The idea is just to generate the matrix in the spiral order. First the up-most row (u), then the right-most column (r), then the down-most row (d), and finally the left-most column (l). After generating a row or a column, update the corresponding variable to continue the generation.
The code is as follows.
1 class Solution { 2 public: 3 vector<vector<int> > generateMatrix(int n) { 4 vector<vector<int> > mat(n, vector<int>(n)); 5 int u = 0, d = n - 1, l = 0, r = n - 1, num = 1; 6 while(true) { 7 // up 8 for(int col = l; col <= r; col++) mat[u][col] = num++; 9 if(++u > d) break; 10 // right 11 for(int row = u; row <= d; row++) mat[row][r] = num++; 12 if(--r < l) break; 13 // down 14 for(int col = r; col >= l; col--) mat[d][col] = num++; 15 if(--d < u) break; 16 // left 17 for(int row = d; row >= u; row--) mat[row][l] = num++; 18 if(++l > r) break; 19 } 20 return mat; 21 } 22 };