题解 叮叮车
就是 Catalan 数，求 \([l, r]\) 中 \(C_i\) 的 \(p\) 的幂次最大值
那么库默尔定理，\(\binom{n+m}{n}\) 中 \(p\) 的幂次就是 \(n+m\) 在 \(p\) 进制下的进位次数
那么要最大化这个东西，可以放到 7 进制下贪心
找到 \(l, r\) 的最高不同位，找到接下来的一段连续进位串
选最高位的 \(>3\) 的，如果没有选最高的 3
将这位 -1，后面的全填 6 即可
点击查看代码
#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define N 1000010
#define pb push_back
#define ll long long
#define int long long
const ll mod=1e9+7;
int tl[N], tr[N], tem[N], tot, now;
struct Int{
int base;
vector<int> a;
Int(){base=678223072849;}
Int(int t){base=678223072849; do {a.pb(t%base); t/=base;} while (t);}
int len() {return a.size();}
inline int& operator [] (int t) {return a[t];}
void adjust() {while (a.size()>1&&!a.back()) a.pop_back();}
void print() {for (int i=a.size()-1; ~i; --i) printf("%lld", a[i]); printf("\n");}
void scan() {
a.clear();
vector<int> tem[2];
int now=0; char c=getchar();
while (!isdigit(c)) c=getchar();
int lst=0, cnt=0;
while (isdigit(c)) {tem[now].pb(c-'0'); c=getchar();}
for (; ; now^=1) {
// cout<<"tem: "; for (auto it:tem[now]) cout<<it<<' '; cout<<endl;
for (auto it:tem[now]) if (it) goto jump; break; jump:
tem[now^1].clear();
ll rest=0; bool any=0;
for (auto it:tem[now]) {
rest=rest*10+it;
if (rest/base||any) tem[now^1].pb(rest/base);
if (rest/base) any=1;
rest%=base;
}
a.pb(rest);
}
adjust();
if (!a.size()) a.pb(0);
}
inline Int operator + (Int b) {
Int ans;
int lim=max(len(), b.len())+2;
ans.a.resize(lim);
for (int i=0; i<lim-1; ++i) {
if (i<len()) ans[i]+=a[i];
if (i<b.len()) ans[i]+=b[i];
ans[i+1]+=ans[i]/base;
ans[i]%=base;
}
ans.adjust();
return ans;
}
inline Int operator * (Int b) {
Int ans; ans.a.resize(len()+b.len()+1);
for (int i=0; i<len(); ++i)
for (int j=0; j<b.len(); ++j) {
ans[i+j]=ans[i+j]+a[i]*b[j];
ans[i+j+1]+=ans[i+j]/base;
ans[i+j]%=base;
}
ans.adjust();
return ans;
}
inline Int operator - (Int b) {
Int ans=*this;
for (int i=0; i<b.len(); ++i) ans[i]-=b[i];
for (int i=0; i<len(); ++i)
if (ans[i]<0) --ans[i+1], ans[i]+=base;
ans.adjust();
return ans;
}
inline Int operator / (int b) {
Int ans; ans.a.resize(len());
ll rest=0;
for (int i=len()-1; ~i; --i) {
rest=rest*base+a[i];
ans[i]=rest/b; rest%=b;
}
ans.adjust();
return ans;
}
inline ll toint() {
ll ans=0;
for (int i=a.size()-1; ~i; --i) ans=(ans*base+a[i])%mod;
return ans;
}
inline bool operator <= (Int b) {
if (len()!=b.len()) return len()<b.len();
for (int i=len()-1; ~i; --i)
if (a[i]!=b[i]) return a[i]<b[i];
return 1;
}
inline bool operator < (Int b) {
if (len()!=b.len()) return len()<b.len();
for (int i=len()-1; ~i; --i)
if (a[i]!=b[i]) return a[i]<b[i];
return 0;
}
bool notzero() {return a.size()>1||a[0]!=0;}
}l, r, ans;
inline Int f(Int n) {
Int ans(0); while (n.notzero()) n=n/7, ans=ans+n;
return ans;
}
signed main()
{
freopen("dingdingcar.in", "r", stdin);
freopen("dingdingcar.out", "w", stdout);
l.scan(); r.scan();
// l.print(); r.print();
l.a.resize(r.len());
ans.a.resize(r.len());
// for (int i=r.len()-1; ~i; --i) {
// if (l[i]==r[i]||!i) ans[i]=r[i];
// else {
// ans[i]=r[i]-1;
// for (int j=i-1; ~j; --j) ans[j]=6;
// break;
// }
// }
// ans.print();
// ll cnt=0;
// ans.a.resize(ans.len()+1);
// for (int i=0,lim=ans.len(); i+1<lim; ++i)
// if (ans[i]>3) ++cnt, ++ans[i+1];
// cout<<cnt<<endl;
for (int i=0,lim=l.len(); i<lim; ++i) {
int t=l[i];
for (int j=1; j<=14; ++j)
tl[++tot]=t%7, t/=7;
}
for (int i=0,lim=r.len(); i<lim; ++i) {
int t=r[i];
for (int j=1; j<=14; ++j)
tr[++now]=t%7, t/=7;
}
// cout<<"tl: "; for (int i=1; i<=tot; ++i) cout<<tl[i]<<' '; cout<<endl;
// cout<<"tr: "; for (int i=1; i<=tot; ++i) cout<<tr[i]<<' '; cout<<endl;
for (int i=tot; i; --i) {
if (tl[i]==tr[i] || i==1) tem[i]=tr[i];
else {
// cout<<"i: "<<i<<endl;
if (tr[i]!=3) {
tem[i]=tr[i]-1;
for (int j=i-1; j; --j) tem[j]=6;
}
else {
int pos1=i, pos2=i-1;
while (pos2 && tr[pos2]>=3) {
if (tr[pos2]>3) pos1=pos2;
--pos2;
}
int maxi=i;
for (int j=pos1; j<=i; ++j) if (tr[j]>3) maxi=j;
for (int j=i; j>=pos1; --j) tem[j]=tr[j];
tem[maxi]=tr[maxi]-1;
for (int j=maxi-1; j; --j) tem[j]=6;
// cout<<"maxi: "<<maxi<<endl;
}
break;
}
}
for (int i=r.len()-1; ~i; --i) {
int t=0;
for (int j=1; j<=14; ++j)
t=t*7+tem[tot--];
ans[i]=t;
}
// cout<<"tot: "<<tot<<endl;
// cout<<max((f(r*Int(2))-Int(2)*f(r)).toint(), (f(ans*Int(2))-Int(2)*f(ans)).toint())<<endl;
cout<<(f(ans*Int(2))-Int(2)*f(ans)).toint()<<endl;
return 0;
}
