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 ] .

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Answer 1

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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.

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Let A be an array of numbers. In the maximum sub-array problem, your goal is to determine the sub-array A[x . . . y] of consecutive terms for which the sum of the entries is as large as possible. For example, if A = [−2, −3, 4, −1, −2, 1, 5, −3], the maximum sub-array is [4, −1, 2, 1, 5], and the largest possible sum is S = 4 − 1 − 2 + 1 + 5 = 7. Suppose A = [1, 2, −4, 8, 16, −32, 64, 128, −256, 512, 1024, −2048]. Determine S, the largest possible sum of a sub-array of A.

Given a large list of positive integers, count the number of k-subsequences. A k-subarray of an array is defined as follows: It is a subarray, i.e. made of contiguous elements in the array The sum of the subarray elements, s, is evenly divisible by _k, _i.e.: sum mod k = 0. Given an array of integers, determine the number of k-subarrays it contains. For example, k = 5 and the array nums = [5, 10, 11, 9, 5]. The 10 k-subarrays are: {5}, {5, 10}, {5, 10, 11, 9}, {5, 10, 11, 9, 5}, {10}, {10, 11, 9}, {10, 11, 9, 5}, {11, 9}, {11, 9, 5}, {5}. **Function Description ** Complete the function kSub in the editor below. The function must return a long integer that represents the number of k-subarrays in the array. kSub has the following parameter(s): k: the integer divisor of a k-subarray nums[nums[0],...nums[n-1]]: an array of integers Constraints 1 ≤ n ≤ 3 × 105 1 ≤ k ≤ 100 1 ≤ nums[i] ≤ 104 Input Format For Custom Testing Input from stdin will be processed as follows and…

An array of size n and two integers D and S are given, the special sum of a subarray is defined as follows:(Sum of all elements of the subarray) (D - p S)Where p = number of distinct prime factors of “product of all elements of the subarray”.Find the maximum special sum by considering all non-empty subarrays of the given array.Input:-First 3 integers will be n, D and S and the following will be the elements of the arrayOutput:- Output maximum special sum considering all non-empty subarrays of the array(single output integer)

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.

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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

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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

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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

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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.

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Chapter 4 Solutions