Consider a variant of the rod cutting problem in which, in addition to length n of the rod, you are given an integer k ≥ 1 that specifies the maximum number of cuts you are allowed to make. For example, if k = 1, you are allowed to make 0 or 1 cuts and not more. As before, the values of subrods are stored in an array p. Let L[i, q] be the maximum value you can get for cutting a rod of length i when you are allowed to make q cuts (we have i ≤ n and q≤k). Write down the recursive formula for L[i, q].

Consider a variant of the rod cutting problem in which, in addition to length n of the rod, you are given an integer k ≥ 1 that specifies the maximum number of cuts you are allowed to make. For example, if k = 1, you are allowed to make 0 or 1 cuts and not more. As before, the values of subrods are stored in an array p. Let L[i, q] be the maximum value you can get for cutting a rod of length i when you are allowed to make q cuts (we have i ≤ n and q≤k). Write down the recursive formula for L[i, q].

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

See similar textbooks

Similar questions

Given two arrays a and b, where both arrays consisting of n positive integers. It is allowed to swap any element from array a with any element from b. Your task is to find the maximum possible sum you can obtain in the array a if you can do no more than (Le. at most) k moves (swaps). Input • The first line of the test case contains two integers n and k (1
Given two arrays a and b, where both arrays consisting of n positive integers. It is allowed to swap any element from array a with any element from b. Your task is to find the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k moves (swaps). Input • The first line of the test case contains two integers n and k (1sns30;0sksn) - where n is the number of elements in a and b, while k is the maximum number of moves you can do. • The second line of the test case contains n integers a1,a2,... an • The third line of the test case contains n integers b1,b2,..,bn Output Print the answer – the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k swaps. Examples: Ex 1: Ex 2: Ex 3: Input 55 53 40 55665 12345 2243 12543 10 9 10 10 9 2423 Output: 27 39 11 • In the first test case of the example, you don't need to swap anything. • In the second test case of the example, you can swap a1=1 with b1=10, a3=3 with b3=10…
Given two arrays a and b, where both arrays consisting of n positive integers. It is allowed to swap any element from array a with any element from b. Your task is to find the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k moves (swaps). Input • The first line of the test case contains two integers n and k (1Sns30;0sksn) - where n is the number of elements in a and b, while k is the maximum number of moves you can do. • The second line of the test case contains n integers a1,a2,... an • The third line of the test case contains n integers b1,b2,..,bn Output Print the answer – the maximum possible sum you can obtain in the array a if you can do no more than (i.e. at most) k swaps. Examples: Ex 1: Ex 2: Ex 3: Input 55 53 40 55665 1234 5 2243 12543 10 9 10 10 9 2423 Output: 27 39 11 • In the first test case of the example, you don't need to swap anything. • In the second test case of the example, you can swap a1=1 with bi=10, a3=3 with b3=10…
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…
You are given an integer array X[1, . . . , n]. You should move each element of X[1, . . . , n] into one of the two arrays A and B such that A and B are non-empty and average(A) = average(B). Return true if it is possible to achieve that and false otherwise. Note that for an array A, average(A) is the sum of all the elements of A over the length of A. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
You're given an array of N integers, and a number K. The maximum K-product of the array is the maximum product of any K length subsequence of the array. For example, the maximum 2-product of the array [-5, 3, 4, -6] is 30 because the product of the subsequence [-5, -6] is 30 and it is impossible to achieve larger subsequence product. What is the maximum K-product you can achieve? Using JAVA programming output the max K- product. Input: 1 42 5 -3 -4 6 Output: 30
You are a movie theater manager. You are given a two-dimensional array with 6 rows and 6 columns - 36 elements with O value, that represent empty theater seats. All 36 tickets for session were sold, so you need to identify all of the seats with value 1. Write a program that replaces all O values in the given array, by 1 and outputs the resulting matrix. Use nested for-loops to iterate over two-dimensional matrix.
Given two arrays A and B of equal size N, the task is to find if given arrays are equal or not. Two arrays are said to be equal if both of them contain same set of elements, arrangements (or permutation) of elements may be different though.Note : If there are repetitions, then counts of repeated elements must also be same for two array to be equal. Example 1: Input: N = 5 A[] = {1,2,5,4,0} B[] = {2,4,5,0,1} Output: 1.
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:
Computer Engineering labYou have to perform various number of operations. In one operation, you can choose one index i (1 ≤ i ≤ N) and increment Ai by 1. Each index can be chosen any number of times.Using python programming you have to find the minimum number of operations required to modify the array A such that for every pair i, j (1 ≤ i, j ≤ N), (Ai % Bi) equals (Aj % Bj). Here, % denotes the modulo operator (the remainder after dividing by Bi). Note that 0 ≤ (Ai % Bi) < Bi.Input:134 2 25 3 4Output:3
can you solve this please ? Given an array of unsorted integers, you are requested to investigate whether there exist a pair of numbers in this array that has a sum equal to a given key or not. For example, if the arr = [8, 7, 2, 5, 3] and the key = 12, the answer will be "Yes" as the array has a pair (7 and 5) where their sum = 12 = key, otherwise "No" is returned. To solve this problem, the following idea can be used: i. Consider every pair in the given array and check if their sum = key. ii. Sort the array first, keeping two pointers to on the minimum and maximum of the array and then move from both directions toward the center of the array while checking whether the sum = key or not. Answer the following questions: a) Transform each of the above ideas (i) & (ii) into algorithm (pseudocode) and compute their complexities b) Critic these two ideas: [Which is better? Why?] c) Design a better solution with less complexity. [note: your idea should be…
Write a program that randomly fills in 0s and 1s into a 6 * 6 matrix, prints the matrix, and finds the first row and first column with the least 1s.