HDOJ 3709 Balanced Number (数位DP)

题意：求[x , y]中有多少个平衡数。

平衡数：选定一位作为支点，若左右的力矩平衡则该数是平衡数，否则不是。For example, 4139 is a balanced number with pivot fixed at 3. The torqueses are 4*2 + 1*1 = 9 and 9*1 = 9

View Code

#include <stdio.h>

#include <string.h>

#define N 19

#define M 1378

typedef __int64 LL;

LL dp[N][N][M];

int digit[N];

LL dfs(int pos,int o,int sum,int f)

{

    if(sum<0)   return 0;

    if(pos==-1) return sum==0;

    if(!f&&dp[pos][o][sum]!=-1) return dp[pos][o][sum];



    LL ret=0;

    int max=f?digit[pos]:9;

    for(int i=0;i<=max;i++)

    {

        ret+=dfs(pos-1,o,sum+(pos-o)*i,f&&i==max);

    }

    if(!f)  dp[pos][o][sum]=ret;

    return ret;

}

LL cal(LL x)

{

    int pos=0;

    while(x)

    {

        digit[pos++]=x%10;

        x/=10;

    }

    LL ret=0;

    for(int o=0;o<pos;o++)

    {

        ret+=dfs(pos-1,o,0,1);

    }

    return ret-pos+1;

}

int main()

{

    int t;

    memset(dp,-1,sizeof(dp));

    scanf("%d",&t);

    while(t--)

    {

        LL x,y;

        scanf("%I64d%I64d",&x,&y);

        printf("%I64d\n",cal(y)-cal(x-1));

    }

    return 0;

}