Given a big list of dates in ’20s, how to efficiently sort the list.
Example:
Input: Date arr[] = {{20, 1, 2014}, {25, 3, 2010}, { 3, 12, 2000}, {18, 11, 2001}, {19, 4, 2015}, { 9, 7, 2005}} Output: Date arr[] = {{ 3, 12, 2000}, {18, 11, 2001}, { 9, 7, 2005}, {25, 3, 2010}, {20, 1, 2014}, {19, 4, 2015}}
A Simple Solution is to use an O(N log N) algorithm like Merge Sort and a custom comparator. But we can sort the list in O(n) time using Radix Sort. In a typical Radix Sort implementation, we first sort by the last digit, then by second last digit, and so on. It is highly recommended to first go through the radix sort to understand this method. In this method we sort in the following order:
- First sort by day using counting sort
- Then sort by month using counting sort
- Finally, sort by year using counting sort
As the number of days, months, and years are fixed, all three steps take O(n) time. Therefore, the overall time complexity is O(n).
Below is the C++ implementation of the above idea:
C++
// C++ program to sort an array // of dates using Radix Sort #include <bits/stdc++.h> using namespace std; // Utilitiy function to obtain // maximum date or month or year int getMax( int arr[][3], int n, int q) { int maxi = INT_MIN; for ( int i=0;i<n;i++){ maxi = max(maxi,arr[i][q]); } return maxi; } // A function to do counting sort of arr[] // according to given q i.e. // (0 for day, 1 for month, 2 for year) void sortDatesUtil( int arr[][3], int n, int q) { int maxi = getMax(arr,n,q); int p = 1; while (maxi>0){ //to extract last digit divide // by p then %10 // Store count of occurrences in cnt[] int cnt[10]={0}; for ( int i=0;i<n;i++) { cnt[(arr[i][q]/p)%10]++; } for ( int i=1;i<10;i++) { cnt[i]+=cnt[i-1]; } int ans[n][3]; for ( int i=n-1;i>=0;i--) { int lastDigit = (arr[i][q]/p)%10; // Build the output array for ( int j=0;j<3;j++) { ans[cnt[lastDigit]-1][j] =arr[i][j]; } cnt[lastDigit]--; } // Copy the output array to arr[], // so that arr[] now // contains sorted numbers // according to current digit for ( int i=0;i<n;i++) { for ( int j=0;j<3;j++) { arr[i][j] = ans[i][j]; } } // update p to get // the next digit p*=10; maxi/=10; } } // The main function that sorts // array of dates // using Radix Sort void sortDates( int dates[][3], int n) { // First sort by day sortDatesUtil(dates, n, 0); // Then by month sortDatesUtil(dates, n, 1); // Finally by year sortDatesUtil(dates, n, 2); } // A utility function to print an array void printArr( int arr[][3], int n) { for ( int i=0;i<6;i++) { for ( int j=0;j<3;j++) { cout<<arr[i][j]<< " " ; } cout<<endl; } } // Driver Code int main() { int dates[][3] = {{20, 1, 2014}, {25, 3, 2010}, { 3, 12, 2000}, {18, 11, 2000}, {19, 4, 2015}, { 9, 7, 2005}}; int n = sizeof (dates)/ sizeof (dates[0]); // Function Call sortDates(dates,n); cout<< "\nSorted Dates\n" ; printArr(dates,n); return 0; } |
Java
// Java program to sort an array // of dates using Radix Sort import java.util.*; class GFG{ // Utilitiy function to obtain // maximum date or month or year static int getMax( int arr[][], int n, int q) { int maxi = Integer.MIN_VALUE; for ( int i = 0 ; i < n; i++) { maxi = Math.max(maxi, arr[i][q]); } return maxi; } // A function to do counting sort of arr[] // according to given q i.e. // (0 for day, 1 for month, 2 for year) static void sortDatesUtil( int arr[][], int n, int q) { int maxi = getMax(arr,n,q); int p = 1 ; while (maxi > 0 ) { // to extract last digit divide // by p then %10 // Store count of occurrences in cnt[] int []cnt = new int [ 10 ]; for ( int i = 0 ; i < n; i++) { cnt[(arr[i][q]/p) % 10 ]++; } for ( int i = 1 ; i < 10 ; i++) { cnt[i] += cnt[i - 1 ]; } int [][]ans = new int [n][ 3 ]; for ( int i = n - 1 ; i >= 0 ; i--) { int lastDigit = (arr[i][q]/p) % 10 ; // Build the output array for ( int j = 0 ; j < 3 ; j++) { ans[cnt[lastDigit]- 1 ][j] =arr[i][j]; } cnt[lastDigit]--; } // Copy the output array to arr[], // so that arr[] now // contains sorted numbers // according to current digit for ( int i = 0 ; i < n; i++) { for ( int j = 0 ; j < 3 ; j++) { arr[i][j] = ans[i][j]; } } // update p to get // the next digit p *= 10 ; maxi /= 10 ; } } // The main function that sorts // array of dates // using Radix Sort static void sortDates( int dates[][], int n) { // First sort by day sortDatesUtil(dates, n, 0 ); // Then by month sortDatesUtil(dates, n, 1 ); // Finally by year sortDatesUtil(dates, n, 2 ); } // A utility function to print an array static void printArr( int arr[][], int n) { for ( int i = 0 ; i < 6 ; i++) { for ( int j = 0 ; j < 3 ; j++) { System.out.print(arr[i][j] + " " ); } System.out.println(); } } // Driver Code public static void main(String[] args) { int dates[][] = {{ 20 , 1 , 2014 }, { 25 , 3 , 2010 }, { 3 , 12 , 2000 }, { 18 , 11 , 2000 }, { 19 , 4 , 2015 }, { 9 , 7 , 2005 }}; int n = dates.length; // Function Call sortDates(dates,n); System.out.print( "\nSorted Dates\n" ); printArr(dates,n); } } // This code is contributed by Rajput-Ji |
Python3
# Python program to sort an array # of dates using Radix Sort import sys # Utilitiy function to obtain # maximum date or month or year def getMax(arr, n, q): maxi = sys.maxsize; for i in range (n): maxi = max (maxi, arr[i][q]); return maxi; # A function to do counting sort of arr # according to given q i.e. # (0 for day, 1 for month, 2 for year) def sortDatesUtil(arr, n, q): maxi = getMax(arr, n, q); p = 1 ; while (maxi > 0 ): # to extract last digit divide # by p then %10 # Store count of occurrences in cnt cnt = [ 0 for i in range ( 10 )]; for i in range (n): cnt[(arr[i][q] / / p) % 10 ] + = 1 ; for i in range ( 1 , 10 ): cnt[i] + = cnt[i - 1 ]; ans = [[ 0 for i in range ( 3 )] for j in range (n)]; for i in range (n - 1 , - 1 , - 1 ): lastDigit = (arr[i][q] / / p) % 10 ; # Build the output array for j in range ( 3 ): ans[cnt[lastDigit] - 1 ][j] = arr[i][j]; cnt[lastDigit] - = 1 ; # Copy the output array to arr, # so that arr now # contains sorted numbers # according to current digit for i in range (n): for j in range ( 3 ): arr[i][j] = ans[i][j]; # update p to get # the next digit p * = 10 ; maxi = maxi / / 10 ; # The main function that sorts # array of dates # using Radix Sort def sortDates(dates, n): # First sort by day sortDatesUtil(dates, n, 0 ); # Then by month sortDatesUtil(dates, n, 1 ); # Finally by year sortDatesUtil(dates, n, 2 ); # A utility function to print an array def printArr(arr, n): for i in range ( 6 ): for j in range ( 3 ): print (arr[i][j], end = " " ); print (); # Driver Code if __name__ = = '__main__' : dates = [[ 20 , 1 , 2014 ],[ 25 , 3 , 2010 ],[ 3 , 12 , 2000 ],[ 18 , 11 , 2000 ],[ 19 , 4 , 2015 ], [ 9 , 7 , 2005 ]] ; n = len (dates); # Function Call sortDates(dates, n); print ( "\nSorted Dates" ); printArr(dates, n); # This code is contributed by gauravrajput1 |
C#
// C# program to sort an array // of dates using Radix Sort using System; public class GFG { // Utilitiy function to obtain // maximum date or month or year static int getMax( int [,]arr, int n, int q) { int maxi = int .MinValue; for ( int i = 0; i < n; i++) { maxi = Math.Max(maxi, arr[i,q]); } return maxi; } // A function to do counting sort of []arr // according to given q i.e. // (0 for day, 1 for month, 2 for year) static void sortDatesUtil( int [,]arr, int n, int q) { int maxi = getMax(arr,n,q); int p = 1; while (maxi > 0) { // to extract last digit divide // by p then %10 // Store count of occurrences in cnt[] int []cnt = new int [10]; for ( int i = 0; i < n; i++) { cnt[(arr[i,q]/p) % 10]++; } for ( int i = 1; i < 10; i++) { cnt[i] += cnt[i - 1]; } int [,]ans = new int [n,3]; for ( int i = n - 1; i >= 0; i--) { int lastDigit = (arr[i,q]/p) % 10; // Build the output array for ( int j = 0; j < 3; j++) { ans[cnt[lastDigit]-1,j] =arr[i,j]; } cnt[lastDigit]--; } // Copy the output array to []arr, // so that []arr now // contains sorted numbers // according to current digit for ( int i = 0; i < n; i++) { for ( int j = 0; j < 3; j++) { arr[i,j] = ans[i,j]; } } // update p to get // the next digit p *= 10; maxi /= 10; } } // The main function that sorts // array of dates // using Radix Sort static void sortDates( int [,]dates, int n) { // First sort by day sortDatesUtil(dates, n, 0); // Then by month sortDatesUtil(dates, n, 1); // Finally by year sortDatesUtil(dates, n, 2); } // A utility function to print an array static void printArr( int [,]arr, int n) { for ( int i = 0; i < 6; i++) { for ( int j = 0; j < 3; j++) { Console.Write(arr[i, j] + " " ); } Console.WriteLine(); } } // Driver Code public static void Main(String[] args) { int [,]dates = {{20, 1, 2014}, {25, 3, 2010}, { 3, 12, 2000}, {18, 11, 2000}, {19, 4, 2015}, { 9, 7, 2005}}; int n = dates.GetLength(0); // Function Call sortDates(dates,n); Console.Write( "\nSorted Dates\n" ); printArr(dates,n); } } // This code is contributed by aashish1995. |
Javascript
<script> // javascript program to sort an array // of dates using Radix Sort // Utilitiy function to obtain // maximum date or month or year function getMax(arr , n , q) { var maxi = Number.MIN_VALUE; for ( var i = 0; i < n; i++) { maxi = Math.max(maxi, arr[i][q]); } return maxi; } // A function to do counting sort of arr // according to given q i.e. // (0 for day, 1 for month, 2 for year) function sortDatesUtil(arr , n , q) { var maxi = getMax(arr, n, q); var p = 1; while (maxi > 0) { // to extract last digit divide // by p then %10 // Store count of occurrences in cnt var cnt = Array(10).fill(0); for ( var i = 0; i < n; i++) { cnt[parseInt((arr[i][q] / p)) % 10]++; } for ( var i = 1; i < 10; i++) { cnt[i] += cnt[i - 1]; } var ans = Array(n).fill().map(()=>Array(3).fill(0)); for ( var i = n - 1; i >= 0; i--) { var lastDigit = parseInt((arr[i][q] / p) % 10); // Build the output array for ( var j = 0; j < 3; j++) { ans[cnt[lastDigit] - 1][j] = arr[i][j]; } cnt[lastDigit]--; } // Copy the output array to arr, // so that arr now // contains sorted numbers // according to current digit for ( var i = 0; i < n; i++) { for ( var j = 0; j < 3; j++) { arr[i][j] = ans[i][j]; } } // update p to get // the next digit p *= 10; maxi = parseInt(maxi/10); } } // The main function that sorts // array of dates // using Radix Sort function sortDates(dates , n) { // First sort by day sortDatesUtil(dates, n, 0); // Then by month sortDatesUtil(dates, n, 1); // Finally by year sortDatesUtil(dates, n, 2); } // A utility function to print an array function printArr(arr , n) { for ( var i = 0; i < 6; i++) { for ( var j = 0; j < 3; j++) { document.write(arr[i][j] + " " ); } document.write( "<br/>" ); } } // Driver Code var dates = [ [ 20, 1, 2014 ], [ 25, 3, 2010 ], [ 3, 12, 2000 ], [ 18, 11, 2000 ], [ 19, 4, 2015 ], [ 9, 7, 2005 ] ]; var n = dates.length; // Function Call sortDates(dates, n); document.write( "\nSorted Dates\n" ); printArr(dates, n); // This code is contributed by gauravrajput1 </script> |
Sorted Dates 18 11 2000 3 12 2000 9 7 2005 25 3 2010 20 1 2014 19 4 2015
This article is contributed by tpriyanshu. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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