Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 6, Problem 13E
Explanation of Solution
Way of updating the numbers efficiently:
- The best idea is to preprocess the constraints.
- So here, for each value of “Xi”, the user should keep track of those variables “Xk” for which an arc from “Xk” to “Xi” is satisfied by that particular value of “Xi”...
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Correct answer will be upvoted else downvoted. Computer science.
You are approached to pick some integer k (k>0) and find a succession an of length k with the end goal that:
1≤a1<a2<⋯<ak≤|s|;
ai−1+1<ai for all I from 2 to k.
The characters at positions a1,a2,… ,ak are taken out, the excess characters are linked without changing the request. Thus, at the end of the day, the situations in the arrangement an ought not be contiguous.
Allow the subsequent to string be s′. s′ is called arranged if for all I from 2 to |s′| s′i−1≤s′i.
Does there exist such a grouping a that the subsequent string s′ is arranged?
Input
The main line contains a solitary integer t (1≤t≤1000) — the number of testcases.
Then, at that point, the portrayals of t testcases follow.
The main line of each testcase contains a string s (2≤|s|≤100). Each character is either '0' or '1'.
Output
For each testcase print "YES" if there exists a grouping a to such an extent that…
code in python attached please
Define a hash table with an associated hash function ℎ(?)h(k) mapping keys ?k to their associated hash value.
b) In simple uniform hashing, each key is assumed to have equal probability to map to any of the hashes in a given table of size m. Given an open-address table of size 500500 and 22 random keys, what is the probability that they hash to the same value? What is the probability that they hash to different values?
Let A = {x ∈ Z : x ≤ 3} and let B = {x ∈ Q : x2 = 9}. Is B ⊆ A? Give a brief reason for your answer.
Chapter 6 Solutions
Artificial Intelligence: A Modern Approach
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- Problem 3. Recollect that the standard implementation of the Dijkstra's algorithm uses a priority queue that supports the Extract-min() and Decrease-Key() operations. Describe a method to implement Dijkstra's algorithm in O((m + n) log n) time without the use of Decrease-Key operation, i.e., your algorithm can use the Extract-Min() operation but not the Decreased-Key() operation. Solution:arrow_forwardRecall that we discussed the "leader-based" deterministic distributed algorithm for 2-colouring a path, that runs in time O(n) on an n node path network. Suppose we now relax the constraint of 2-colouring to mean, it is okay for one of the neighbours of a node to x get the same colour as the mode x, as long as the other neighbour gets a different colour. The end points must get a different colour from their respective unique neighbours. The running time for a best efficiency deterministic distributed algorithm, using unique identifiers for nodes, for this problem would be:arrow_forwardThe off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n}under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S berepresented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) ofINSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtainedfrom insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m,extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n)for i = 1 to n determine j such that i ∈ Kj if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, Kjreturn extracted (1) Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where eachnumber stands for its insertion. Draw a…arrow_forward
- The off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n}under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S berepresented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) ofINSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtainedfrom insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m,extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n)for i = 1 to n determine j such that i ∈ Kj if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, destoying Kjreturn extracted Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where eachnumber stands for its insertion.…arrow_forwardThe off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n}under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S berepresented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) ofINSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtainedfrom insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m,extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n)for i = 1 to n determine j such that i ∈ ?? if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, destroying ????return extracted (1) Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where eachnumber stands for its…arrow_forwardThe off-line minimum problem maintains a dynamic set T of elements from the domain {1, 2,...,n}under the operations INSERT and EXTRACT-MIN. A sequence S of n INSERT and m EXTRACT-MIN calls are given, where each key in {1, 2,...,n} is inserted exactly once. Let a sequence S berepresented by I1 , E, I2, E, ... , E, Im+1 , where each Ij stands for a subsequence (possibly empty) ofINSERT and each E stands for a single EXTRACT-MIN. Let Kj be the set of keys initially obtainedfrom insertions in Ij. The algorithm to build an array extracted[1..m], where for i = 1, 2, ..., m,extracted[i] is the key returned by the ith EXTRACT-MIN call is given below: Off-Line-Minimum(m, n)for i = 1 to n determine j such that i ∈ Kj if j ≠ m + 1 extracted[j] = i let L be the smallest value greater than j for which KL exists KL = KL U Kj, destoying Kjreturn extracted Given the operation sequence 9, 4, E, 6, 2, E, E, 5, 8, E, 1, 7, E, E, 3; where eachnumber stands for its insertion.…arrow_forward
- Let L = { <M> | M is a TM that accepts sR whenever it accepts s } . Show that L is undecidable.arrow_forwardsecurity pr As we mentioned in class, a universal hash function is a function UH(K, M) that takes a key K, a message M and produces a fixed length digest. The universal hash is defined to be "secure" if for any two messages M₁ and M2, if K is selected uniformly at random, then the probability that UH(K, M₁) UH(K, M₂) is approximately zero. == Suppose that H is a secure hash function. Is UH(K, M) = H(K||M) a secure universal hash function? Either prove the answer is "yes" using the security properties of H (which can be assumed), or show how the security of UH could be violated. VOarrow_forwardProblem 2: In this problem we assume that h: U → {0, 1,..., m - 1} is a good hash function, that is, every key k has the same probability to map to any place in the table T of length m. 1 m (i) What is the probability that three pairwise distinct elements u₁, U2, U3 EU are mapped by the function h to the same place in the table (that is, h(u₁) = h(u₂) = h(uz))?arrow_forward
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