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Gilles 'SO- stop being evil'
Gilles 'SO- stop being evil'
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Why is 'Manhatten'Manhattan distance' a better heuristic for 15 puzzle than 'number of tiles misplaced'?

Consider two heuristics $h1(n)$$h_1$ and $h2(n)$$h_2$ defined for the 15 puzzle problem as:

  1. $h1(n)$=number$h_1(n)$ = number of misplaced tiles
  2. $h2(n)$=total$h_2(n)$ = total Manhatten distance

15 Puzzle

Could anyone tell why $h2(n)$$h_2$ is a better heuristic than $h1(n)$.I$h_1$? I would like to know why the number of nodes generated for $h1(n)$$h_1$ is greater than that for $h2(n)$$h2$.Also Also why going deeper into the state space the number of nodes increase drastically for both heuristics.

Source:  Informed Search

Why is 'Manhatten distance' a better heuristic for 15 puzzle than 'number of tiles misplaced'

Consider two heuristics $h1(n)$ and $h2(n)$ defined for the 15 puzzle problem as:

  1. $h1(n)$=number of misplaced tiles
  2. $h2(n)$=total Manhatten distance

15 Puzzle

Could anyone tell why $h2(n)$ is a better heuristic than $h1(n)$.I would like to know why the number of nodes generated for $h1(n)$ is greater than that for $h2(n)$.Also why going deeper into the state space the number of nodes increase drastically for both heuristics.

Source:Informed Search

Why is 'Manhattan distance' a better heuristic for 15 puzzle than 'number of tiles misplaced'?

Consider two heuristics $h_1$ and $h_2$ defined for the 15 puzzle problem as:

  1. $h_1(n)$ = number of misplaced tiles
  2. $h_2(n)$ = total Manhatten distance

15 Puzzle

Could anyone tell why $h_2$ is a better heuristic than $h_1$? I would like to know why the number of nodes generated for $h_1$ is greater than that for $h2$. Also why going deeper into the state space the number of nodes increase drastically for both heuristics.

Source:  Informed Search

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justin
justin
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Why is 'Manhatten distance' a better heuristic for 15 puzzle than 'number of tiles misplaced'

Consider two heuristics $h1(n)$ and $h2(n)$ defined for the 15 puzzle problem as:

  1. $h1(n)$=number of misplaced tiles
  2. $h2(n)$=total Manhatten distance

15 Puzzle

Could anyone tell why $h2(n)$ is a better heuristic than $h1(n)$.I would like to know why the number of nodes generated for $h1(n)$ is greater than that for $h2(n)$.Also why going deeper into the state space the number of nodes increase drastically for both heuristics.

Source:Informed Search