HDU 6156(Palindrome Function-数位dp)

令fi,j=(i在j进制下回文)?j:1
求∑Ri=L∑rj=lf(i,j)
1<=L,R<=1e18,2<=j<=36
数位dp，
由于j进制的长度为l的回文串长度能直接算出来(j−1)j⌊l+12⌋，所以不用在数位dp时考虑前导0

#include<cstdio>#include<cstring>#include<cstdlib>#include<algorithm>#include<functional>#include<iostream>#include<cmath>#include<cctype>#include<ctime>#include<vector>#include<set>#include<string>#include<queue>#include<complex>#include<stack>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=pre[x];p;p=next[p])#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,0x3f,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define MEMx(a,b) memset(a,b,sizeof(a));#define INF (0x3f3f3f3f)#define F (1000000007)#define pb push_back#define mp make_pair#define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;#define PRi2D(a,n,m) For(i,n) { \                        For(j,m-1) cout<<a[i][j]<<' ';\                        cout<<a[i][m]<<endl; \                        } #pragma comment(linker, "/STACK:102400000,102400000")#define ALL(x) (x).begin(),(x).end()#define gmax(a,b) a=max(a,b);#define gmin(a,b) a=min(a,b);typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return ((a-b)%F+F)%F;}void upd(ll &a,ll b){a=(a+b);}inline int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} bool check();int T;#define MAXN (50)struct FastIO {    static const int S = 5 << 20; //MB    int wpos; char wbuf[S];    FastIO() : wpos(0) {}    inline int xchar() {        static char buf[S];        static int len = 0, pos = 0;        if(pos == len)            pos = 0, len = fread(buf, 1, S, stdin);        if(pos == len) return -1;        return buf[pos ++];    }    inline int xuint() {        int c = xchar(), x = 0;        while(~c && c <= 32) c = xchar();        for(; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';        return x;    }    inline int xint() {        int s = 1, c = xchar(), x = 0;        while(c <= 32) c = xchar();        if(c == '-') s = -1, c = xchar();        for(; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';        return x * s;    }    inline void xstring(char* s) {        int c = xchar();        while(c <= 32) c = xchar();        for(; c > 32; c = xchar()) * s++ = c;        *s = 0;    }    inline void wchar(int x) {        if(wpos == S) fwrite(wbuf, 1, S, stdout), wpos = 0;        wbuf[wpos ++] = x;    }    inline void wint(ll x) {        if(x < 0) wchar('-'), x = -x;        char s[24];        int n = 0;        while(x || !n) s[n ++] = '0' + x % 10, x /= 10;        while(n--) wchar(s[n]);    }    inline void wstring(const char* s) {        while(*s) wchar(*s++);    }    ~FastIO() {        if(wpos) fwrite(wbuf, 1, wpos, stdout), wpos = 0;    }} io;int a[MAXN];ll f[MAXN][MAXN][2];int n,k;//first i,j tian j not qiandao0, y is==n ll calc() {    ll ans=0;    Rep(i,n+1) Fork(j,i,i) Rep(y,2) f[i][j][y]=0;    f[0][0][1]=1;    Rep(i,n) {        int j=i; Rep(y,2) {            if (f[i][j][y]) {                Rep(t,k) {                    int nj=(!t&&!j)?(0):(j+1);                    int ny=(y&&t==a[i+1]);                    if (y&&t>a[i+1]) continue;                    if (j>=n-i) continue;                    f[i+1][nj][ny]+=f[i][j][y];                }            }        }    }    For(i,n) {        int j=i;        Rep(y,2) {            if (j>=n-i) {                ans+=f[i][j][y];            }        }    }    if (!check()) ans--;    For(i,n-1) {        int len=(i-1)/2;        ll p=k-1;        For(i,len) p*=k;        ans+=p;     }    return ans;}bool check() {    Fork(i,(n+1)/2+1,n) {        if (a[i]>a[n-i+1]) return 1;        else if (a[i]<a[n-i+1]) return 0;    }    return 1;}int make_k(ll n,ll k){    int len=0;    while(n) a[++len]=n%k,n/=k;    For(i,len/2) swap(a[i],a[len-i+1]);    if (!len) a[len=1]=0;    return len;}int main(){//  freopen("G.in","r",stdin);//  freopen("G.out","w",stdout);    int T=io.xuint();    For(kcase,T) {        ll ANS=0,L=io.xint()-1,R=io.xint(),l=io.xint(),r=io.xint();        for(k=l;k<=r;k++) {            n=make_k(R,k);            ll p=calc();            n=make_k(L,k);            ll q=calc();            ANS+=R-L+(k-1)*(p-q);        }        io.wstring("Case #");        io.wint(kcase);        io.wstring(": ");        io.wint(ANS);        io.wchar('\n');    }    return 0;}