V

V - How Many Zeroes?

 

题意：

求任意区间的数中0的出现次数

思路：

数位dp，注意判断是否是前导0 注意用长整型

代码：

#include <cstdio>#include <cstring>#include <cmath>#include <iostream>#include <algorithm>using namespace std;typedef long long ll;int bit[20];ll dp[20][20];ll dfs(int pos,int sum,int zero,int limit){//zero前导0，sum是0的个数     if(pos<0) return zero?1:sum;    if(!zero&&!limit&& dp[pos][sum] != -1) return dp[pos][sum];    int up=limit?bit[pos] : 9;        ll ans = 0;    for(int i=0; i<=up; i++){            if(zero&&!i) ans+=dfs(pos-1,0,1,limit&&up==i);//判断前导零                else if(!i) ans+=dfs(pos-1,sum+1,0,limit&&i ==up);//第二次访问加1                else  ans+=dfs(pos-1,sum,0,limit&&i==up);     }    if(!zero&&!limit) dp[pos][sum] = ans;    return ans;}ll cal(ll x){if(x<0)return 0;     if(x== 0) return 1;    memset(dp,-1,sizeof(dp));    int pos=0;    while(x){        bit[pos++] = x%10;        x/=10;    }    return dfs(pos-1,0,1,1);}int main(){    int T,ans=1;    ll n,m;    scanf("%d",&T);    while(T--){        scanf("%lld %lld",&n,&m);        printf("Case %d: %lld\n",ans++,cal(m) - cal(n-1));    }    return 0;}