Given an array arr[] of N pairs of integers (A, B) where N is even, the task is to find the minimum sum of choosing N elements such that value A and B from all the pairs are chosen exactly (N/2) times.
Examples:
Input: N = 4, arr[][] = { {7, 20}, {300, 50}, {30, 200}, {30, 20} }
Output: 107
Explanation:
Choose value-A from 1st pair = 7.
Choose value-B from 2nd pair = 50.
Choose value-A from 3rd pair = 30.
Choose value-B from 4th pair = 20.
The minimum sum is 7 + 50 + 30 + 20 = 107.Input: N = 4, arr[][] = { {10, 20}, {400, 50}, {30, 200}, {30, 20} }
Output: 110
Explanation:
Choose value-A from 1st pair = 10.
Choose value-B from 2nd pair = 50.
Choose value-A from 3rd pair = 30.
Choose value-B from 4th pair = 20.
The minimum sum is 10 + 50 + 30 + 20 = 110.
Approach: This problem can be solved using Greedy Approach. Below are the steps:
- For each pair (A, B) in the given array, store the value of (B – A) with the corresponding index in temporary array(say temp[]). The value (B – A) actually defines how much cost is minimized if A is chosen over B for each element.
- The objective is to minimize the total cost. Hence, sort the array temp[] in decreasing order.
- Pick the first N/2 elements from the array temp[] by choosing A as first N/2 elements will have the maximum sum when A is chosen over B.
- For remaining N/2 elements choose B as the sum of values can be minimized.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to choose the elements A // and B such the sum of all elements // is minimum int minSum(int arr[][2], int n) { // Create an array of pair to // store Savings and index pair<int, int> temp[n]; // Traverse the given array of pairs for (int i = 0; i < 2 * n; i++) { // Sum minimized when A // is chosen over B for // i-th element. temp[i].first = arr[i][1] - arr[i][0]; // Store index for the // future reference. temp[i].second = i; } // Sort savings array in // non-increasing order. sort(temp, temp + 2 * n, greater<pair<int, int> >()); // Storing result int res = 0; for (int i = 0; i < 2 * n; i++) { // First n elements choose // A and rest choose B if (i < n) res += arr[temp[i].second][0]; else res += arr[temp[i].second][1]; } // Return the final Sum return res; } // Driver Code int main() { // Given array of pairs int arr[4][2] = { { 7, 20 }, { 300, 50 }, { 30, 200 }, { 30, 20 } }; // Function Call cout << minSum(arr, 2); } |
107
Time Complexity: O(N*log(N))
Auxiliary Space Complexity: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
Recommended Posts:
- Minimum sum by choosing minimum of pairs from array
- Total distinct pairs from two arrays such that second number can be obtained by inverting bits of first
- Find the maximum cost of an array of pairs choosing at most K pairs
- Minimum cost of choosing the array element
- Find minimum value of the expression by choosing K elements from given array
- Minimum cost of choosing 3 increasing elements in an array of size N
- Minimum number of pairs required to make two strings same
- Minimum sum obtained from groups of four elements from the given array
- Minimum number of swaps required for arranging pairs adjacent to each other
- Minimum steps in which N can be obtained using addition or subtraction at every step
- Minimum integer that can be obtained by swapping adjacent digits of different parity
- Find the final number obtained after performing the given operation
- Number of pairs such that path between pairs has the two vertices A and B
- Minimum LCM of all pairs in a given array
- Find minimum GCD of all pairs in an array
- Find the minimum value of the given expression over all pairs of the array
- Minimum sum of absolute difference of pairs of two arrays
- Minimum and Maximum sum of absolute differences of pairs
- Minimum sum of product of elements of pairs of the given array
- Maximum of minimum difference of all pairs from subsequences of given size
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : nidhi_biet
