Generate N sized binary string with prefix S and is lexicographically smallest possible

Given a binary string S, the task is to make a binary string of size N from the given string S (don't change the position of characters) following the below conditions:

• The prefix of the string is S.
• If is the lexicographically smallest possible.
• Absolute difference between the number of 1s and 0s is minimum.

Examples:

Input: S = "101", N = 8
Output: 10100011
Explanation: The prefix of output string is same as the string S. 
The absolute difference between number of 0s and 1s is 0.
It is the lexicographically smallest possible which follows all the given condition.

Input: S = "001", N = 7
Output: 0010011 

Approach: This problem can be solved by using the Greedy Approach based on the following idea:

In the case of a binary string, a string starting with '0' is lexicographically smaller than the one starting with '1'.
So, firstly make S the prefix and then find how many more 0s and 1s can be added. To make it lexicographically smallest, add all the 0s first and then the 1s. 

Follow the steps mentioned below to implement the approach.

• Count numbers of 1's and 0's and store them (say in count1 and count0 respectively).
• Find the difference between (say g) count0 and count1 and between N and length of S (say in a variable l).
• Calculate the size which we need to increment in string length to make string length = N and store it in l.
• Now add as many 0s (which will be (l-g)/2) such that the number of 0 becomes the same as N/2 and then add 1s for the remaining places.

Below is the implementation of the above approach:

#include <iostream>

using namespace std;

// Function to build string
string find_string(int n, string s)
{
    // Declaring variable
    int count0 = 0, count1 = 0;

    // Check number of 1's and 0's
    for (int i = 0; i < s.length(); i++) {
        if (s[i] == '0') {
            count0++;
        }
        else {
            count1++;
        }
    }
    string sb = s;

    // Store difference in number of 1's
    // and 0's
    int g = count0 - count1;

    // l store the value that how much 0's
    // or 1's we need to add in string
    int l = n - s.length();
    l -= g;

    // u store the count of
    // number of 0's we need to insert
    int u = l / 2;
    while (u > 0) {
        sb += '0';
        u--;
    }
    if (l % 2 != 0) {
        sb += '0';
    }

    while (sb.length() < n) {
        sb += '1';
    }

    // Return result
    return sb;
}

// Driver code
int main()
{
    int N = 7;
    string S = "001";

    // Function call
    cout << find_string(N, S);
}

// This code is contributed by phasing17

// Java program for above approach

import java.io.*;
import java.lang.*;

class GFG {

    // Function to build string
    String find_string(int n, String s)
    {
        // Declaring variable
        int count0 = 0, count1 = 0;

        // Check number of 1's and 0's
        for (int i = 0; i < s.length(); i++) {
            if (s.charAt(i) == '0') {
                count0++;
            }
            else {
                count1++;
            }
        }
        String sb = s;

        // Store difference in number of 1's
        // and 0's
        int g = count0 - count1;

        // l store the value that how much 0's
        // or 1's we need to add in string
        int l = n - s.length();
        l -= g;

        // u store the count of
        // number of 0's we need to insert
        int u = l / 2;
        while (u > 0) {
            sb += '0';
            u--;
        }
        if (l % 2 != 0) {
            sb += '0';
        }

        while (sb.length() < n) {
            sb += '1';
        }

        // Return result
        return sb;
    }

    // Driver code
    public static void main(String[] args)
    {
        int N = 7;
        String S = "001";
        GFG g = new GFG();

        // Function call
        System.out.println(g.find_string(N, S));
    }
}

# Python program for above approach

# Function to build string
def find_string(n, s):
  
    # Declaring variable
    count0 = 0
    count1 = 0

    # Check number of 1's and 0's
    for i in range(len(s)):
        if (s[i] == '0'):
            count0 += 1
        else:
            count1 += 1
    sb = s

    # Store difference in number of 1's
    # and 0's
    g = count0 - count1

    # l store the value that how much 0's
    # or 1's we need to add in string
    l = n - len(s)
    l -= g

    # u store the count of
    # number of 0's we need to insert
    u = l // 2
    while (u > 0):
        sb += '0'
        u -= 1
    if (l % 2 != 0):
        sb += '0'

    while (len(sb) < n):
        sb += '1'

    # Return result
    return sb

# Driver Code
N = 7
S = "001"

# Function call
print(find_string(N, S))

# This code is contributed by shinjanpatra

// C# code to implement the above approach
using System;

class GFG {

    // Function to build string
    string find_string(int n, string s)
    {
        // Declaring variable
        int count0 = 0, count1 = 0;

        // Check number of 1's and 0's
        for (int i = 0; i < s.Length; i++) {
            if (s[i] == '0') {
                count0++;
            }
            else {
                count1++;
            }
        }
        string sb = s;

        // Store difference in number of 1's
        // and 0's
        int g = count0 - count1;

        // l store the value that how much 0's
        // or 1's we need to add in string
        int l = n - s.Length;
        l -= g;

        // u store the count of
        // number of 0's we need to insert
        int u = l / 2;
        while (u > 0) {
            sb += '0';
            u--;
        }
        if (l % 2 != 0) {
            sb += '0';
        }

        while (sb.Length < n) {
            sb += '1';
        }

        // Return result
        return sb;
    }

// Driver code
public static void Main()
{
        int N = 7;
        string S = "001";
        GFG g = new GFG();

        // Function call
        Console.Write(g.find_string(N, S));
}
}

// This code is contributed by sonjoy_62.

<script>
// Javascript program for above approach

// Function to build string
function find_string(n, s)
{
  
    // Declaring variable
    let count0 = 0;
    let count1 = 0;

    // Check number of 1's and 0's
    for (let i = 0; i < s.length; i++) {
        if (s[i] == '0') {
            count0++;
        }
        else {
            count1++;
        }
    }
    let sb = s;

    // Store difference in number of 1's
    // and 0's
    let g = count0 - count1;

    // l store the value that how much 0's
    // or 1's we need to add in string
    let l = n - s.length;
    l -= g;

    // u store the count of
    // number of 0's we need to insert
    let u = Math.floor(l / 2);
    while (u > 0) {
        sb += '0';
        u--;
    }
    if (l % 2 != 0) {
        sb += '0';
    }

    while (sb.length < n) {
        sb += '1';
    }

    // Return result
    return sb;
}

// Driver Code
let N = 7;
let S = "001";

// Function call
document.write(find_string(N, S));

// This code is contributed by Samim Hossain Mondal.
</script>

0010011

Time Complexity: O(N)
Auxiliary Space: O(1)