Find the unit place digit of sum of N factorials
Given a number N, the task is to find units place digit of the first N natural numbers factorials, i.e. 1!+2!+3!+….N! where N<=10e18.
Examples:
Input: n = 2 Output: 3 1! + 2! = 3 Last digit is 3 Input: n = 3 Output: 9 1! + 2! + 3! = 9 Last digit is 9
Naive Approach: In this approach, simply calculate factorial of each number and find sum of these. Finally get the unit place digit of sum. This will take a lot of time and unnecessary calculations.
Efficient Approach: In this approach, only unit’s digit of N is to be calculated in the range [1, 5], because:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
so on.
As 5!=120, and factorial of number greater than 5 have trailing zeros. So, N>=5 doesn’t contribrute in unit place while doing sum.
Therefore:
if (n < 5)
ans = (1 ! + 2 ! +..+ n !) % 10;
else
ans = (1 ! + 2 ! + 3 ! + 4 !) % 10;
Note : We know (1! + 2! + 3! + 4!) % 10 = 3
So we always return 3 when n is greater
than 4.Below is the implementation of the efficient approach:
C++
// C++ program to find the unit place digit// of the first N natural numbers factorials#include <iostream>using namespace std;// Function to find the unit's place digitint get_unit_digit(long long int N){ // Let us write for cases when // N is smaller than or equal // to 4. if (N == 0 || N == 1) return 1; else if (N == 2) return 3; else if (N == 3) return 9; // We know following // (1! + 2! + 3! + 4!) % 10 = 3 else // (N >= 4) return 3;}// Driver codeint main(){ long long int N = 1; for (N = 0; N <= 10; N++) cout << "For N = " << N << " : " << get_unit_digit(N) << endl; return 0;} |
Java
// Java program to find the unit place digit// of the first N natural numbers factorialsimport java.io.*;class GFG { // Function to find the unit's place digitstatic int get_unit_digit( int N){ // Let us write for cases when // N is smaller than or equal // to 4. if (N == 0 || N == 1) return 1; else if (N == 2) return 3; else if (N == 3) return 9; // We know following // (1! + 2! + 3! + 4!) % 10 = 3 else // (N >= 4) return 3;}// Driver code public static void main (String[] args) { int N = 1; for (N = 0; N <= 10; N++) System.out.println ("For N = " + N + " : " + get_unit_digit(N)); }}//This Code is Contributed by ajit |
Python3
# Python3 program to find the unit# place digit of the first N natural# numbers factorials# Function to find the unit's place digitdef get_unit_digit(N): # Let us write for cases when # N is smaller than or equal # to 4. if (N == 0 or N == 1): return 1 elif (N == 2): return 3 elif(N == 3): return 9 # We know following # (1! + 2! + 3! + 4!) % 10 = 3 else: return 3# Driver codeN = 1for N in range(11): print("For N = ", N, ":", get_unit_digit(N), sep = ' ')# This code is contributed# by sahilshelangia |
C#
// C# program to find the unit// place digit of the first N// natural numbers factorialsusing System;class GFG{ // Function to find the unit's// place digitstatic int get_unit_digit( int N){ // Let us write for cases when // N is smaller than or equal // to 4. if (N == 0 || N == 1) return 1; else if (N == 2) return 3; else if (N == 3) return 9; // We know following // (1! + 2! + 3! + 4!) % 10 = 3 else // (N >= 4) return 3;}// Driver codestatic public void Main (){ int N = 1; for (N = 0; N <= 10; N++) Console.WriteLine ("For N = " + N + " : " + get_unit_digit(N));}}// This Code is Contributed by akt_mit |
PHP
<?php// PHP program to find the unit place digit// of the first N natural numbers factorials// Function to find the unit's place digitfunction get_unit_digit($N){ // Let us write for cases when // N is smaller than or equal // to 4. if ($N == 0 || $N == 1) return 1; else if ($N == 2) return 3; else if ($N == 3) return 9; // We know following // (1! + 2! + 3! + 4!) % 10 = 3 else // (N >= 4) return 3;}// Driver code$N = 1;for ($N = 0; $N <= 10; $N++) echo "For N = " . $N. " : " . get_unit_digit($N) . "\n";// This code is contributed// by ChitraNayal?> |
Javascript
<script>// Javascript program to find the unit place digit// of the first N natural numbers factorials// Function to find the unit's place digitfunction get_unit_digit(N){ // Let us write for cases when // N is smaller than or equal // to 4. if (N == 0 || N == 1) return 1; else if (N == 2) return 3; else if (N == 3) return 9; // We know following // (1! + 2! + 3! + 4!) % 10 = 3 else // (N >= 4) return 3;}// Driver codevar N = 1;for (N = 0; N <= 10; N++) document.write( "For N = " + N + " : " + get_unit_digit(N)+"<br>") </script> |
Output:
For N = 0 : 1 For N = 1 : 1 For N = 2 : 3 For N = 3 : 9 For N = 4 : 3 For N = 5 : 3 For N = 6 : 3 For N = 7 : 3 For N = 8 : 3 For N = 9 : 3 For N = 10 : 3
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