• Nie Znaleziono Wyników

Depth-first Search

N/A
N/A
Info
Pobierz
Protected

Academic year: 2021

Share "Depth-first Search"

Copied!
7
0
0

Ładowanie.... (Zobacz pełny tekst teraz)

Pobierz teraz ( 7 Stron )

Pełen tekst

(1)

Depth-first Search

➤

Depth-first search treats the frontier as a stack

➤

It always selects one of the last elements added to the frontier.

➤

If the frontier is [p1, p2, . . .]

➣

p1 is selected. Paths that extend p1 are added to the front of the stack (in front of p2.

➣

p2 is only selected when all paths from p1 have been explored.

(2)

2

3

4

5 7

12

13

14

15 16

(3)

Complexity of Depth-first Search

➤

Depth-first search isn’t guaranteed to halt on infinite graphs or on graphs with cycles.

➤

The space complexity is linear in the size of the path being explored.

➤

Search is unconstrained by the goal until it happens to stumble on the goal.

☞

(4)

➤

Breadth-first search treats the frontier as a queue.

➤

It always selects one of the earliest elements added to the frontier.

➤

If the frontier is [p1, p2, . . . , pr]:

➣

p1 is selected. Its neighbors are added to the end of the queue, after pr.

(5)

Illustrative Graph — Breadth-first Search

1

2 3

4 5 6 7

8 9 10 11 12 13 14

15 16

☞

(6)

➤

The branching factor of a node is the number of its neighbors.

➤

If the branching factor for all nodes is finite, breadth-first search is guaranteed to find a solution if one exists.

It is guaranteed to find the path with fewest arcs.

➤

Time complexity is exponential in the path length:

bn, where b is branching factor, n is path length.

➤

(7)

Lowest-cost-first Search

➤

Sometimes there are costs associated with arcs. The cost of a path is the sum of the costs of its arcs.

cost(n0, . . . , nk) =

k

i=1

|ni−1, ni|

➤

At each stage, lowest-cost-first search selects a path on the frontier with lowest cost.

➤

The frontier is a priority queue ordered by path cost.

➤

It finds a least-cost path to a goal node.

➤

When arc costs are equal ⇒ breadth-first search.

Cytaty

Pobierz teraz ( PDF - 7 Stron - 38.07 KB )

Powiązane dokumenty

Abstract. It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius–Perron or Harris then it is strongly asymptotically cyclic.

It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports1. If moreover P is Frobenius–Perron or Harris then it is

1. Introduction. A binary algebra (L, +, ·) is said to be a lattice if it satisfies the following identities:

Since the identity (x + y)y = y in Theorem 1.1 is nonregular we see that according to the last lemma we consider in the sequel bi-near-semilattices with one absorption

if D is simply connected • “<” if D is an annulus (Suita

Berndtsson-Lempert Proof 2 can be improved to obtain the Ohsawa- Takegoshi extension theorem with optimal constant (one has to use Berndtsson’s positivity of direct

if D is simply connected • “<” if D is an annulus (Suita

Using similar methods one can obtain a slightly more general result, the extension theorem with negligible weight and optimal

1. Consider the statement “If a figure is a square, then it is a rhombus”.

(a) Write the following statements in symbolic logic form (i) “If the sun is shining then I will walk to school.”.. (ii) “If I do not walk to school then the sun is

Find the coordinates of the point on L that is nearest to the origin.

(b) Find the Cartesian equation of the plane Π that contains the two lines.. The line L passes through the midpoint

Find the probability that it is not raining on that day

(b) Find the probability that a randomly selected student from this class is studying both Biology and

Find f if • f0(x

• Suppose that a population grows according to a logistic model with carrying capacity 6,000 and k = 0.0015 per year.. Write the logistic differential equation for