Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 5.3, Problem 4E
Program Plan Intro
To show that each element
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+ program to read 4*4 2D-array, then update each , and then find the summation of even elements wi
Pseudo Code shown in Figure Q1(a) is an algorithm for binary searching for an array
with n number of elements. By applying this algorithm, show step by step approach on
how to find number 11 in an array as depicted in Figure Q1(b).
low + 0
high e n-1
while (low s high) do
ix + (low + high) /2
if (t = Alix)) then
return ix
else if (t < A[ix]) then
high e ix - 1
else
low + ix + 1
return -1
Figure Ql(a)
2
4
6
9
11
12 | 25
[0] [1)
[2]
[3] (4) [5)
[6]
Figure Q1(b)
Sparse matrix-vector multiplication in Python is similar to numpy.dot operation,
however the provided @ operator is used. Let us consider multiplying a 5 by 5
sparse matrix with a 5 by 3 sparse matrix shown below.
01000
00010
10001
10000
01000
100
001
x 000
010
100
The Python code to implement multiplication of these two sparse matrices
Chapter 5 Solutions
Introduction to Algorithms
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Similar questions
- You are given an array J[1 : n] which includes the scores of n players in a game. You are additionally given an array P[1 : m] with the score of m new players. Design and analyze an algorithm that given both arrays J and P, can find the rank of each player P inside the array J, i.e., for each P[i], determines what would be the rank of P[i] in the array consisting of all elements of J plus P[i]. Your algorithm should run in O((n + m) ·log n) time.arrow_forwardGiven an array arr[] of N non-negative integers representing the height of blocks. If width of each block is 1, compute how much water can be trapped between the blocks during the rainy season. Example 1: Input: N = 6 arr[] Output: 10 = {3,0,0,2,0,4}arrow_forwardYou are given an array A[1 : n] which includes the scores of n players in a game. They areranked in the following way: Rank of a player is an integer r if there are exactly r −1 distinct scores strictlysmaller than the score of this player (irrespective of the number of players). Question: Design and analyze an algorithm that given the array A, can find the rank of all players in the arrayin O(n log n) time.arrow_forward
- You wish to find duplicates in an unsorted n-element array A. 1,..., 2n integers.arrow_forward16. Given an n-element array with n > 100, is it possible to find an algorithm that can find an element that is neither the maximum nor the minimum with fewer than 10 comparisons? (a) yes (b) noarrow_forwardThe number of poles lying on right side of S-Plane for the following R-H array are= S5 1 b a S4 -3 f S3 -12 s? 6 f so -4 4 3. 2.arrow_forward
- You have been given an array A of size N and an integer K. This array consists of N integers ranging from 1 to 10^7. Each element in this array is said to have a Special Weight. The special weight of an element a[i] is a[i]%K. You now need to sort this array in Non-Increasing order of the weight of each element, i.e the element with the highest weight should appear first, then the element with the second highest weight and so on. In case two elements have the same weight, the one with the lower value should appear in the output first. Input Format: The first line consists of two space separated integers N and K. The next line consists of N space separated integers denoting the elements of array A. Output Format: Print N space separated integers denoting the elements of the array in the order in which they are required. Constraints: 1≤N≤10^5 1≤A[i]≤10^7 1≤K≤10^7 Note: You need to print the value of each element and not their weight. SAMPLE INPUT 5 21 2 3 4 5 SAMPLE OUTPUT 1 3 5 2 4…arrow_forwardLet M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.arrow_forwardPseudo Code shown in Figure Q2(c)(i) is an algorithm for binary searching for an array with n number of elements. By applying this algorithm, show step by step approach on how to find number 11 in an array as shown in Figure Q2(c)(ii). low + 0 high + n-1 while (low S high) do ix + (low + high)/2 if (t = A[ix]) then return ix else if (t < A[ix]) then high e ix - 1 else low + ix + 1 return -1 Figure Q2(c)(i) 9 | 10 | 11 | 12 [2] [3] [4] [5] [6] [7] 1 13 | 19 | 33| 45 55 [0] [1] [8] [9] Figure Q2(c)(ii)arrow_forward
- Create an array for (20-1)(20+1)arrow_forwardGiven an array arg[] below, use the incremental approach to sort it in assending order 11 42 35 38 22 45 18 39 3arrow_forward20. Given a 4-element array with distinct elements, say {x1, x2, x3, x4}, it is known that x1 is not the minimum. How to use 2 comparisons to find an element that is neither the maximum nor the minimum? Solution:arrow_forward
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