Codeforces1073E Segment Sum 【数位DP】

题目分析：

裸的数位DP，注意细节。

#include<bits/stdc++.h>
using namespace std;

const int mod = 998244353;
int k;

int dp[25][1024],sz[25][1024],cnt[25][1024];
int pw10[25],hp[25],num;

int dfs(int now,int lst){
    if(now == 0) return 0;
    int ans = 0;
    for(int i=0;i<hp[now];i++){
    for(int j=0;j<(1<<10);j++){
        int pp = (lst==0&&i==0?0:(1<<i));
        int z = __builtin_popcount(j|pp|lst);
        if(z > k) continue;
        ans += 1ll*sz[now-1][j]*pw10[now-1]%mod*i%mod; ans %= mod;
        ans += dp[now-1][j]; ans %= mod;
    }
    }
    if(now == num){
    for(int i=1;i<num-1;i++){
        for(int j=0;j<(1<<10);j++){
        int z = __builtin_popcount(j);
        if(z > k) continue;
        z = __builtin_popcount(j|1);
        if(z <= k) continue;
        ans += dp[i][j]; ans %= mod;
        }
    }
    }
    for(int i=0;i<(1<<10);i++){
    int z = __builtin_popcount(i|(1<<hp[now])|lst);
    if(z > k) continue;
    ans += 1ll*cnt[now-1][i]*pw10[now-1]%mod*hp[now]%mod;
    ans %= mod;
    }
    ans += dfs(now-1,lst|(1<<hp[now]));
    ans %= mod;
    return ans;
}

int solve(long long now){
    num = 0;
    memset(cnt,0,sizeof(cnt));cnt[0][0] = 1;
    while(now){hp[++num] = now%10;now /= 10;}
    for(int i=1;i<=num;i++){
    for(int j=0;j<hp[i];j++){
        for(int k=0;k<(1<<10);k++){
        cnt[i][k|(1<<j)] += sz[i-1][k];
        cnt[i][k|(1<<j)] %= mod;
        }
    }
    for(int k=0;k<(1<<10);k++){
        cnt[i][k|(1<<hp[i])] += cnt[i-1][k];
        cnt[i][k|(1<<hp[i])] %= mod;
    }
    }
    return dfs(num,0);
}

int main(){
    long long l,r;
    cin >>l >> r >> k;
    sz[0][0] = 1;pw10[0] = 1;
    for(int i=1;i<=20;i++) pw10[i] = 1ll*pw10[i-1]*10%mod;
    for(int i=1;i<=20;i++){
    for(int f = 1;f<=9;f++){
        for(int j=0;j<(1<<10);j++){
        sz[i][j|(1<<f)] += sz[i-1][j]; sz[i][j|(1<<f)]%=mod;
        dp[i][j|(1<<f)] += dp[i-1][j]; dp[i][j|(1<<f)] %= mod;
        dp[i][j|(1<<f)] += 1ll*sz[i-1][j]*pw10[i-1]%mod*f%mod;
        dp[i][j|(1<<f)] %= mod;
        for(int k=0;k<i-1;k++){
            sz[i][j|(1<<f)|1] += sz[k][j]; sz[i][j|(1<<f)|1]%=mod;
            dp[i][j|(1<<f)|1] += dp[k][j]; dp[i][j|(1<<f)|1]%=mod;
            dp[i][j|(1<<f)|1] += 1ll*sz[k][j]*pw10[i-1]*f%mod;
            dp[i][j|(1<<f)|1] %= mod;
        }
        }
    }
    }
    for(int i=1;i<=20;i++){
    for(int j=0;j<(1<<10);j++){
        sz[i][j|1] += sz[i-1][j];
        dp[i][j|1] += dp[i-1][j];
        sz[i][j|1] %= mod; dp[i][j|1] %= mod;
    }
    }
    long long ans = solve(r)-solve(l-1);
    ans+=mod; ans %= mod;
    cout<<ans<<endl;
    return 0;
}