交错和(数位dp)

交错和

数位DP

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int mod = 1e9 + 7;

struct Node{
    LL sum, cnt;
}dp[21][10][2][410];
int bit[21];
LL base[21];
Node dfs(int pos, int cur, int lead, int lim, int sum){
    Node temp;
    temp.sum = 0; temp.cnt = 0;
    if(pos < 0) return temp;
    if(!lim && dp[pos][cur][lead][sum + 200].cnt != -1) return dp[pos][cur][lead][sum + 200];
    if(pos == 0){
        if(sum == cur) {
            temp.sum = sum;
            temp.cnt = 1;
        }
        return temp;
    }
    int up = lim ? bit[pos - 1] : 9;
    Node t;
    for(int i = 0; i <= up; i++){
        if(lead) t = dfs(pos - 1, i, i == 0, lim && (i == up), sum);
        else t = dfs(pos - 1, i, 0, lim && (i == up), cur - sum);
        temp.cnt += t.cnt;
        temp.sum = (temp.sum + t.sum + (t.cnt * cur % mod * base[pos]) % mod) % mod;
    }
    if(!lim) dp[pos][cur][lead][sum + 200] = temp;
    return temp;

}
int k;
LL solve(LL x){
    int pos = 0;
    while(x){
        bit[pos++] = x % 10;
        x /= 10;
    }
    Node temp = dfs(pos, 0, 1, 1, k);
    return temp.sum;
}

int main(){
    LL a, b;
    base[0] = 1;
    for(int i = 0; i < 21; i++){
        for(int j = 0; j < 10; j++){
            for(int k = 0; k < 2; k++){
                for(int p = 0; p < 410; p++) {
                    dp[i][j][k][p].sum = 0;
                    dp[i][j][k][p].cnt = -1;
                }
            }
        }
    }
    for(int i = 1; i < 21; i++) base[i] = base[i - 1] * 10 % mod;
    while(scanf("%lld %lld %d", &a, &b, &k) != EOF){
        printf("%lld
", (solve(b) - solve(a - 1) + mod) % mod);
    }
}