HDU 3709 Balanced Number (数位DP)

Balanced Number

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 6038    Accepted Submission(s): 2887

Problem Description

A balanced number is a non-negative integer that can be balanced if a pivot is placed at some digit. More specifically, imagine each digit as a box with weight indicated by the digit. When a pivot is placed at some digit of the number, the distance from a digit to the pivot is the offset between it and the pivot. Then the torques of left part and right part can be calculated. It is balanced if they are the same. A balanced number must be balanced with the pivot at some of its digits. For example, 4139 is a balanced number with pivot fixed at 3. The torqueses are 4*2 + 1*1 = 9 and 9*1 = 9, for left part and right part, respectively. It's your job
to calculate the number of balanced numbers in a given range [x, y].

 

Input

The input contains multiple test cases. The first line is the total number of cases T (0 < T ≤ 30). For each case, there are two integers separated by a space in a line, x and y. (0 ≤ x ≤ y ≤ 10¹⁸).

 

Output

For each case, print the number of balanced numbers in the range [x, y] in a line.

 

Sample Input

2 0 9 7604 24324

 

Sample Output

10 897

 

Author

GAO, Yuan

 

Source

2010 Asia Chengdu Regional Contest

 

Recommend

zhengfeng

枚举支点

dp[i][j][k]表示i+1~len位数字已确定，搜索第i位数字，支点为j，力矩为k的可能性

#include 
#include 
#include 
#include 
#define maxn 2520
typedef long long ll;
using namespace std;
ll x,y,dp[20][20][3010];
int digit[20];
ll dfs(int p,int cent,int bal,int limit)
{
	ll ans=0;
	int num,i;
	if(p==0)
		return bal==0;
	if(bal<0)
		return 0;
	if(!limit&&dp[p][cent][bal]!=-1)
		return dp[p][cent][bal];
	num=limit?digit[p]:9;
	for(i=0;i<=num;i++)
	{
		ans+=dfs(p-1,cent,bal+i*(p-cent),limit&&i==num);;
	}
	if(!limit)
		dp[p][cent][bal]=ans;
	return ans;
}
ll work(ll n)
{
	int len=0;
	while(n)
	{
		digit[++len]=n%10;
		n/=10;
	}
	int i;
	long long ans=0;
	for(i=1;i<=len;i++)
	{
		ans+=dfs(len,i,0,1);
	}
	return ans-len+1;
}
int main ()
{
	int t;
	scanf("%d",&t);
	memset(dp,-1,sizeof(dp));
	while(t--)
	{
		scanf("%lld %lld",&x,&y);
		printf("%lld\n",work(y)-work(x-1));
	}
	return 0;
}