Algorithm
problem link- https://www.spoj.com/problems/LASTDIG2/
LASTDIG2 - The last digit re-visited
Pappu was doing the work of his math class about three days but he is tired of make operations a lot and he should deliver his task tomorrow. His math’s teacher gives two numbers a and b. The problem consist in find the last digit of the potency of base a and index b. Help Pappu with his problem. You are given two integer numbers: the base a (number of digits d, such that 1 <= d <= 1000) and the index b (0 <= b <= 922*10^15). You have to find the last digit of a^b.
Input
The first line of input contains an integer t, the number of test cases (t <= 30). t test cases follow. For each test case will appear a and b separated by space.
Output
For each test case output an integer per line representing the result.
Example
Input: 3 3 10 6 2 150 53 Output: 9 6 0
Code Examples
#1 Code Example with Python Programming
Code -
Python Programming
def power(a, b):
if b == 0:
return 1
if b % 2 == 1:
return power(a, b - 1) * a % 10
half = power(a, b >> 1)
return half * half % 10
T = int(input())
for i in range(T):
a, b = map(int, raw_input().split())
print(power(a % 10, b))Input
3 10
6 2
150 53
Output
6
0
#2 Code Example with Java Programming
Code -
Java Programming
import java.util.*;
import java.lang.Math.*;
import java.math.*;
class lastdig{
public static void main(String[] args){
Scanner scan = new Scanner(System.in);
int testCases = scan.nextInt();
BigInteger a = new BigInteger("0");
BigInteger b = new BigInteger("0");
BigInteger lastDigit = new BigInteger("0");
for(int i = 0; i < testCases; i++){
a = scan.nextBigInteger();
b = scan.nextBigInteger();
lastDigit = b.modPow(a, BigInteger.valueOf(10));
System.out.println(lastDigit);
}
}}Input
3 10
6 2
150 53
Output
6
0
#3 Code Example with C++ Programming
Code -
C++ Programming
#include <iostream>
using namespace std;
#define ll long long
int bigmod(ll a, ll b)
{
if(b==0) return 1;
else{
int x = bigmod(a, b/2);
x = (x*x)%10;
if(b%2==1) x = (x*a)%10;
return x;
}
}
int main() {
ll t,a,b;
string s;
cin>>t;
while(t--){
cin>>s>>b;
a = s[s.size()-1]-'0';
cout<<bigmod(a,b)<<endl;
}
return 0;
} Input
3 10
6 2
150 53
Output
6
0
Demonstration
SPOJ Solution-The last digit re-visited-Solution in C, C++, Java, Python