CodeForces 258B Little Elephant and Elections 数位DP

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <climits>
#include <string>
#include <iostream>
#include <map>
#include <cstdlib>
#include <list>
#include <set>
#include <queue>
#include <stack>

using namespace std;

typedef long long LL;
const int maxn = 20;
const LL MOD = 1e9 + 7;
int M,lim[maxn],len;
bool vis[maxn][maxn];
struct EE {
LL cnt[maxn];
EE() {
memset(cnt,0,sizeof(cnt));
}
};
EE f[maxn][maxn], ans;

void getlim(int num) {
len = 0;
memset(lim,0,sizeof(lim));
while(num) {
lim[len++] = num % 10;
num /= 10;
}
}

EE dfs(int now,int cnt,int bound) {
if(now == 0) {
EE ret;
ret.cnt[cnt] = 1;
return ret;
}
if(!bound && vis[now][cnt]) return f[now][cnt];
int m = bound ? lim[now - 1] : 9;
EE ret;
for(int i = 0;i <= m;i++) {
EE nret = dfs(now - 1,cnt + (i == 4 || i == 7),bound && i == m);
for(int i = 0;i <= len;i++) ret.cnt[i] += nret.cnt[i];
}
if(!bound) {
f[now][cnt] = ret;
vis[now][cnt] = true;
}
return ret;
}

LL A(LL m,LL n) {
LL ret = 1;
for(int i = 1;i <= n;i++) {
ret *= m; m--; ret %= MOD;
}
return ret;
}

LL rest[maxn],rcnt[maxn];
LL dfs1(int now,int sum,int limm) {
if(sum >= limm) return 0;
if(now == 7) {
LL ret = 1;
for(int i = 0;i < limm;i++) if(rcnt[i]) {
ret = (ret * A(ans.cnt[i],rcnt[i])) % MOD;
}
return ret;
}
LL ret = 0;
for(int i = 0;i < limm;i++) if(rest[i]) {
rcnt[i]++; rest[i]--;
ret = (ret + dfs1(now + 1,sum + i,limm)) % MOD;
rcnt[i]--; rest[i]++;
}
return ret;
}

void solve() {
memset(vis,0,sizeof(vis));
getlim(M);
ans = dfs(len,0,1);
ans.cnt[0]--;
LL out = 0;
for(int i = 1;i <= len;i++) if(ans.cnt[i]) {
memcpy(rest,ans.cnt,sizeof(rest));
memset(rcnt,0,sizeof(rcnt));
out = (dfs1(1,0,i) * ans.cnt[i] % MOD + out) % MOD;
}
cout << out << endl;
}

int main() {
cin >> M;
solve();
return 0;
}