ps4n2 - 2 The problem space is basically just a mesh of...

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2. The problem space is basically just a mesh of vertices that is only connected to 4 adjacent neighbors, and we’re trying to find a local minimum (a vertex n whose value is lower than all 4 of its neighbors) in this mesh. Algorithm : We begin by considering two cases: 1. We look at the 4*n vertices on the border of the chessboard and probe the neighbors of each vertex to find if any are local minimums. If there are, return immediately. 2. We now look at the subproblem where we are guaranteed that the border does not contain an optimum. We can try to divide the problem into 4 quadrants and check one, but we have to first ensure that the borders of those 4 quadrants do not contain an optimum. Since the main border is presumably checked by the precondition of this subproblem in the previous instance, we now only need to check the middle row and column (cross) to check the rest of the border of the quadrants. Since there are 2*n vertices to consider, this is still linear.
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ps4n2 - 2 The problem space is basically just a mesh of...

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