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I think we can improve the run time by not traversing row wise, but on the borders of the grid. Keep min-i, max-i, min-j, max -j as the four variables (as in 1st comment to this problem) and also maintain flags for them. as soon as all the four variables are modified we are done. Once the exterior most border is traversed move on to one level below and so on. The worst case for this will still be O(n^2).
- prawal July 05, 2012