Given two arrays A[] and B[] of size N and M respectively, where each element is in the range [0, 9], the task is to make each element of the array A[] strictly greater than or smaller than every element in the array B[] by changing any element from either array to any number in the range [0, 9], minimum number of times.
Examples:
Input: A[] = [0, 1, 0], B[] = [2, 0, 0]
Output: 2
Explanation:
Modifying the array B[] to [2, 2, 2] makes every element in the array A[] strictly less than every element in the array B[].
Hence, the minimum number of changes required = 2.Input: A[] = [0, 0, 1, 3, 3], B[] = [0, 2, 3]
Output: 3
Explanation:
Modifying the array B[] to [4, 4, 4] makes every element in the array A[] strictly less than every element in the array B[].
Hence, the minimum number of changes required = 3.
Approach: The idea to solve the given problem is to use two auxiliary arrays prefix_a[] and prefix_b[] of size 10, where prefix_a[i] and prefix_b[i] stores the number of elements in the array A[] ≤ i and the number of elements in the array B[] ≤ i respectively. Follow the steps below to solve the problem:
- Initialize two arrays, prefix_a[] and prefix_b[] of size 10 with {0}.
- Store the frequencies of every element in the arrays A[] and B[] in arrays prefix_a, and prefix_b respectively.
- Perform the prefix sum on the array prefix_a by iterating in the range [1, 9] using the variable i and update prefix_a[i] as (prefix[i] + prefix_a[i – 1]).
- Repeat the above step for the array prefix_b[].
- Iterate in the range [0, 9] using the variable i
- Store the number of operations to make every element in the array A[] strictly greater than the digit i and make every element in the array B[] less than digit i in a variable, say X.
- Initialize it with prefix_a[i] + M – prefix_b[i].
- Similarly, store the number of operations to make every element in the array B[] strictly greater than digit i and make every element in the array A[] less than digit i in a variable, say Y.
- Initialize it with prefix_b[i] + N – prefix_a[i].
- Update the overall minimum number of operations as the minimum of X and Y. Store the minimum obtained in a variable, say ans.
- After completing the above steps, print the value of ans as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the minimize// replacements to make every element// in the array A[] strictly greater// than every element in B[] or vice-versavoid MinTime(int* a, int* b, int n, int m){ // Store the final result int ans = INT_MAX; // Create two arrays and // initialize with 0s int prefix_a[10] = { 0 }; int prefix_b[10] = { 0 }; // Traverse the array a[] for (int i = 0; i < n; i++) { // Increment prefix_a[a[i]] by 1 prefix_a[a[i]]++; } // Traverse the array b[] for (int i = 0; i < m; i++) { // Increment prefix_b[b[i]] by 1 prefix_b[b[i]]++; } // Calculate prefix sum // of the array a[] for (int i = 1; i <= 9; i++) { prefix_a[i] += prefix_a[i - 1]; } // Calculate prefix sum // of the array b[] for (int i = 1; i <= 9; i++) { prefix_b[i] += prefix_b[i - 1]; } // Iterate over the range [0, 9] for (int i = 0; i <= 9; i++) { // Make every element in array // a[] strictly greater than digit // i and make every element in the // array b[] less than digit i ans = min(ans, prefix_a[i] + m - prefix_b[i]); // Make every element in array // b[] strictly greater than digit // i and make every element in // array a[] less than digit i ans = min(ans, n - prefix_a[i] + prefix_b[i]); } // Print the answer cout << ans;}// Driver Codeint main(){ int A[] = { 0, 0, 1, 3, 3 }; int B[] = { 2, 0, 3 }; int N = sizeof(A) / sizeof(A[0]); int M = sizeof(B) / sizeof(B[0]); MinTime(A, B, N, M); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{ // Function to find the minimize// replacements to make every element// in the array A[] strictly greater// than every element in B[] or vice-versastatic void MinTime(int []a, int []b, int n, int m){ // Store the final result int ans = 2147483647; // Create two arrays and // initialize with 0s int []prefix_a = new int[10]; int []prefix_b = new int[10]; // Traverse the array a[] for (int i = 0; i < n; i++) { // Increment prefix_a[a[i]] by 1 prefix_a[a[i]]++; } // Traverse the array b[] for (int i = 0; i < m; i++) { // Increment prefix_b[b[i]] by 1 prefix_b[b[i]]++; } // Calculate prefix sum // of the array a[] for (int i = 1; i <= 9; i++) { prefix_a[i] += prefix_a[i - 1]; } // Calculate prefix sum // of the array b[] for (int i = 1; i <= 9; i++) { prefix_b[i] += prefix_b[i - 1]; } // Iterate over the range [0, 9] for (int i = 0; i <= 9; i++) { // Make every element in array // a[] strictly greater than digit // i and make every element in the // array b[] less than digit i ans = Math.min(ans, prefix_a[i] + m - prefix_b[i]); // Make every element in array // b[] strictly greater than digit // i and make every element in // array a[] less than digit i ans = Math.min(ans, n - prefix_a[i] + prefix_b[i]); } // Print the answer System.out.println(ans);}// Driver Codepublic static void main(String [] args){ int []A = { 0, 0, 1, 3, 3 }; int []B = { 2, 0, 3 }; int N = A.length; int M = B.length; MinTime(A, B, N, M);}}// This code is contributed by chitranayal. |
Python3
# Python program for the above approach# Function to find the minimize# replacements to make every element# in the array A[] strictly greater# than every element in B[] or vice-versadef MinTime(a, b, n, m): # Store the final result ans = float('inf') # Create two arrays and # initialize with 0s prefix_a = [ 0 ]*10 prefix_b = [ 0 ]*10 # Traverse the array a[] for i in range(n): # Increment prefix_a[a[i]] by 1 prefix_a[a[i]] += 1 # Traverse the array b[] for i in range(m): # Increment prefix_b[b[i]] by 1 prefix_b[b[i]] += 1 # Calculate prefix sum # of the array a[] for i in range(1, 10): prefix_a[i] += prefix_a[i - 1] # Calculate prefix sum # of the array b[] for i in range(1, 10): prefix_b[i] += prefix_b[i - 1] # Iterate over the range [0, 9] for i in range(1, 10): # Make every element in array # a[] strictly greater than digit # i and make every element in the # array b[] less than digit i ans = min(ans, prefix_a[i] + m- prefix_b[i]) # Make every element in array # b[] strictly greater than digit # i and make every element in # array a[] less than digit i ans = min(ans, n - prefix_a[i] + prefix_b[i]) # Print the answer print(ans)# Driver CodeA = [ 0, 0, 1, 3, 3 ]B = [ 2, 0, 3 ]N = len(A)M = len(B)MinTime(A, B, N, M)# This code is contributed by rohitsingh07052. |
C#
// C# program for the above approachusing System;using System.Collections.Generic;class GFG{ // Function to find the minimize// replacements to make every element// in the array A[] strictly greater// than every element in B[] or vice-versastatic void MinTime(int []a, int []b, int n, int m){ // Store the final result int ans = 2147483647; // Create two arrays and // initialize with 0s int []prefix_a = new int[10]; int []prefix_b = new int[10]; Array.Clear(prefix_a,0,prefix_a.Length); Array.Clear(prefix_b,0,prefix_b.Length); // Traverse the array a[] for (int i = 0; i < n; i++) { // Increment prefix_a[a[i]] by 1 prefix_a[a[i]]++; } // Traverse the array b[] for (int i = 0; i < m; i++) { // Increment prefix_b[b[i]] by 1 prefix_b[b[i]]++; } // Calculate prefix sum // of the array a[] for (int i = 1; i <= 9; i++) { prefix_a[i] += prefix_a[i - 1]; } // Calculate prefix sum // of the array b[] for (int i = 1; i <= 9; i++) { prefix_b[i] += prefix_b[i - 1]; } // Iterate over the range [0, 9] for (int i = 0; i <= 9; i++) { // Make every element in array // a[] strictly greater than digit // i and make every element in the // array b[] less than digit i ans = Math.Min(ans, prefix_a[i] + m - prefix_b[i]); // Make every element in array // b[] strictly greater than digit // i and make every element in // array a[] less than digit i ans = Math.Min(ans, n - prefix_a[i] + prefix_b[i]); } // Print the answer Console.WriteLine(ans);}// Driver Codepublic static void Main(){ int []A = { 0, 0, 1, 3, 3 }; int []B = { 2, 0, 3 }; int N = A.Length; int M = B.Length; MinTime(A, B, N, M);}}// This code is contributed by bgangwar59. |
Javascript
<script>// Javascript program for the above approach// Function to find the minimize// replacements to make every element// in the array A[] strictly greater// than every element in B[] or vice-versafunction Mletime(a, b, n, m){ // Store the final result let ans = 2147483647; // Create two arrays and // initialize with 0s let prefix_a = []; for (let i = 0; i < 10; i++) { prefix_a[i] = 0; } let prefix_b = []; for (let i = 0; i < 10; i++) { prefix_b[i] = 0; } // Traverse the array a[] for (let i = 0; i < n; i++) { // Increment prefix_a[a[i]] by 1 prefix_a[a[i]]++; } // Traverse the array b[] for (let i = 0; i < m; i++) { // Increment prefix_b[b[i]] by 1 prefix_b[b[i]]++; } // Calculate prefix sum // of the array a[] for (let i = 1; i <= 9; i++) { prefix_a[i] += prefix_a[i - 1]; } // Calculate prefix sum // of the array b[] for (let i = 1; i <= 9; i++) { prefix_b[i] += prefix_b[i - 1]; } // Iterate over the range [0, 9] for (let i = 0; i <= 9; i++) { // Make every element in array // a[] strictly greater than digit // i and make every element in the // array b[] less than digit i ans = Math.min(ans, prefix_a[i] + m - prefix_b[i]); // Make every element in array // b[] strictly greater than digit // i and make every element in // array a[] less than digit i ans = Math.min(ans, n - prefix_a[i] + prefix_b[i]); } // Print the answer document.write(ans);}// Driver Code let A = [ 0, 0, 1, 3, 3 ]; let B = [ 2, 0, 3 ]; let N = A.length; let M = B.length; Mletime(A, B, N, M);</script> |
Output:
3
Time Complexity: O(N + M)
Auxiliary Space: O(N)
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