lightoj 1205 数位dp

Posted 2020-10-10 LuZhiyuan

1205 - Palindromic Numbers

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Time Limit: 2 second(s)

Memory Limit: 32 MB

A palindromic number or numeral palindrome is a ‘symmetrical‘ number like 16461 that remains the same when its digits are reversed. In this problem you will be given two integers i j, you have to find the number of palindromic numbers between i and j (inclusive).

Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing two integers i j (0 ≤ i, j ≤ 10¹⁷).

Output

For each case, print the case number and the total number of palindromic numbers between i and j (inclusive).

Sample Input	Output for Sample Input
4 1 10 100 1 1 1000 1 10000	Case 1: 9 Case 2: 18 Case 3: 108 Case 4: 198

 

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PROBLEM SETTER: JANE ALAM JAN

题意：

求区间内回文串数的个数

//开个数组存一下回文串，还要处理前导零。sta表示到目前为止是否合法
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long ll;
int t,bit[20],num[20];
ll f[20][20][2],P,Q;
ll dfs(int pos,int s,int sta,bool limit)
{
    if(pos==0) return sta;
    if(!limit&&f[pos][s][sta]!=-1) return f[pos][s][sta];
    int max_b=(limit?bit[pos]:9);
    ll ans=0;
    for(int i=0;i<=max_b;i++){
        num[pos]=i;
        if(pos==s&&i==0)
            ans+=dfs(pos-1,s-1,sta,limit&&(i==max_b));
        else if(sta&&pos<=s/2)
            ans+=dfs(pos-1,s,num[s-pos+1]==i,limit&&(i==max_b));
        else ans+=dfs(pos-1,s,sta,limit&&(i==max_b));
    }
    if(!limit) f[pos][s][sta]=ans;
    return ans;
}
ll solve(ll x)
{
    if(x<0) return 0;
    int pos=0;
    while(x){
        bit[++pos]=x%10;
        x/=10;
    }
    return dfs(pos,pos,1,1);
}
int main()
{
    memset(f,-1,sizeof(f));
    scanf("%d",&t);
    for(int cas=1;cas<=t;cas++){
        scanf("%lld%lld",&P,&Q);
        if(P>Q) swap(P,Q);
        printf("Case %d: %lld\n",cas,solve(Q)-solve(P-1));
    }
    return 0;
}