Original title
Code implementation (first brush self-solving)
int findPaths(int m, int n, int N, int i, int j){
long dp1[53][53],dp2[53][53],I,J,K;
long temp,count;
unsigned long long sum = 0;
memset(dp2,0,sizeof(dp2));
dp2[i+1][j+1] = 1;
int move[4][2] = {
{
0,1},{
1,0},{
0,-1},{
-1,0}};
for(I=1;I<=N;I++)
{
temp = I%2;
if(temp) memset(dp1,0,sizeof(dp1));
else memset(dp2,0,sizeof(dp2));
for(J=1;J<=m;J++)
{
for(K=1;K<=n;K++)
{
if(temp && dp2[J][K])
{
for(count=0;count<4;count++)
{
dp1[J+move[count][0]][K+move[count][1]] = (dp1[J+move[count][0]][K+move[count][1]] + dp2[J][K]) % 1000000007;
if(!(J+move[count][0]) || J+move[count][0] == m+1 || !(K+move[count][1]) || K+move[count][1] == n+1)
sum += dp2[J][K];
}
}
else if(!temp && dp1[J][K])
{
for(count=0;count<4;count++)
{
dp2[J+move[count][0]][K+move[count][1]] = (dp2[J+move[count][0]][K+move[count][1]] + dp1[J][K]) % 1000000007;
if(!(J+move[count][0]) || J+move[count][0] == m+1 || !(K+move[count][1]) || K+move[count][1] == n+1)
sum += dp1[J][K] ;
}
}
}
}
}
return sum % 1000000007;
}