**PROBLEM LINK:** Digit Game

**AUTHOR:** sohit_1212

**DIFFICULTY:** Medium

**PREREQUISITES:** Dynamic Programming , Recursion

This is a standard DP question. We maintain a DP state A[N][M] ; where N=10000 (the upper limit for the 4 digit number) and M=101(The number of chances)

We make 4 recursive call at each turn by modifying the digit at all the four places, when *i* is even we take the minimum value and store it in A[n][i] and when *i* is odd, we take the maximum.

```
#include <iostream>
#include <cstring>
#define N 10000
#define M 110
using namespace std;
int A[N][M];
int foo(int n, int i, int m) {
if(i>m) return n;
if(A[n][i] != -1) return A[n][i];
int a=n/10,b=n/100,c=n/1000,d=0;
a = a*10+((n%10+1)%10);
b = b*100+((n%100+10)%100);
c = c*1000+((n%1000+100)%1000);
d = (n+1000)%10000;
if(i%2 == 1) {
A[n][i] = max(max(foo(a,i+1,m),foo(b,i+1,m)),
max(foo(c,i+1,m),foo(d,i+1,m)));
//return A[n][i];
}
else {
A[n][i] = min(min(foo(a,i+1,m),foo(b,i+1,m)),
min(foo(c,i+1,m),foo(d,i+1,m)));
}
return A[n][i];
}
int main() {
int t;
scanf("%d",&t);
while(t--) {
int n,m;
scanf("%d%d",&n,&m);
memset(A,-1,sizeof(A));
int val = foo(n,1,m);
if(val > n) printf("Berlin\n");
else printf("Professor\n");
}
return 0;
}
```