"BZOJ1026" Windy number

1026: [Scoi2009]windy number time limit:1 Sec Memory limit:162 MB
submit:7195 solved:3238
[Submit] [Status] [Discuss] Description

Windy defines a windy number. A positive integer that does not contain a leading 0 and the difference of at least 2 of the adjacent two digits is called the windy number. Windy want to know,
What is the total number of windy between A and B, including A and b?

Input

Contains two integers, A B.

Output

An integer

Sample Input"Input Sample One"
1 10
"Input Sample Two"
theSample Output"Output Example One"
9
"Output Example II"
-HINT

"Data size and conventions"

100% data, meet 1 <= A <= B <= 2000000000.

Source

Sol:

Re-learn digital DP

Set $f[i][j]$ to indicate that the current number has an I bit, and the number of scenarios where I bit is J

So obviously the transfer is $f[i][j]=f[i-1][k] (|j-k| \ge 2) $

If this number has a $len$ bit

When we count the answers, we first count all the numbers in the first bit of the $len$ that are smaller and not 0.

We then enumerate all the numbers from the $len-1$ bit to the $1$ bit and then calculate

And then this time the first one fixed US enumerate the rest of the digits if it's illegal to quit immediately.

/*To the End of the Galaxy*/#include<cstdio>#include<cstdlib>#include<iostream>#include<cstring>#include<algorithm>#include<queue>#include<iomanip>#include<bitset>#include<stack>#include<map>#include<Set>#include<cmath>#include<complex>#defineDebug (x) cerr<< #x << "=" <<x<<endl#defineINF 0x7f7f7f7f#defineLlinf 0X7FFFFFFFFFFFLL#defineP (x, Y) (((x-1) *c) +y)using namespaceStd;typedef pair<int,int>Pii;typedefLong LongLl;inlineintinit () {intnow=0, ju=1;CharCBOOLflag=false;  while(1) {C=GetChar (); if(c=='-') ju=-1; Else if(c>='0'&&c<='9') { now=now*Ten+c-'0'; Flag=true; }        Else if(flag)returnnow*Ju; }}inlineLong LongLlinit () {Long Longnow=0, ju=1;CharCBOOLflag=false;  while(1) {C=GetChar (); if(c=='-') ju=-1; Else if(c>='0'&&c<='9') { now=now*Ten+c-'0'; Flag=true; }        Else if(flag)returnnow*Ju; }}ll f[ -][Ten];voidCalc () { for(intI=0; i<=9; i++) {f[1][i]=1; }     for(intI=2; i<= -; i++)    {         for(intj=0; j<=9; j + +)        {             for(intk=0; k<=9; k++)            {                if(ABS (J-K) >=2) {F[i][j]+=f[i-1][k]; }            }        }    }}intnum[ -];intCnt=0; ll solve (ll x) {intCnt=0; ll ans=0;  while(x) {num[++cnt]=x%Ten; X/=Ten; }     for(intI=1; i<cnt;i++)    {         for(intj=1; j<=9; j + +) {ans+=F[i][j]; }    }     for(intI=1; i<num[cnt];i++) {ans+=F[cnt][i]; }     for(inti=cnt-1; i>=1; i--)    {         for(intj=0; j<num[i];j++)        {            if(ABS (num[i+1]-J) >=2) ans+=F[i][j]; }        if(ABS (num[i]-num[i+1]) <2) Break; }    returnans;} #ifdef UNIX#defineLLD "%lld"#else    #defineLLD "%i64d"#endifintMain () {ll A, B;    Calc (); A=llinit (); b=Llinit (); printf (Lld,solve (b+1)-solve (a)); return 0;}

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"BZOJ1026" Windy number