Need solution to problem urgently

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Source: https://www.geeksforgeeks.org/media-net-interview-experience-for-sde-on-campus/

There is some line missing in the problem statement so I am writing here. Also the code for solution is provided but I am not able to understand

We are given strings containing 1 and 2.

When is string a good ? If we are at index i then we can either move a[i] units left or a[i] units right. We have to start at first index and reach last index such that every index is visited once. If we are able to do the it is a good string

Give 2 strings a, b which are initially good. You can select an array of indexes and for each index i, swap(a[i], b[i]). How many ways are there of selecting an array of indexes such that both strings remain good

Main observation

Code of solution(if you are lazy to open link)

bool validate(int num, char value, int& newNum) {
    if(value == '1') {
    newNum = 0;
      return (num != 1);
    }
    if(value == '2'){
    if(num == 1){
      newNum = 2;
        return true;
    }
      else if(num == 0){
      newNum = 1;
        return true;
      }
      else{
      return false;
      }   
    }
}
   
  string A,B; 
  int n = A.size();
  int dp[n][3][3];//initialised to 0
  int solve(int s, int j, int k){
              
      char a = A[s];
      char b = B[s];
      
      int nextj,nextk;
      
      if(validate(j,a,nextj) && validate(k,b,nextk)){
                 dp[s][nextj][nextk] += dp[s-1][j][k];
      }
      
            if(validate(j,b,nextj) && validate(k,a,nextk)){
            dp[s][nextj][nextk] += dp[s-1][j][k];
        }
      
  }
  
  int main(){
      //inputs
    
    for(int i=0;i<n;i++){
      for(int j=0;j<=2;j++){
        for(int k=0;k<=2;k++){
          solve(i,j,k);
        }
      }
    }
      
      cout<<dp[n-2][0][0]*2;
  }

Sample test case

Can someone explain the solution please?

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