# 2021 icpc Shenyang J-Luggage Lock

Immediately after the game ended, there was a replay with the team-mates and they were beaten up.
_J is to give you a lock with 4 digits, each of which is 0-9, and then give you the current lock status and password status. You can move up or down several consecutive positions at the same time, or you can move in a single position to ask you how many last steps you need.
The common solution should be bfs, making a table and the smallest step needed to move from 0000 to any location, which I thought at first, but I don't know why my brain chose dp at the end.
Solution:
_It is easy to know that if a location is either dialed up or down, then each one is actually two cases, and the four is 222*2=16 cases.
_If an ans=need[1]+need[2]+need[3]+need[3] is dialed individually at all locations, need[i] is the number of steps required to move the first to the final from the initial to the final.
_If two consecutive digits (i,j) are simultaneously pushed up (or down), it is easy to see that the minimum number of steps required is max(need[i],need[j]).
_If three consecutive digits (i,j,k) are moved at the same time, then there are three cases. The first two are need[i] or need[k], which obviously degenerates into two consecutive digits (i,j). The third is need[j], which is the smallest. Then, it is clear that j is the first to reach the final state, then I and K will be dialed out the remaining steps separately. Then ans=need[j]+(need[i]-need[j])+(need[k]-need[j]) means ans=need[i]+need[k]-need[j].
_If four consecutive bits (i,j,k,t) are moved at the same time, then there are four cases. The first two are the minimum of need[i] or need[t], which obviously degenerates to the situation of three consecutive bits (i,j,k). The other two are the minimum of need[j] or need[k]. It is easy to get ans=need[i]+max(need[k],need[t])-need[j] and ans=need[t]+max(need[i], need[j]-need], need[k], need[k] It is the combination of three consecutive dials and two consecutive dials.
_In addition to the above, consider the case that when a need[x]==0, it can be moved along with the others at this time, and then finally dialed back to the original position, that is, there must be ans<=10 at this time.

```#include <iostream>
#include<bits/stdc++.h>
#define scd(x) scanf("%d",&x)
#define scdd(x,y) scanf("%d%d",&x,&y)
#define scddd(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define mst(x,y) memset(x,y,sizeof(x));
using namespace std;
typedef long long ll;
const int maxn=1e2+5;
int a[10],b[10];
int sum(int p[5],int len)
{
int mn=100,mx=0;
if(len==4)
{
for(int i=1;i<=4;i++)mn=min(mn,p[i]),mx=max(mx,p[i]);
if(p[2]==mn)return p[1]+max(p[3],p[4])-p[2];
if(p[3]==mn)return max(p[1],p[2])+p[4]-p[3];
if(p[1]==mn)return sum(p+1,3);
else return sum(p,3);
}
else
{
for(int i=1;i<=3;i++)mn=min(mn,p[i]),mx=max(mx,p[i]);
if(mn==p[2])return p[1]+p[3]-p[2];
return mx;
}
}
int g(int k,int flag)
{
if(flag==0)
{
return a[k]<=b[k]?b[k]-a[k]:b[k]+10-a[k];
}
return a[k]>=b[k]?a[k]-b[k]:a[k]+10-b[k];
}
int main()
{
#ifdef local
freopen("1.txt","r",stdin);
#endif // local
int T;
scd(T);
while(T--)
{
int ans=100;
char s[maxn];
scanf("%s",s+1);
for(int i=1;i<=4;i++)a[i]=s[i]-'0';
scanf("%s",s+1);
for(int i=1;i<=4;i++)b[i]=s[i]-'0';
for(int i=0;i<=(1<<4)-1;i++)
{
int t=i;
int p[5];
int x[5];
for(int j=1;j<=4;j++)x[j]=(t>>(j-1))&1;
for(int j=1;j<=4;j++)p[j]=g(j,x[j]);
for(int j=1;j<=4;j++)
if(p[j]==0)
ans=min(ans,10);
if(x[2]==x[3])//2==3
{
if(x[1]==x[2])//1==2==3
{
if(x[4]==x[2])//1==2==3==4
ans=min(ans,sum(p,4));
else//1==2==3!=4
ans=min(ans,sum(p,3)+p[4]);
}
else if(x[4]==x[2])//1!=2==3==4
ans=min(ans,sum(p+1,3)+p[1]);
else//0!=1==2!=3
ans=min(p[1]+max(p[2],p[3])+p[4],ans);
}
else if(x[1]==x[2]&&x[3]==x[4])ans=min(ans,max(p[1],p[2])+max(p[3],p[4]));
else if(x[1]==x[2]&&x[3]!=x[4])ans=min(ans,max(p[1],p[2])+p[3]+p[4]);
else if(x[1]!=x[2]&&x[3]==x[4])ans=min(ans,p[1]+p[2]+max(p[3],p[4]));
else ans=min(ans,p[1]+p[2]+p[3]+p[4]);
}
printf("%d\n",ans);
}
return 0;
}

```

We can only say that bfs is much simpler. I don't know why we have to consider so many situations to make DPS torture us.

Posted on Sun, 21 Nov 2021 15:04:36 -0500 by burnside