Given a large number, n (having number digits up to 10^6) and various queries of the below form :
Query(l, r) : find if the sub-string between the indices l and r (Both inclusive) are divisible by 11.
Examples:
Input: n = 122164154695 Queries: l = 0 r = 3, l = 1 r = 2, l = 5 r = 9, l = 0 r = 11 Output: True False False True Explanation: In the first query, 1221 is divisible by 11 In the second query, 22 is divisible by 11 and so on.
We know that any number is divisible by 11 if the difference between the sum of odd indexed digits and the sum of even indexed digits is divisible by 11, i.e.,
Sum(digits at odd places) – Sum(digits at even places) should be divisible by 11.
Hence, the idea is to pre-process an auxiliary array that would store the sum of digits at odd and even places.
To evaluate a query we can use the auxiliary array to answer it in O(1).
C++
// C++ program to check divisibility by 11 in // substrings of a number string #include <iostream> using namespace std;
const int MAX = 1000005;
// To store sums of even and odd digits struct OddEvenSums
{ // Sum of even placed digits
int e_sum;
// Sum of odd placed digits
int o_sum;
}; // Auxiliary array OddEvenSums sum[MAX]; // Utility function to evaluate a character's // integer value int toInt( char x)
{ return int (x) - 48;
} // This function receives the string representation // of the number and precomputes the sum array void preCompute(string x)
{ // Initialize everb
sum[0].e_sum = sum[0].o_sum = 0;
// Add the respective digits depending on whether
// they're even indexed or odd indexed
for ( int i=0; i<x.length(); i++)
{
if (i%2==0)
{
sum[i+1].e_sum = sum[i].e_sum+toInt(x[i]);
sum[i+1].o_sum = sum[i].o_sum;
}
else
{
sum[i+1].o_sum = sum[i].o_sum+toInt(x[i]);
sum[i+1].e_sum = sum[i].e_sum;
}
}
} // This function receives l and r representing // the indices and prints the required output bool query( int l, int r)
{ int diff = (sum[r+1].e_sum - sum[r+1].o_sum) -
(sum[l].e_sum - sum[l].o_sum);
return (diff%11==0);
} //driver function to check the program int main()
{ string s = "122164154695" ;
preCompute(s);
cout << query(0, 3) << endl;
cout << query(1, 2) << endl;
cout << query(5, 9) << endl;
cout << query(0, 11) << endl;
return 0;
} |
Java
// Java program to check divisibility by 11 in // subStrings of a number String class GFG
{ static int MAX = 1000005 ;
// To store sums of even and odd digits static class OddEvenSums
{ // Sum of even placed digits
int e_sum;
// Sum of odd placed digits
int o_sum;
}; // Auxiliary array static OddEvenSums []sum = new OddEvenSums[MAX];
// Utility function to evaluate a character's // integer value static int toInt( char x)
{ return x - 48 ;
} // This function receives the String representation // of the number and precomputes the sum array static void preCompute(String x)
{ // Initialize everb
sum[ 0 ].e_sum = sum[ 0 ].o_sum = 0 ;
// Add the respective digits depending on whether
// they're even indexed or odd indexed
for ( int i = 0 ; i < x.length(); i++)
{
if (i % 2 == 0 )
{
sum[i + 1 ].e_sum = sum[i].e_sum + toInt(x.charAt(i));
sum[i + 1 ].o_sum = sum[i].o_sum;
}
else
{
sum[i + 1 ].o_sum = sum[i].o_sum + toInt(x.charAt(i));
sum[i + 1 ].e_sum = sum[i].e_sum;
}
}
} // This function receives l and r representing // the indices and prints the required output static boolean query( int l, int r)
{ int diff = (sum[r + 1 ].e_sum - sum[r + 1 ].o_sum) -
(sum[l].e_sum - sum[l].o_sum);
return (diff % 11 == 0 );
} //driver function to check the program public static void main(String[] args)
{ for ( int i = 0 ; i < MAX; i++) {
sum[i] = new OddEvenSums();
}
String s = "122164154695" ;
preCompute(s);
System.out.println(query( 0 , 3 ) ? 1 : 0 );
System.out.println(query( 1 , 2 ) ? 1 : 0 );
System.out.println(query( 5 , 9 ) ? 1 : 0 );
System.out.println(query( 0 , 11 ) ? 1 : 0 );
} } // This code is contributed by Rajput-Ji |
Python3
# Python3 program to check divisibility by # 11 in subStrings of a number String MAX = 1000005
# To store sums of even and odd digits class OddEvenSums:
def __init__( self , e_sum, o_sum):
# Sum of even placed digits
self .e_sum = e_sum
# Sum of odd placed digits
self .o_sum = o_sum
sum = [OddEvenSums( 0 , 0 ) for i in range ( MAX )]
# This function receives the String # representation of the number and # precomputes the sum array def preCompute(x):
# Initialize everb
sum [ 0 ].e_sum = sum [ 0 ].o_sum = 0
# Add the respective digits
# depending on whether
# they're even indexed or
# odd indexed
for i in range ( len (x)):
if (i % 2 = = 0 ):
sum [i + 1 ].e_sum = ( sum [i].e_sum +
int (x[i]))
sum [i + 1 ].o_sum = sum [i].o_sum
else :
sum [i + 1 ].o_sum = ( sum [i].o_sum +
int (x[i]))
sum [i + 1 ].e_sum = sum [i].e_sum
# This function receives l and r representing # the indices and prints the required output def query(l, r):
diff = (( sum [r + 1 ].e_sum -
sum [r + 1 ].o_sum) -
( sum [l].e_sum -
sum [l].o_sum))
if (diff % 11 = = 0 ):
return True
else :
return False
# Driver code if __name__ = = "__main__" :
s = "122164154695"
preCompute(s)
print ( 1 if query( 0 , 3 ) else 0 )
print ( 1 if query( 1 , 2 ) else 0 )
print ( 1 if query( 5 , 9 ) else 0 )
print ( 1 if query( 0 , 11 ) else 0 )
# This code is contributed by rutvik_56 |
C#
// C# program to check // divisibility by 11 in // subStrings of a number String using System;
class GFG{
static int MAX = 1000005;
// To store sums of even // and odd digits public class OddEvenSums
{ // Sum of even placed digits
public int e_sum;
// Sum of odd placed digits
public int o_sum;
}; // Auxiliary array static OddEvenSums []sum =
new OddEvenSums[MAX];
// Utility function to // evaluate a character's // integer value static int toInt( char x)
{ return x - 48;
} // This function receives the // String representation of the // number and precomputes the sum array static void preCompute(String x)
{ // Initialize everb
sum[0].e_sum = sum[0].o_sum = 0;
// Add the respective digits
// depending on whether they're
// even indexed or odd indexed
for ( int i = 0; i < x.Length; i++)
{
if (i % 2 == 0)
{
sum[i + 1].e_sum = sum[i].e_sum +
toInt(x[i]);
sum[i + 1].o_sum = sum[i].o_sum;
}
else
{
sum[i + 1].o_sum = sum[i].o_sum +
toInt(x[i]);
sum[i + 1].e_sum = sum[i].e_sum;
}
}
} // This function receives l and r // representing the indices and // prints the required output static bool query( int l, int r)
{ int diff = (sum[r + 1].e_sum -
sum[r + 1].o_sum) -
(sum[l].e_sum -
sum[l].o_sum);
return (diff % 11 == 0);
} // Driver function to check the program public static void Main(String[] args)
{ for ( int i = 0; i < MAX; i++)
{
sum[i] = new OddEvenSums();
}
String s = "122164154695" ;
preCompute(s);
Console.WriteLine(query(0, 3) ? 1 : 0);
Console.WriteLine(query(1, 2) ? 1 : 0);
Console.WriteLine(query(5, 9) ? 1 : 0);
Console.WriteLine(query(0, 11) ? 1 : 0);
} } // This code is contributed by gauravrajput1 |
Javascript
<script> // Javascript program to check divisibility by 11 in // subStrings of a number String let MAX = 1000005; // To store sums of even and odd digits class OddEvenSums { constructor()
{
this .e_sum = 0;
this .o_sum = 0;
}
} // Auxiliary array let sum = new Array(MAX);
// Utility function to evaluate a character's // integer value function toInt(x)
{ return x.charCodeAt(0) - 48;
} // This function receives the String representation // of the number and precomputes the sum array function preCompute(x)
{ // Initialize everb
sum[0].e_sum = sum[0].o_sum = 0;
// Add the respective digits depending on whether
// they're even indexed or odd indexed
for (let i = 0; i < x.length; i++)
{
if (i % 2 == 0)
{
sum[i + 1].e_sum = sum[i].e_sum + parseInt(x[i]);
sum[i + 1].o_sum = sum[i].o_sum;
}
else
{
sum[i + 1].o_sum = sum[i].o_sum + parseInt(x[i]);
sum[i + 1].e_sum = sum[i].e_sum;
}
}
} // This function receives l and r representing // the indices and prints the required output function query(l,r)
{ let diff = (sum[r + 1].e_sum - sum[r + 1].o_sum) -
(sum[l].e_sum - sum[l].o_sum);
return (diff % 11 == 0);
} // driver function to check the program for (let i = 0; i < MAX; i++) {
sum[i] = new OddEvenSums();
} let s = "122164154695" ;
preCompute(s); document.write((query(0, 3) ? 1 : 0)+ "<br>" );
document.write((query(1, 2) ? 1 : 0)+ "<br>" );
document.write((query(5, 9) ? 1 : 0)+ "<br>" );
document.write((query(0, 11) ? 1 :0)+ "<br>" );
// This code is contributed by unknown2108 </script> |
Output:
1 1 0 1
Recommended Articles