Given a set of distinct positive integers, find the largest subset such that every pair of elements in the subset (i, j) satisfies either i % j = 0 or j % i = 0.For example, given the set [3, 5, 10, 20, 21], you should return [5, 10, 20]. Given [1, 3, 6, 24], return [1, 3, 6, 24]
Question
Given a set of distinct positive integers, find the largest subset such that every pair of elements in the subset (i, j) satisfies either i % j = 0 or j % i = 0.For example, given the set [3, 5, 10, 20, 21], you should return [5, 10, 20]. Given [1, 3, 6, 24], return [1, 3, 6, 24]
Solution
This problem can be solved using dynamic programming. Here are the steps:
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Sort the array in increasing order. This is because if i % j = 0 or j % i = 0, then i must be greater than or equal to j.
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Initialize an array dp of the same length as the input array, where dp[i] is the maximum size of the subset including nums[i]. Set all elements of dp to 1, because a single number is always a subset.
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For each number in the array (from index 1 to the end), check all previous numbers (from index 0 to current index - 1). If the current number is
Similar Questions
Test time left: 22:45Write the codeGiven a set of distinct positive integers, find the largest subset such that every pair of elements in the subset (i, j) satisfies either i % j = 0 or j % i = 0.For example, given the set [3, 5, 10, 20, 21], you should return [5, 10, 20]. Given [1, 3, 6, 24], return [1, 3, 6, 24]
Find the maximum element from the given array of integers.
You have been given an array 'A' of N integers. You need to find the maximum value of j - i subjected to the constraint of A[i] <= A[j], where ‘i’ and ‘j’ are the indices of the array.For example :If 'A' = {3, 5, 4, 1}then the output will be 2.Maximum value occurs for the pair (3, 4)Detailed explanation ( Input/output format, Notes, Images )Constraints:1 <= T <= 1001 <= N <= 10 ^ 4-10 ^ 5 <= A[i] <= 10 ^ 5Time limit: 1 sec.Sample Input 1:1934 8 10 3 2 80 30 33 1Sample Output 1:6Explanation:Maximum value occurs for the pair (8, 33)Sample Input 2:1109 2 3 4 5 6 7 8 18 0Sample Output 2:8Explanation:Maximum value occurs for the pair (9, 18)
Given an array a of n positive integers. The task is to find the maximum of j - i subjected to the constraint of a[i] < a[j] and i < j.
Write a program for the maximum possible difference between two subsets of an array.Given an array of n integers. The array may contain repetitive elements, but the highest frequency of any element must not exceed two. Make two subsets such that the difference of the sum of their elements is maximum and both of them jointly contain all elements of the given array along with the most important condition, no subset should contain repetitive elements. ExampleInput:45 8 -1 4Output:Maximum Difference = 18Explanation:Suppose arr[ ] = {5, 8, -1, 4}Let Subset A = {5, 8, 4} & Subset B = {-1}Sum of elements of subset A = 17, of subset B = -1Difference of Sum of Both subsets = 17 - (-1) = 18Input format :The first input line consists of the size of an array, n.The second input consists of the array elements, separated by space.Output format :The output displays the maximum possible difference between two subsets of an array.Refer to the sample output for the formatting specifications.Code constraints :2 ≤ n ≤ 100Sample test cases :Input 1 :74 2 -3 3 -2 -2 8Output 1 :Maximum Difference = 20Input 2 :45 8 -1 4Output 2 :Maximum Difference = 18
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