To show that an array is Monge if and only if for all i = 1 , 2 , .... , m − 1 and j = 1 , 2 , ..... , n − 1 it has A [ i , j ] + A [ i + 1 , j + 1 ] ≤ A [ i , j + 1 ] + A [ i + 1 , j 0 ] .

Question

Want to see the full answer?

Answer 1

Question

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

A unimodal array is an array that has a sequence of monotonically increasing integers followed by a sequence of monotonically decreasing integers, assuming all elements in the array are unique. Example: А- (4, 5, 8, 9, 10, 11, 7, 3, 2, 1}: A is a unimodal array because there is an increasing sequence followed by a decreasing sequence and the maximum element is 11. B= {11, 9, 8, 7, 5, 4, 3, 2, 1}: B is not a unimodal array because there is no increasing sequence It is simply a decreasing sequence and the maximum element is 11. C= {1, 2, 3, 4, 5, 7, 8, 9, 11}: C is not a unimodal array because There is an increasing sequence, but there is no decreasing sequence and the maximum element is 11. Design an efficient algorithm with the lowest possible complexity to state whether a given array is unimodal or not, and explain why your algorithm is efficient. Analyze the complexity of your algorithm.

16. 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) no

Given an 8-element array: A = {x1, X2, X3, X4, X5, X6, 7, x8}, we would like to find its 3rd smallest element. It is known that x₁ and 8 are the two extreme elements: max and min, but we do not know which one is the max and which one is the min. It is also known that x4 and x5 are the two medians: left-median and right-median. What is the minimum number of comparisons you need to find the 3rd smallest element of the original array? Ans:

Answer 2

Question

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Answer 6

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

Answer 7

Chapter 4, Problem 6P

(a)

Program Plan Intro

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

Answer 8

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

Answer 9

(b)

Program Plan Intro

To modify one element in order that it becomes aMonge array.

Answer 10

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

Answer 11

(c)

Program Plan Intro

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

Answer 12

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

Answer 13

(d)

Program Plan Intro

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

Answer 14

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Answer 15

(e)

Program Plan Intro

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 19

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - Prob. 5E

To show that an array is Monge if and only if for all i = 1 , 2 , .... , m − 1 and j = 1 , 2 , ..... , n − 1 it has A [ i , j ] + A [ i + 1 , j + 1 ] ≤ A [ i , j + 1 ] + A [ i + 1 , j 0 ] .

Concept explainers

To show that an array is Monge if and only if for all i=1,2,....,m−1 and j=1,2,.....,n−1 it has A[i,j]+A[i+1,j+1]≤A[i,j+1]+A[i+1,j0].

To modify one element in order that it becomes aMonge array.

To prove that array is Monge if f(1)≤f(2)≤........≤f(m) for any m*n .

To explain the computation of the leftmost minimum in the odd-numbered rows of A in O(m+n) time.

To give the recurrence relation that computes leftmost minimum in O(m+nlgm) time.

Want to see the full answer?

Chapter 4 Solutions