Algorithms Test
Pradeep reddy Pinninti - 85025
1- Depth-first search always expands at least as many nodes as A* search with an admissible heuristic
FALSE.
Depth-first search may possibly, sometimes, expand fewer nodes than A* search with an admissible heuristic.
E.g., it is logically possible that sometimes, by good luck, depth-first search may march directly to the goal with no back-tracking.
2- h(n) = 0 is an admissible heuristic for the 8-puzzle TRUE. h(n)=0 NEVER over-estimates the remaining optimal distance to a goal node.
3- A* is of no use in robotics because percepts, states, and actions are continuous
FALSE,
the continuous spaces can be discretized. A* (or variants) are widely used
4- Breadth-first search is complete even if zero step costs are allowed.
TRUE
Because if there exists a goal it occurs at finite depth d and will be found in O(bd) steps.
“Complete” means “will find a goal when one exists” --- and does NOT imply “optimal,” which means “will find a lowest-cost goal when one exists.” Thus, the step costs are irrelevant to “Complete.”
5- Assume that a rook can move on a chessboard any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces. Manhattan distance is an admissible heuristic for the problem of moving the rook from square A to square B in the smallest number of moves.
FALSE
The Manhattan distance may over-estimate the optimal remaining number of moves to the goal because a rook may cover several squares in a single move. NOTE: If the path cost instead were the number of squares covered, then Manhattan distance would be admissible
6- Breadth-first search is a special case of uniform-cost search.
When all step costs are equal, g(n) ? depth(n), so uniform-cost search reproduces breadth-first search
7- Depth-first search is a special case of best-first tree search.
Depth-first search is best-first search with f(n) = −depth(n); breadth-first search is best-first search with f(n) = depth(n);
1- Depth-first search always expands at least as many nodes as A* search with an admissible heuristic
FALSE.
Depth-first search may possibly, sometimes, expand fewer nodes than A* search with an admissible heuristic.
E.g., it is logically possible that sometimes, by good luck, depth-first search may march directly to the goal with no back-tracking.
2- h(n) = 0 is an admissible heuristic for the 8-puzzle TRUE. h(n)=0 NEVER over-estimates the remaining optimal distance to a goal node.
3- A* is of no use in robotics because percepts, states, and actions are continuous
FALSE,
the continuous spaces can be discretized. A* (or variants) are widely used
4- Breadth-first search is complete even if zero step costs are allowed.
TRUE
Because if there exists a goal it occurs at finite depth d and will be found in O(bd) steps.
“Complete” means “will find a goal when one exists” --- and does NOT imply “optimal,” which means “will find a lowest-cost goal when one exists.” Thus, the step costs are irrelevant to “Complete.”
5- Assume that a rook can move on a chessboard any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces. Manhattan distance is an admissible heuristic for the problem of moving the rook from square A to square B in the smallest number of moves.
FALSE
The Manhattan distance may over-estimate the optimal remaining number of moves to the goal because a rook may cover several squares in a single move. NOTE: If the path cost instead were the number of squares covered, then Manhattan distance would be admissible
6- Breadth-first search is a special case of uniform-cost search.
When all step costs are equal, g(n) ? depth(n), so uniform-cost search reproduces breadth-first search
7- Depth-first search is a special case of best-first tree search.
Depth-first search is best-first search with f(n) = −depth(n); breadth-first search is best-first search with f(n) = depth(n);