# Find the last remaining Character in the Binary String according to the given conditions

• Last Updated : 28 Mar, 2022

Given a binary string str consisting of only 0’s and 1’s. The following two operations can be performed on it:

1. One digit can delete another digit i.e. a 0 can delete a 1 and vice versa.
2. If at any moment, the entire string consists only 0’s or 1’s, then the respective digit is printed.

The task is to print the remaining digit which will be left at the end.
Examples:

Input: str = “100”
Output:
Explanation:
The 1st digit is 1 and it deletes the next digit 0.
The 2nd digit, i.e. 0, is deleted and now does not exists.
Now, the 3rd digit 0 deletes the 1st digit 1.
Since now only 0 is left, the output is 0.
Input: str = “10”
Output:

Approach: For this queue data structure is used. The following steps can be followed to compute the answer:

1. All the digits are added to the queue.
2. Two counters are maintained as an array of size 2 del[2] which will represent the number of floating deletes present for each digit.
3. The queue is traversed until there exits at least one digit of both the types.
4. Then for each digit in the queue if the delete counter for this digit is not 0, then it is deleted.
5. Else, the delete counter for the opposite digit is incremented and placed back into the queue.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach``#include ``using` `namespace` `std;` `string remainingDigit(string S, ``int` `N)``{``    `  `    ``// Delete counters for each to``    ``// count the deletes``    ``int` `del[] = { 0, 0 };` `    ``// Counters to keep track``    ``// of characters left from each type``    ``int` `count[] = { 0, 0 };` `    ``// Queue to simulate the process``    ``queue<``int``> q;` `    ``// Initializing the queue``    ``for` `(``int` `i = 0; i < N; i++)``    ``{``        ``int` `x = S[i] == ``'1'` `? 1 : 0;``        ``count[x]++;``        ``q.push(x);``    ``}` `    ``// Looping till at least 1 digit is``    ``// left from both the type``    ``while` `(count[0] > 0 && count[1] > 0)``    ``{``        ``int` `t = q.front();``        ``q.pop();` `        ``// If there is a floating delete for``        ``// current character we will``        ``// delete it and move forward otherwise``        ``// we will increase delete counter for``        ``// opposite digit``        ``if` `(del[t] > 0)``        ``{``            ``del[t]--;``            ``count[t]--;``        ``}``        ``else``        ``{``            ``del[t ^ 1]++;``            ``q.push(t);``        ``}``    ``}` `    ``// If 0 are left``    ``// then answer is 0 else``    ``// answer is 1``    ``if` `(count[0] > 0)``        ``return` `"0"``;``    ``return` `"1"``;``}` `// Driver Code``int` `main()``{` `    ``// Input String``    ``string S = ``"1010100100000"``;` `    ``// Length of String``    ``int` `N = S.length();` `    ``// Printing answer``    ``cout << remainingDigit(S, N);``}` `// This code is contributed by tufan_gupta2000`

## Java

 `// Java implementation of the above approach` `import` `java.util.*;` `public` `class` `GfG {``    ``private` `static` `String remainingDigit(String S, ``int` `N)``    ``{``        ``// Converting string to array``        ``char` `c[] = S.toCharArray();` `        ``// Delete counters for each to``        ``// count the deletes``        ``int` `del[] = { ``0``, ``0` `};` `        ``// Counters to keep track``        ``// of characters left from each type``        ``int` `count[] = { ``0``, ``0` `};` `        ``// Queue to simulate the process``        ``Queue q = ``new` `LinkedList<>();` `        ``// Initializing the queue``        ``for` `(``int` `i = ``0``; i < N; i++) {``            ``int` `x = c[i] == ``'1'` `? ``1` `: ``0``;``            ``count[x]++;``            ``q.add(x);``        ``}` `        ``// Looping till at least 1 digit is``        ``// left from both the type``        ``while` `(count[``0``] > ``0` `&& count[``1``] > ``0``) {``            ``int` `t = q.poll();` `            ``// If there is a floating delete for``            ``// current character we will``            ``// delete it and move forward otherwise``            ``// we will increase delete counter for``            ``// opposite digit``            ``if` `(del[t] > ``0``) {``                ``del[t]--;``                ``count[t]--;``            ``}``            ``else` `{``                ``del[t ^ ``1``]++;``                ``q.add(t);``            ``}``        ``}` `        ``// If 0 are left``        ``// then answer is 0 else``        ``// answer is 1``        ``if` `(count[``0``] > ``0``)``            ``return` `"0"``;``        ``return` `"1"``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{` `        ``// Input String``        ``String S = ``"1010100100000"``;` `        ``// Length of String``        ``int` `N = S.length();` `        ``// Printing answer``        ``System.out.print(remainingDigit(S, N));``    ``}``}`

## Python3

 `# Python3 implementation of the above approach``from` `collections ``import` `deque;` `def` `remainingDigit(S, N):``    ` `    ``# Converting string to array``    ``c ``=` `[i ``for` `i ``in` `S]` `    ``# Delete counters for each to``    ``# count the deletes``    ``de ``=` `[``0``, ``0``]` `    ``# Counters to keep track``    ``# of characters left from each type``    ``count ``=` `[``0``, ``0``]` `    ``# Queue to simulate the process``    ``q ``=` `deque()` `    ``# Initializing the queue``    ``for` `i ``in` `c:``        ``x ``=` `0``        ``if` `i ``=``=` `'1'``:``            ``x ``=` `1``        ``count[x] ``+``=` `1``        ``q.append(x)` `    ``# Looping till at least 1 digit is``    ``# left from both the type``    ``while` `(count[``0``] > ``0` `and` `count[``1``] > ``0``):``        ``t ``=` `q.popleft()` `        ``# If there is a floating delete for``        ``# current character we will``        ``# delete it and move forward otherwise``        ``# we will increase delete counter for``        ``# opposite digit``        ``if` `(de[t] > ``0``):``            ``de[t] ``-``=` `1``            ``count[t] ``-``=` `1``        ``else``:``            ``de[t ^ ``1``] ``+``=` `1``            ``q.append(t)` `    ``# If 0 are left``    ``# then answer is 0 else``    ``# answer is 1``    ``if` `(count[``0``] > ``0``):``        ``return` `"0"``    ``return` `"1"` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:` `    ``# Input String``    ``S ``=` `"1010100100000"` `    ``# Length of String``    ``N ``=` `len``(S)` `    ``# Printing answer``    ``print``(remainingDigit(S, N))` `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation of the above approach``using` `System;``using` `System.Collections.Generic;` `public` `class` `GfG``{``    ``private` `static` `String remainingDigit(String S, ``int` `N)``    ``{``        ``// Converting string to array``        ``char` `[]c = S.ToCharArray();` `        ``// Delete counters for each to``        ``// count the deletes``        ``int` `[]del = { 0, 0 };` `        ``// Counters to keep track``        ``// of characters left from each type``        ``int` `[]count = { 0, 0 };` `        ``// Queue to simulate the process``        ``List<``int``> q = ``new` `List<``int``>();` `        ``// Initializing the queue``        ``for` `(``int` `i = 0; i < N; i++)``        ``{``            ``int` `x = c[i] == ``'1'` `? 1 : 0;``            ``count[x]++;``            ``q.Add(x);``        ``}` `        ``// Looping till at least 1 digit is``        ``// left from both the type``        ``while` `(count[0] > 0 && count[1] > 0)``        ``{``            ``int` `t = q[0];``            ``q.RemoveAt(0);` `            ``// If there is a floating delete for``            ``// current character we will``            ``// delete it and move forward otherwise``            ``// we will increase delete counter for``            ``// opposite digit``            ``if` `(del[t] > 0)``            ``{``                ``del[t]--;``                ``count[t]--;``            ``}``            ``else``            ``{``                ``del[t ^ 1]++;``                ``q.Add(t);``            ``}``        ``}` `        ``// If 0 are left``        ``// then answer is 0 else``        ``// answer is 1``        ``if` `(count[0] > 0)``            ``return` `"0"``;``        ``return` `"1"``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String []args)``    ``{` `        ``// Input String``        ``String S = ``"1010100100000"``;` `        ``// Length of String``        ``int` `N = S.Length;` `        ``// Printing answer``        ``Console.Write(remainingDigit(S, N));``    ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

`0`

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

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