st := 1 to n do
44     begin
45       fillchar(max,sizeof(max),0);
46       fillchar(min,sizeof(min),10);
47       for i := 1 to n do
48         begin
49           if st+i-1 > n then mid := st+i-1-n else mid := st+i-1;
50           max[i,1] := sum[st,mid];
51           min[i,1] := sum[st,mid];
52           //writeln(st,'',i,'',max[i,1]);
53         end;
54       for i := 1 to n do
55         for j := 2 to gmin(i,m) do
56           begin
57             for k := 1 to i-1 do
58               begin
59                 if st+k > n then mid := st+k-n else mid := st+k;
60                 if st+i-1 > n then mid2 := st+i-1-n else mid2 := st+i-1;
61                 max[i,j] := gmax(max[i,j],max[k,j-1]*sum[mid,mid2]);
62                 min[i,j] := gmin(min[i,j],min[k,j-1]*sum[mid,mid2]);
63               end;
64             //writeln(st,'',i,'',j,'',max[i,j]);
65           end;
66       //writeln(st,'',max[n,m],'',min[n,m]);
67       ansa := gmax(ansa,max[n,m]);
68       ansi := gmin(ansi,min[n,m]);
69     end;
70   //if ansi < 0 then ansi := 0;
71   writeln(ansi);
72   writeln(ansa);
73 end;
74 
75 begin
76   assign(input,'d:\1.in');reset(input);
77   assign(output,'d:\1.out');rewrite(output);
78   init;
79   work;
80   close(input);
81   close(output);
82 end.