You are given two arrays of integers a1,a2,…,an and b1,b2,…,bn. Before applying any operations, you can reorder the elements of each array as you wish. Then, in one operation, you will perform both of the following actions, if the arrays are not empty:1. Choose any element from array a and remove it (all remaining elements are shifted to a new array a)2. Choose any element from array b and remove it (all remaining elements are shifted to a new array b)Let k be the final size of both arrays. You need to find the minimum number of operations required to satisfy aiInput Format2 (size of arrays a & b)1 1 (array a)3 2 (array b)Constraintsall inputs are positive integersOutput Format0 (number of minimum operations)Sample Input 041 5 1 53 8 3 3Sample Output 01
Question
You are given two arrays of integers a1,a2,…,an and b1,b2,…,bn. Before applying any operations, you can reorder the elements of each array as you wish. Then, in one operation, you will perform both of the following actions, if the arrays are not empty:1. Choose any element from array a and remove it (all remaining elements are shifted to a new array a)2. Choose any element from array b and remove it (all remaining elements are shifted to a new array b)Let k be the final size of both arrays. You need to find the minimum number of operations required to satisfy aiInput Format2 (size of arrays a & b)1 1 (array a)3 2 (array b)Constraintsall inputs are positive integersOutput Format0 (number of minimum operations)Sample Input 041 5 1 53 8 3 3Sample Output 01
Solution
The problem is asking to find the minimum number of operations required to make the sum of elements in both arrays equal. An operation consists of removing one element from each array. Before performing any operations, we can reorder the elements in each array.
Here are the steps to solve this problem:
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First, we need to calculate the sum of elements in both arrays. If the sums are already equal, then no operations are needed, so the answer is 0.
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If the sums are not equal, we need to make them equal by performing operations. We should start by sorting both arrays in descending order. This is because we want to remove the largest elements first to minimize the number of operations.
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Then, we start removing elements from the end of the arrays (since they are sorted in descending order, the end contains the smallest elements). We remove one element from each array in each operation. We continue this process until the sums of the elements in both arrays are equal.
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The number of operations performed is the answer to the problem.
For example, consider the sample input:
4 (size of arrays a & b) 1 5 1 5 (array a) 3 8 3 3 (array b)
First, we calculate the sum of elements in both arrays. The sum of array a is 12 and the sum of array b is 17. Since the sums are not equal, we need to perform operations.
We sort both arrays in descending order:
5 5 1 1 (array a) 8 3 3 3 (array b)
Then, we start removing elements from the end of the arrays. After one operation, the arrays become:
5 5 1 (array a) 8 3 3 (array b)
The sum of array a is now 11 and the sum of array b is 14. We need to perform more operations. After two more operations, the arrays become:
5 (array a) 8 (array b)
Now, the sum of both arrays is 8, so we have made the sums equal. The number of operations performed is 3, so the answer is 3.
Similar Questions
Given two sorted arrays arr1[] and arr2[] of sizes n and m in non-decreasing order. Merge them in sorted order without using any extra space. Modify arr1 so that it contains the first N elements and modify arr2 so that it contains the last M elements.
Given two arrays of size N and M, insert them into two sets A and B.Implement the following operations in the same sequential order:Union of A and B: Find the union of A and B, print the elements of the resulting set in sorted order.Intersection of A and B: Find the intersection of A and B, print the elements of the resulting set in sorted order.Symmetric Difference of A and B: Find the symmetric difference of A and B, print the elements of the resulting set in sorted order.Check if A and B are disjoint sets: If yes, print true, otherwise, print false.Check if A is a subset of B: If yes, print true, otherwise, print false.Check if A is a superset of B: If yes, print true, otherwise, print false.Input FormatThe first line of input contains N, the size of array1. The second line of input contains N elements of array1.The third line of input contains M, the size of array2. The fourth line of input contains M elements of array2.Output FormatFor subset, superset, and disjoint operations print True or False. And for remaining all operations, if resulting set is not empty, print the sorted set separated by spaces, otherwise skip printing the set.Constraints1 <= N, M <= 501 <= array1[i], array2[i] <= 100ExampleInput49 6 8 739 9 6Output6 7 8 96 97 8falsefalsetrue
Write a function bool equals(int a[], int a_size, int b[], int b_size) that checks whether two arrays have the same elements in the same order.
You are given two integer arrays nums1 and nums2, sorted in non-decreasing order, and two integers m and n, representing the number of elements in nums1 and nums2 respectively.Merge nums1 and nums2 into a single array sorted in non-decreasing order.The final sorted array should not be returned by the function, but instead be stored inside the array nums1. To accommodate this, nums1 has a length of m + n, where the first m elements denote the elements that should be merged, and the last n elements are set to 0 and should be ignored. nums2 has a length of n. Example 1:Input: nums1 = [1,2,3,0,0,0], m = 3, nums2 = [2,5,6], n = 3Output: [1,2,2,3,5,6]Explanation: The arrays we are merging are [1,2,3] and [2,5,6].The result of the merge is [1,2,2,3,5,6] with the underlined elements coming from nums1.Example 2:Input: nums1 = [1], m = 1, nums2 = [], n = 0Output: [1]Explanation: The arrays we are merging are [1] and [].The result of the merge is [1].Example 3:Input: nums1 = [0], m = 0, nums2 = [1], n = 1Output: [1]Explanation: The arrays we are merging are [] and [1].The result of the merge is [1].Note that because m = 0, there are no elements in nums1. The 0 is only there to ensure the merge result can fit in nums1. Constraints:nums1.length == m + nnums2.length == n0 <= m, n <= 2001 <= m + n <= 200-109 <= nums1[i], nums2[j] <= 109 Follow up: Can you come up with an algorithm that runs in O(m + n) time?
You are given two integer arrays: array a𝑎 of length n𝑛 and array b𝑏 of length n+1𝑛+1.You can perform the following operations any number of times in any order:choose any element of the array a𝑎 and increase it by 11;choose any element of the array a𝑎 and decrease it by 11;choose any element of the array a𝑎, copy it and append the copy to the end of the array a𝑎.Your task is to calculate the minimum number of aforementioned operations (possibly zero) required to transform the array a𝑎 into the array b𝑏. It can be shown that under the constraints of the problem, it is always possible.InputThe first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases.Each test case consists of three lines:the first line contains a single integer n𝑛 (1≤n≤2⋅1051≤𝑛≤2⋅105);the second line contains n𝑛 integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109);the third line contains n+1𝑛+1 integers b1,b2,…,bn+1𝑏1,𝑏2,…,𝑏𝑛+1 (1≤bi≤1091≤𝑏𝑖≤109).Additional constraint on the input: the sum of n𝑛 over all test cases doesn't exceed 2⋅1052⋅105.OutputFor each test case, print a single integer — the minimum number of operations (possibly zero) required to transform the array a𝑎 into the array b𝑏.ExampleinputCopy3121 323 33 3 344 2 1 22 1 5 2 3outputCopy318NoteIn the first example, you can transform a𝑎 into b𝑏 as follows: [2]→[2,2]→[1,2]→[1,3][2]→[2,2]→[1,2]→[1,3].
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