hdu 5898 odd-even number(数位dp）

Posted 2020-08-17 Gealo

Problem Description

For a number,if the length of continuous odd digits is even and the length of continuous even digits is odd,we call it odd-even number.Now we want to know the amount of odd-even number between L,R(1<=L<=R<= 9*10^18). 

 

 

Input

First line a t,then t cases.every line contains two integers L and R. 

 

 

Output

Print the output for each case on one line in the format as shown below.

 

题意：一个数中所有连续的奇数长度都为偶数，所有连续偶数的长度都为奇数。我们要找一个区间内一共有多少个这样的数。

区间范围（1～9*10^18)所以显然是数位dp搞。设dp[len][count][temp]，temp=1表示偶数，temp=2表示奇数，temp=0表示取首位0时，

count表示到len位置有几个奇数或偶数个。显然简单的搜索，标准数位dp

 

 

#include <iostream>
#include <cstring>
using namespace std;
typedef long long ll;
ll dp[22][22][3];
int dig[20];
ll dfs(int len , int count , int temp , int flag , int first) {
    if(len == 0) {
        if(temp == 1) {
            if(count % 2 != 0) {
                return 1;
            }
            else {
                return 0;
            }
        }
        if(temp == 2) {
            if(count % 2 == 0) {
                return 1;
            }
            else {
                return 0;
            }
        }
        return 0;
    }
    if(!flag && !first && dp[len][count][temp] != -1) {
        return dp[len][count][temp];
    }
    int n = flag ? dig[len] : 9;
    ll sum = 0;
    for(int i = 0 ; i <= n ; i++) {
        if(first) {
            if(i == 0) {
                sum += dfs(len - 1 , 0 , 0 , flag && i == n , first && i == 0);
            }
            else {
                if(i % 2 == 0) {
                    sum += dfs(len - 1 , count + 1 , 1 , flag && i == n , first && i == 0);
                }
                else {
                    sum += dfs(len - 1 , count + 1 , 2 , flag && i == n , first && i == 0);
                }
            }
        }
        else {
            if(i % 2 == 0) {
                if(temp == 1) {
                    sum += dfs(len - 1 , count + 1 , 1 , flag && i == n , first && i == 0);
                }
                if(temp == 2) {
                    if(count % 2 == 0) {
                        sum += dfs(len - 1 , 1 , 1 , flag && i == n , first && i == 0);
                    }
                }
            }
            else {
                if(temp == 1) {
                    if(count % 2 != 0) {
                        sum += dfs(len - 1 , 1 , 2 , flag && i == n , first && i == 0);
                    }
                }
                if(temp == 2) {
                    sum += dfs(len - 1 , count + 1 , 2 , flag && i == n , first && i == 0);
                }
            }
        }
    }
    if(!flag && !first) {
        dp[len][count][temp] = sum;
    }
    return sum;
}
ll Get(ll x) {
    int len = 0;
    memset(dp , -1 , sizeof(dp));
    memset(dig , 0 , sizeof(dig));
    if(x == 0)
        len = 1;
    while(x) {
        dig[++len] = x % 10;
        x /= 10;
    }
    return dfs(len , 0 , 0 , 1 , 1);
}
int main()
{
    int t;
    cin >> t;
    int ans = 0;
    while(t--) {
        ans++;
        ll l , r , gg;
        cin >> l >> r;
        cout << "Case #" << ans << ": " << Get(r) - Get(l - 1) << endl;
    }
    return 0;
}