Backtracking General method • Useful technique for optimizing search under some constraints • Express the desired solution as an n-tuple (x1 ‚ . . . ‚ xn ) where each xi ∈ Si ‚ Si being a finite set • The solution is based on finding one or more vectors that maximize‚ minimize‚ or satisfy a criterion function P (x1 ‚ . . . ‚ xn ) • Sorting an array a[n] – Find an n-tuple where the element xi is the index of ith smallest element in a – Criterion function is given by a[xi ] ≤ a[xi+1 ] for 1 ≤ i < n
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& Quadratic Equations‚ Linear Inequations‚ Differentiation‚ Sequences and Series (A.P. & G.P. Misc.)‚ Trigonometry‚ Cartesian System of Rectangular Coordinates‚ Straight Lines and Family of Straight Lines‚ Circles‚ Conic Section‚ Trigonometry‚ Permutations and Combinations‚ Binomial Theorem‚ Statistics‚ Mathematical Logic‚ Limits‚ Probability‚ Introduction to 3-D Geometry. Section – II (Logical and Analytical Reasoning) : Verbal and Non-verbal Reasoning. Section – III (Computers and IT) : History
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normal range‚ intermediate‚ permutation‚ or a full mutation of the FMR1 gene. Individuals with less than 45 CGG repeats have a normal FMR1 gene. Those with 45-54 CGG repeats have what is called an intermediate or grey zone allele‚ which does not cause FXS. Individuals with 55-200 CGG repeats have a permutation‚ which means they carry on unstable mutation of the gene that can expand in the future generations and cause FXS in their children or grandchildren. The permutation has no immediate and observable
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outcomes = 64. Step 4: P (event) = Step 5: == 0.5 Step 6: The theoretical probability that the coin lands on a black square is 0.5. A. Permutation and Combination * The various ways in which objects from a set may be selected‚ generally without replacement‚ to form subsets. This selection of subsets is called a permutation when the order of selection is a factor‚ a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number
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This equations speaks to the relationship between combinatorials and permutations. Proven {n \choose k} = \frac{n!}{k!(n -k)!} P(n;k) = n! / (n-k)! permutation equation‚ (number of combinations (order doesn’t matter) of k length combinations derived from a set of n elements k! = number of combinations k elements can be recombined (same characters different orders). therefore if you divide the number of permutations by k! you get {n \choose k} = \frac{n!}{k!(n -k)!} Prove {n \choose
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Chapter 1: Permutations 1. In how many ways can three different awards be distributed among 20 students in the following situations? a. No student may receive more than one award. b. There is no limit on the number of awards won by one student. Answer: a) 6840 b)8000 2. Consider the word BASKETBALL: a. How many permutations are there? b. How many permutations begin with the letter K? c. How many permutations
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Note: These are not sample questions‚ but questions that explore some of the concepts that may be used. The intention is that you should get prepared with the concepts rather than just focusing on a set of questions. ----------------------------------------------------------------------------------1. What are the total number of divisors of 600(including 1 and 600)? a. b. c. d. 24 40 16 20 2. What is the sum of the squares of the first 20 natural numbers (1 to 20)? a. b. c.
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COMPARISMS OF OPTIMIZATION STRATEGIES FOR THE TRAVELLING SALESMAN PROBLEM Department of Information Systems and Computing B.Sc. (Hons) Computer Science‚ Artificial Intelligence Academic Year 2012-2013 Comparison of Optimization Strategies for the Travelling Salesman Problem Adewale Oluwaseun Mako (0941620) A Report Submitted in the partial fulfilment of the requirement for the degree of Bachelor of Science Brunel University Department of Information Systems and Computing Uxbridge
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and Luan [10] presented a high dimensional permutation bit-level method based on chaos system. Wang et al [11] presented a new color images encryption algorithm based on Logistic mapping and used the combination of confusion and diffusion to reduce relation between color components. In [12]‚ the spatiotemporal chaos is employed to confuse blocks and change pixel values simultaneously. In [13] an image encryption algorithm presented based on bit permutation of three-dimensional matrix. Enayatifar et
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uni-lj.si Contents 1 Pajek 2 3 Data objects Main Window Tools 3.1 File . . . . . . 3.2 Net . . . . . . 3.3 Nets . . . . . . 3.4 Operations . . 3.5 Partition . . . 3.6 Partitions . . . 3.7 Vector . . . . . 3.8 Vectors . . . . 3.9 Permutation . 3.10 Permutations . 3.11 Cluster . . . . 3.12 Hierarchy . . . 3.13 Options . . . . 3.14 Info . . . . . . 3.15 Tools . . . . . 3 6 8 8 12 31 33 42 43 44 45 46 47 47 47 48 51 52 55 55 55 57 59 59 59 59 59 59 63 66 66 66 . . . . . . . . . . . . . . .
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