Given a numeric string S representing a positive decimal integer, the task is to find the minimum number of positive Deci-Binary numbers required to obtain the sum S.
Deci-Binary Numbers: Decimal numbers consisting of only 0s and 1s as its digits.
Examples:
Input: S = “31”
Output: 3
Explanation: S can be represented as the sum of minimum of 3 Deci-Binary numbers {10, 10, 11}.Input: S = “82734”
Output: 8
Explanation: S can be represented as sum minimum of 8 Deci-Binary numbers {11111, 11111, 10111, 10101, 10100, 10100, 10100, 10000}.
Approach: The given problem can be solved based on the following observations:
Suppose X Deci-Binary numbers are needed to obtain the sum S. To make the sum of X Deci-Binary numbers at i-th place equal to a digit d in S, there must be exactly d Deci-Binary numbers among X numbers having 1 at the ith position.
Therefore, the minimum number of Deci-Binary numbers required to obtain a sum S is equal to the maximum value of any of the digits of S.
Therefore, to solve the problem, iterate over the characters of the string S and find the maximum digit present in it.
Below is the implementation of the above approach:
// C++ Program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the count of minimum // Deci-Binary numbers required to obtain S int minimum_deci_binary_number(string s)
{ // Stores the minimum count
int m = INT_MIN;
// Iterate over the string s
for ( int i = 0; i < s.size(); i++) {
// Convert the char to its
// equivalent integer
int temp = s[i] - '0' ;
// If current character is
// the maximum so far
if (temp > m) {
// Update the maximum digit
m = temp;
}
}
// Print the required result
return m;
} // Driver Code int main()
{ string S = "31" ;
cout << minimum_deci_binary_number(S);
return 0;
} |
// Java program to implement // the above approach class GFG{
// Function to find the count of minimum // Deci-Binary numbers required to obtain S static int minimum_deci_binary_number(String s)
{ // Stores the minimum count
int m = Integer.MIN_VALUE;
// Iterate over the string s
for ( int i = 0 ; i < s.length(); i++)
{
// Convert the char to its
// equivalent integer
int temp = s.charAt(i) - '0' ;
// If current character is
// the maximum so far
if (temp > m)
{
// Update the maximum digit
m = temp;
}
}
// Print the required result
return m;
} // Driver Code public static void main (String[] args)
{ String S = "31" ;
System.out.println(minimum_deci_binary_number(S));
} } // This code is contributed by AnkThon |
# Python3 Program to implement # the above approach # Function to find the count of minimum # Deci-Binary numbers required to obtain S def minimum_deci_binary_number(s):
# Stores the minimum count
m = - 10 * * 19
# Iterate over the string s
for i in range ( len (s)):
# Convert the char to its
# equivalent integer
temp = ord (s[i]) - ord ( '0' )
# If current character is
# the maximum so far
if (temp > m):
# Update the maximum digit
m = temp
# Print required result
return m
# Driver Code if __name__ = = '__main__' :
S = "31"
print (minimum_deci_binary_number(S))
# This code is contributed by mohit kumar 29 |
// C# program to implement // the above approach using System;
class GFG
{ // Function to find the count of minimum
// Deci-Binary numbers required to obtain S
static int minimum_deci_binary_number( string s)
{
// Stores the minimum count
int m = int .MinValue;
// Iterate over the string s
for ( int i = 0; i < s.Length; i++)
{
// Convert the char to its
// equivalent integer
int temp = s[i] - '0' ;
// If current character is
// the maximum so far
if (temp > m)
{
// Update the maximum digit
m = temp;
}
}
// Print the required result
return m;
}
// Driver Code
public static void Main (String[] args)
{
string S = "31" ;
Console.WriteLine(minimum_deci_binary_number(S));
}
} // This code is contributed by AnkThon |
<script> // JavaScript program to implement // the above approach // Function to find the count of minimum // Deci-Binary numbers required to obtain S function minimum_deci_binary_number(s)
{ // Stores the minimum count
let m = Number.MIN_VALUE;
// Iterate over the string s
for (let i = 0; i < s.length; i++)
{
// Convert the char to its
// equivalent integer
let temp = s[i] - '0' ;
// If current character is
// the maximum so far
if (temp > m)
{
// Update the maximum digit
m = temp;
}
}
// Print the required result
return m;
} // Driver code let S = "31" ;
document.write(minimum_deci_binary_number(S));
</script> |
3
Time Complexity: O(N)
Auxiliary Space: O(1)