C++ (Inelus Gabriel)

    1 #include <cstdio>
    2 int N, M, A[1005][1005];
    3 int main()
    4 {
    5     scanf("%d%d", &N, &M);
    6     for(int i = 1; i <= N; ++i)
    7     {
    8         A[i][0] = A[i][M+1] = -1;
    9         for(int j = 1; j <= M; ++j)
   10             scanf("%d",&A[i][j]);
   11     }
   12 
   13     for(int j = 1; j <= M; ++j)
   14         A[0][j] = A[N+1][j] = -1;
   15 
   16     int i = 1, j = 1, ok = 1;
   17     printf("%d ",A[i][j]); A[i][j] = -1;
   18     while(ok) {
   19         ok = 0;
   20         while(A[i][j+1] != -1) { ok = 1; ++j; printf("%d ", A[i][j]); A[i][j] = -1; }
   21         while(A[i+1][j] != -1) { ok = 1; ++i; printf("%d ", A[i][j]); A[i][j] = -1; }
   22         while(A[i][j-1] != -1) { ok = 1; --j; printf("%d ", A[i][j]); A[i][j] = -1; }
   23         while(A[i-1][j] != -1) { ok = 1; --i; printf("%d ", A[i][j]); A[i][j] = -1; }
   24     }
   25     return 0;
   26 }

Python 2.7 (Sergiu Puscas)

    1 n, m = map(int, raw_input().split())
    2 a = [list(raw_input().split()) for i in range(n)]
    3 
    4 U, D, L, R = 0, n-1, 0, m-1
    5 direction = 0
    6 i, j = 0, 0
    7 
    8 for step in range(n*m):
    9     print a[i][j],
   10 
   11     if direction == 0:          # right
   12         if j+1 > R:             # change to down
   13             direction = 1
   14             R -= 1
   15             i += 1
   16         else:
   17             j += 1
   18 
   19     elif direction == 1:        # down
   20         if i+1 > D:             # change to left
   21             direction = 2
   22             D -= 1
   23             j -= 1
   24         else:
   25             i += 1
   26 
   27     elif direction == 2:        # left
   28         if j - 1 < L:           # change to up
   29             direction = 3
   30             L += 1
   31             i -= 1
   32         else:
   33             j -= 1
   34 
   35     elif direction == 3:        # up
   36         if i - 1 <= U:          # change to right
   37             direction = 0
   38             U += 1
   39             j += 1
   40         else:
   41             i -= 1