【HDOJ6148】Valley Numer（数位DP）

题意：

 1≤T≤200

● 1≤length(N)≤100

思路：

设f[i,j,k,l]为第i位为j，前i位是否贴上限(0/1)，递减或递增(0/1)方案数

g[i,j,k]为不到n位，第i位为j，递减或递增方案数

const mo=1000000007;
var f:array[0..105,0..10,0..2,0..2]of longint;
    g:array[0..105,0..10,0..2]of longint;
    a:array[1..105]of longint;
    v,n,i,j,k,l,jj,kk,ans,cas,ll:longint;
    ch:string;

begin

 readln(cas);
 for v:=1 to cas do
 begin
  readln(ch);
  n:=length(ch);
  for i:=1 to n do a[i]:=0;
  for i:=1 to n do a[i]:=ord(ch[i])-ord('0');
  for i:=1 to n do
   for j:=0 to 9 do
    for k:=0 to 1 do
     for l:=0 to 1 do f[i,j,k,l]:=0;
  for i:=1 to a[1]-1 do f[1,i,0,0]:=1;
  f[1,a[1],1,0]:=1;
  for i:=2 to n do
   for j:=0 to 9 do
    for k:=0 to 1 do
     for l:=0 to 1 do
      for jj:=0 to 9 do
      begin
       if k=0 then kk:=0;
       if (k=1)and(jj<a[i]) then kk:=0;
       if (k=1)and(jj=a[i]) then kk:=1;
       if (k=1)and(jj>a[i]) then break;
       for ll:=l to 1 do
       begin
        if (ll=0)and(j<jj) then continue;
        if (ll=1)and(j>jj) then continue;
        if (ll<>l)and(j=jj) then continue;
        f[i,jj,kk,ll]:=(f[i,jj,kk,ll]+f[i-1,j,k,l]) mod mo;
       end;
      end;
  for i:=1 to n-1 do
   for j:=0 to 9 do
    for k:=0 to 1 do g[i,j,k]:=0;
  for i:=1 to 9 do g[1,i,0]:=1;
  for i:=2 to n-1 do
    for j:=0 to 9 do
     for k:=0 to 1 do
      for jj:=0 to 9 do
       for kk:=k to 1 do
       begin
        if (kk=0)and(j<jj) then continue;
        if (kk=1)and(j>jj) then continue;
        if (k<>kk)and(j=jj) then continue;
        g[i,jj,kk]:=(g[i,jj,kk]+g[i-1,j,k]) mod mo;
       end;
  ans:=0;
  for j:=0 to 9 do
   for k:=0 to 1 do
    for l:=0 to 1 do ans:=(ans+f[n,j,k,l]) mod mo;
  for i:=1 to n-1 do
   for j:=0 to 9 do
    for k:=0 to 1 do ans:=(ans+g[i,j,k]) mod mo;
  writeln(ans);
 end;

end.