P2602 [ZJOI2010]數字計數

P2602 [ZJOI2010]數字計數

給定兩個正整數a和b，求在[a,b]中的全部整數中，每一個數碼(digit)各出現了多少次。

Solution

一眼識數位dp
以 \(dp[i][j]\) 對某個指定的數碼， 填了 \(i\) 位， 其中有 \(j\) 位填了特定數碼的 總數碼數
而後分一下前導零， 最高位， 數位dp便可
看代碼

Code

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>
#include<climits>
#define LL long long
#define REP(i, x, y) for(LL i = (x);i <= (y);i++)
using namespace std;
LL RD(){
    LL out = 0,flag = 1;char c = getchar();
    while(c < '0' || c >'9'){if(c == '-')flag = -1;c = getchar();}
    while(c >= '0' && c <= '9'){out = out * 10 + c - '0';c = getchar();}
    return flag * out;
    }
const LL maxn = 19;
LL num[maxn];
LL mem[maxn];
LL dp[maxn][maxn];//填完i位，填了j個給定數碼的數碼總數
LL a, b;
LL DP(LL Index, LL sum, LL state, bool zero, bool limit){
    if(Index == 0)return sum;//填完一組新的，總數累加sum
    if(!zero && !limit && dp[Index][sum] != -1)return dp[Index][sum];
    LL ans = 0, up = limit ? num[Index] : 9, add = 0;
    REP(i, 0, up){
        if(state != 0 || (state == 0 && !zero))add = (i == state);
        ans += DP(Index - 1, sum + add, state, zero && i == 0, limit && i == num[Index]);
        }
    if(!zero && !limit)dp[Index][sum] = ans;
    return ans;
    }
LL get_num(LL x, LL state){
    LL len = 0;
    while(x){
        num[++len] = x % 10;
        x /= 10;
        }
    return DP(len, 0, state, 1, 1);
    }
void init(){
    a = RD(), b = RD();
    memset(dp, -1, sizeof(dp));
    }
void solve(){
    REP(i, 0, 9){
        printf("%lld ", get_num(b, i) - get_num(a - 1, i));
        }
    puts("");
    }
int main(){
    init();
    solve();
    return 0;
    }