Sequence type Dp:⑨ to write a letter

Title Description Description

Qi Cirno (Ice Goblin) has the ability to control the air-conditioning. It is more dangerous to freeze a small thing in an instant than a normal goblin. had been releasing the air-conditioner around her always very cold.

Due to the following three points reason ...

• Qi Cirno's Fuca symbol "Icicle Fall"-easy of the bomb screen is enough stupid, as long as standing in front of her there is no play will touch you;

• Zun in "Red Devil Township" introduced her when she said she was a bit stupid;

• In the Zun release "Oriental Phantasmagoria Tomb" Introduction map, in the picture put the Qi Lulu in the position of ⑨, and with "⑨ idiot" simple take, from "⑨" and "idiot" became her alias ...

So Kiki Cirno got the nickname of "idiot".

One day, Kiki Cirno again 2 ...

She wrote n letters to be loaded into N envelopes, but all were wrong ... Now you want to know how many kinds of possibilities are wrong.

Enter a description Input Description

Number of letters and envelopes N.

Output description Output Description

The number of possibilities to mount the error.

The category label says it's a serial DP, and it feels like this is a combinatorial math mismatch problem.

A total of n elements, with a number of DN

D2=1; d3=2;

Assuming that N is ranked K, K has (n-1) species may

If k is in the position of N, the remaining Dn-2 species may

If k is not in the position of N, then the nth bit is reconsidered as a new "K-bit", when the number of remaining n-1, including K, is equivalent to the wrong row of only the number of n-1 (only the K-bit will be replaced by the nth bit). The number of rows is Dn-1.

So, dn= (n-1) * (dn-1+dn-2)

High-precision Operation

var num1,num2,num:array[1..10000]of integer;
    N:longint;
    I,j,k,len:longint;

Begin READLN (n);
      Num1[1]:=1;
      num2[1]:=2;
      Len:=1;
      For j:=4 to N do
          Begin for I:=1 to Len do
                    Num[i]:=num1[i]+num2[i];
                For I:=1 to Len do
                    Begin Num[i+1]:=num[i+1]+num[i] DIV 10;
                          Num[i]:=num[i] MoD 10;
                    End
                If num[len+1]<>0
                   Then Inc (LEN);
                For I:=1 to Len do
                    num[i]:=num[i]* (j-1);
                For I:=1 to Len do
                    Begin Num[i+1]:=num[i+1]+num[i]div 10;
                          Num[i]:=num[i] MoD 10;
                    End
                While num[len+1]<>0 do
                      Inc (LEN);
                num1:=num2;
                Num2:=num;
          End
      For I:=len Downto 1 do
          Write (Num[i]);
End.

Sequence type Dp:⑨ to write a letter