How to efficiently sort a big list dates in 20’s

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>

Output

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