We have a rectangular grid of points where one corner is (0,0) and the other corner...
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We have a rectangular grid of points where one corner is (0,0) and the other corner is (W, H), where W, H represent the width and height of the grid, respectively. From each point (x, y), we can move along one of the cardinal directions to (x,y) = {(x+1, y), (x1,y), (x, y + 1), (x, y − 1)}, as long as 0 < x <W and 0 ≤ y ≤ H (i.e, we are not allowed to move out of the grid). Furthermore, we specify a set of k circles C = {(x1,y1,1),..., (xk, yk, rk)} where each circle has center (x, y) and radius ri. The goal is to find a path from (0, 0) to (W, H) while avoiding any point on the surface of or inside the circles in C. If such a path is found, your algorithm should return the path as a list of grid points. If not, your algorithm should return the empty list. Example 1 Consider W = H = 3 and two circles C = {(1, 2, 1), (2, 2, 0.5)}. 3 2 1 0.5 1 0 0 1 2 3 The red lines show a path from (0,0) to (3, 3). Your algorithm may return a list [(0,0), (1,0), (2,0), (3, 0), (3,1), (3,2), (3,3)] (there is another path in this case and any of them may be returned. Example 2 Consider W = H = 3 and two circles C = {(1, 2, 1), (2, 2, 1)}. 3 1 2 1 0 ° 1 2 3 We have a rectangular grid of points where one corner is (0,0) and the other corner is (W, H), where W, H represent the width and height of the grid, respectively. From each point (x, y), we can move along one of the cardinal directions to (x,y) = {(x+1, y), (x1,y), (x, y + 1), (x, y − 1)}, as long as 0 < x <W and 0 ≤ y ≤ H (i.e, we are not allowed to move out of the grid). Furthermore, we specify a set of k circles C = {(x1,y1,1),..., (xk, yk, rk)} where each circle has center (x, y) and radius ri. The goal is to find a path from (0, 0) to (W, H) while avoiding any point on the surface of or inside the circles in C. If such a path is found, your algorithm should return the path as a list of grid points. If not, your algorithm should return the empty list. Example 1 Consider W = H = 3 and two circles C = {(1, 2, 1), (2, 2, 0.5)}. 3 2 1 0.5 1 0 0 1 2 3 The red lines show a path from (0,0) to (3, 3). Your algorithm may return a list [(0,0), (1,0), (2,0), (3, 0), (3,1), (3,2), (3,3)] (there is another path in this case and any of them may be returned. Example 2 Consider W = H = 3 and two circles C = {(1, 2, 1), (2, 2, 1)}. 3 1 2 1 0 ° 1 2 3
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Initialize a grid to represent the rectangular area Mark cells inside or on the boundary of forbidden circles as blocked Use DepthFirst Search DFS to find a path from while avoiding blocked cells Retu... View the full answer
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