# Print N-bit binary numbers having more 1’s than 0’s in all prefixes

Given a positive integer n, print all n-bit binary numbers having more 1’s than 0’s for any prefix of the number.

Examples:

```Input : n = 2
Output : 11 10

Input : n = 4
Output : 1111 1110 1101 1100 1011 1010```

A simple but not efficient solution will be to generate all N-bit binary numbers and print those numbers that satisfy the conditions. The time complexity of this solution is exponential.

An efficient solution is to generate only those N-bit numbers that satisfy the given conditions. We use recursion, At each point in the recursion, we append 0 and 1 to the partially formed number and recur with one less digit.

Implementation:

## C++

 `// C++ program to print all N-bit binary` `#include ` `using` `namespace` `std;`   `/* function to generate n  digit numbers*/` `void` `printRec(string number, ``int` `extraOnes,` `              ``int` `remainingPlaces)` `{` `    ``/* if number generated */` `    ``if` `(0 == remainingPlaces) {` `        ``cout << number << ``" "``;` `        ``return``;` `    ``}`   `    ``/* Append 1 at the current number and reduce` `       ``the remaining places by one */` `    ``printRec(number + ``"1"``, extraOnes + 1,` `             ``remainingPlaces - 1);`   `    ``/* If more ones than zeros, append 0 to the` `       ``current number and reduce the remaining` `       ``places by one*/` `    ``if` `(0 < extraOnes)` `        ``printRec(number + ``"0"``, extraOnes - 1,` `                 ``remainingPlaces - 1);` `}`   `void` `printNums(``int` `n)` `{` `    ``string str = ``""``;` `    ``printRec(str, 0, n);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 4;` `  `  `    ``// Function call` `    ``printNums(n);` `    ``return` `0;` `}`

## Java

 `// Java program to print all N-bit binary` `import` `java.io.*;`   `class` `GFG {` `    ``// function to generate n digit numbers` `    ``static` `void` `printRec(String number, ` `                         ``int` `extraOnes,` `                         ``int` `remainingPlaces)` `    ``{` `        ``// if number generated` `        ``if` `(``0` `== remainingPlaces) {` `            ``System.out.print(number + ``" "``);` `            ``return``;` `        ``}`   `        ``// Append 1 at the current number and` `        ``// reduce the remaining places by one` `        ``printRec(number + ``"1"``, extraOnes + ``1``,` `                 ``remainingPlaces - ``1``);`   `        ``// If more ones than zeros, append 0 to the` `        ``// current number and reduce the remaining` `        ``// places by one` `        ``if` `(``0` `< extraOnes)` `            ``printRec(number + ``"0"``, extraOnes - ``1``,` `                     ``remainingPlaces - ``1``);` `    ``}`   `    ``static` `void` `printNums(``int` `n)` `    ``{` `        ``String str = ``""``;` `        ``printRec(str, ``0``, n);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `n = ``4``;` `      `  `        ``// Function call` `        ``printNums(n);` `    ``}` `}`   `// This code is contributed by vt_m`

## Python3

 `# Python 3 program to print all N-bit binary`   `# function to generate n digit numbers`     `def` `printRec(number, extraOnes, remainingPlaces):`   `    ``# if number generated` `    ``if` `(``0` `=``=` `remainingPlaces):` `        ``print``(number, end``=``" "``)` `        ``return`   `    ``# Append 1 at the current number and` `    ``# reduce the remaining places by one` `    ``printRec(number ``+` `"1"``, extraOnes ``+` `1``,` `             ``remainingPlaces ``-` `1``)`   `    ``# If more ones than zeros, append 0 to` `    ``# the current number and reduce the` `    ``# remaining places by one` `    ``if` `(``0` `< extraOnes):` `        ``printRec(number ``+` `"0"``, extraOnes ``-` `1``,` `                 ``remainingPlaces ``-` `1``)`     `def` `printNums(n):` `    ``str` `=` `""` `    ``printRec(``str``, ``0``, n)`     `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``n ``=` `4` `     `  `    ``# Function call` `    ``printNums(n)`   `# This code is contributed by` `# Surendra_Gangwar`

## C#

 `// C# program to print all N-bit binary` `using` `System;`   `class` `GFG {`   `    ``// function to generate n digit numbers` `    ``static` `void` `printRec(String number, ` `                         ``int` `extraOnes,` `                         ``int` `remainingPlaces)` `    ``{`   `        ``// if number generated` `        ``if` `(0 == remainingPlaces) ` `        ``{` `            ``Console.Write(number + ``" "``);` `            ``return``;` `        ``}`   `        ``// Append 1 at the current number and` `        ``// reduce the remaining places by one` `        ``printRec(number + ``"1"``, extraOnes + 1,` `                 ``remainingPlaces - 1);`   `        ``// If more ones than zeros, append` `        ``// 0 to the current number and` `        ``// reduce the remaining places` `        ``// by one` `        ``if` `(0 < extraOnes)` `            ``printRec(number + ``"0"``, extraOnes - 1,` `                     ``remainingPlaces - 1);` `    ``}` `    ``static` `void` `printNums(``int` `n)` `    ``{` `        ``String str = ``""``;` `        ``printRec(str, 0, n);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 4;` `      `  `        ``// Function call` `        ``printNums(n);` `    ``}` `}`   `// This code is contributed by Nitin Mittal.`

## PHP

 `

## Javascript

 ``

Output

`1111 1110 1101 1100 1011 1010 `

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

A non-recursive solution also exists, the idea is to directly generate the numbers in the range of 2N to 2(N-1) then require, only these which satisfies the condition:

Implementation:

## C++

 `// C++ program to print all N-bit binary` `#include ` `#include ` `using` `namespace` `std;`     `// Function to get the binary representation` `// of the number N` `string getBinaryRep(``int` `N, ``int` `num_of_bits)` `{` `    ``string r = ``""``;` `    ``num_of_bits--;` `  `  `    ``// loop for each bit` `    ``while` `(num_of_bits >= 0) ` `    ``{` `        ``if` `(N & (1 << num_of_bits))` `            ``r.append(``"1"``);` `        ``else` `            ``r.append(``"0"``);` `        ``num_of_bits--;` `    ``}` `    ``return` `r;` `}`   `vector NBitBinary(``int` `N)` `{` `    ``vector r;` `    ``int` `first = 1 << (N - 1);` `    ``int` `last = first * 2;` `    `  `    ``// generate numbers in the range of (2^N)-1 to 2^(N-1)` `    ``// inclusive` `    ``for` `(``int` `i = last - 1; i >= first; --i)` `    ``{` `        ``int` `zero_cnt = 0;` `        ``int` `one_cnt = 0;` `        ``int` `t = i;` `        ``int` `num_of_bits = 0;` `        `  `        ``// longest prefix check` `        ``while` `(t) ` `        ``{` `            ``if` `(t & 1)` `                ``one_cnt++;` `            ``else` `                ``zero_cnt++;` `            ``num_of_bits++;` `            ``t = t >> 1;` `        ``}` `      `  `        ``// if counts of 1 is greater than` `        ``// counts of zero` `        ``if` `(one_cnt >= zero_cnt)` `        ``{` `            ``// do sub-prefixes check` `            ``bool` `all_prefix_match = ``true``;` `            ``int` `msk = (1 << num_of_bits) - 2;` `            ``int` `prefix_shift = 1;` `            ``while` `(msk) ` `            ``{`   `                ``int` `prefix = (msk & i) >> prefix_shift;` `                ``int` `prefix_one_cnt = 0;` `                ``int` `prefix_zero_cnt = 0;` `                ``while` `(prefix)` `                ``{` `                    ``if` `(prefix & 1)` `                        ``prefix_one_cnt++;` `                    ``else` `                        ``prefix_zero_cnt++;` `                    ``prefix = prefix >> 1;` `                ``}` `                ``if` `(prefix_zero_cnt > prefix_one_cnt)` `                ``{` `                    ``all_prefix_match = ``false``;` `                    ``break``;` `                ``}` `                ``prefix_shift++;` `                ``msk = msk & (msk << 1);` `            ``}` `            ``if` `(all_prefix_match)` `            ``{` `                ``r.push_back(getBinaryRep(i, num_of_bits));` `            ``}` `        ``}` `    ``}` `    ``return` `r;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 4;` `  `  `    ``// Function call` `    ``vector results = NBitBinary(n);` `    ``for` `(``int` `i = 0; i < results.size(); ++i)` `        ``cout << results[i] << ``" "``;` `    ``cout << endl;` `    ``return` `0;` `}`

## Java

 `// Java program to print all N-bit binary` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG ` `{`   `  ``// Function to get the binary representation` `  ``// of the number N` `  ``static` `String getBinaryRep(``int` `N, ``int` `num_of_bits)` `  ``{` `    ``String r = ``""``;` `    ``num_of_bits--;`   `    ``// loop for each bit` `    ``while` `(num_of_bits >= ``0``) ` `    ``{` `      ``if` `((N & (``1` `<< num_of_bits))!=``0``)` `        ``r += ``"1"``;` `      ``else` `        ``r += ``"0"``;` `      ``num_of_bits--;` `    ``}` `    ``return` `r;` `  ``}`   `  ``static` `ArrayList NBitBinary(``int` `N)` `  ``{` `    ``ArrayList r = ``new` `ArrayList();` `    ``int` `first = ``1` `<< (N - ``1``);` `    ``int` `last = first * ``2``;`   `    ``// generate numbers in the range of (2^N)-1 to 2^(N-1)` `    ``// inclusive` `    ``for` `(``int` `i = last - ``1``; i >= first; --i)` `    ``{` `      ``int` `zero_cnt = ``0``;` `      ``int` `one_cnt = ``0``;` `      ``int` `t = i;` `      ``int` `num_of_bits = ``0``;`   `      ``// longest prefix check` `      ``while` `(t > ``0``) ` `      ``{` `        ``if` `((t & ``1``) != ``0``)` `          ``one_cnt++;` `        ``else` `          ``zero_cnt++;` `        ``num_of_bits++;` `        ``t = t >> ``1``;` `      ``}`   `      ``// if counts of 1 is greater than` `      ``// counts of zero` `      ``if` `(one_cnt >= zero_cnt)` `      ``{` `        ``// do sub-prefixes check` `        ``boolean` `all_prefix_match = ``true``;` `        ``int` `msk = (``1` `<< num_of_bits) - ``2``;` `        ``int` `prefix_shift = ``1``;` `        ``while` `(msk > ``0``) ` `        ``{`   `          ``int` `prefix = (msk & i) >> prefix_shift;` `          ``int` `prefix_one_cnt = ``0``;` `          ``int` `prefix_zero_cnt = ``0``;` `          ``while` `(prefix > ``0``)` `          ``{` `            ``if` `((prefix & ``1``)!=``0``)` `              ``prefix_one_cnt++;` `            ``else` `              ``prefix_zero_cnt++;` `            ``prefix = prefix >> ``1``;` `          ``}` `          ``if` `(prefix_zero_cnt > prefix_one_cnt)` `          ``{` `            ``all_prefix_match = ``false``;` `            ``break``;` `          ``}` `          ``prefix_shift++;` `          ``msk = msk & (msk << ``1``);` `        ``}` `        ``if` `(all_prefix_match)` `        ``{` `          ``r.add(getBinaryRep(i, num_of_bits));` `        ``}` `      ``}` `    ``}` `    ``return` `r;` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `main (String[] args) ` `  ``{`   `    ``int` `n = ``4``;`   `    ``// Function call` `    ``ArrayList results = NBitBinary(n);` `    ``for` `(``int` `i = ``0``; i < results.size(); ++i)` `      ``System.out.print(results.get(i)+``" "``);` `    ``System.out.println();` `  ``}` `}`   `// This code is contributed by avanitrachhadiya2155`

## Python3

 `# Python3 program to print ` `# all N-bit binary`   `# Function to get the binary ` `# representation of the number N` `def` `getBinaryRep(N, num_of_bits):`   `    ``r ``=` `"";` `    ``num_of_bits ``-``=` `1` `  `  `    ``# loop for each bit` `    ``while` `(num_of_bits >``=` `0``):    ` `        ``if` `(N & (``1` `<< num_of_bits)):` `            ``r ``+``=` `(``"1"``);` `        ``else``:` `            ``r ``+``=` `(``"0"``);` `        ``num_of_bits ``-``=` `1` `    `  `    ``return` `r;`   `def` `NBitBinary(N):`   `    ``r ``=` `[]` `    ``first ``=` `1` `<< (N ``-` `1``);` `    ``last ``=` `first ``*` `2``;` `    `  `    ``# generate numbers in the range ` `    ``# of (2^N)-1 to 2^(N-1) inclusive` `    ``for` `i ``in` `range` `(last ``-` `1``,` `                    ``first ``-` `1``, ``-``1``):    ` `        ``zero_cnt ``=` `0``;` `        ``one_cnt ``=` `0``;` `        ``t ``=` `i;` `        ``num_of_bits ``=` `0``;` `        `  `        ``# longest prefix check` `        ``while` `(t):        ` `            ``if` `(t & ``1``):` `                ``one_cnt ``+``=` `1` `            ``else``:` `                ``zero_cnt ``+``=` `1` `            ``num_of_bits ``+``=` `1` `            ``t ``=` `t >> ``1``;        ` `      `  `        ``# if counts of 1 is greater ` `        ``# than counts of zero` `        ``if` `(one_cnt >``=` `zero_cnt):` `        `  `            ``# do sub-prefixes check` `            ``all_prefix_match ``=` `True``;` `            ``msk ``=` `(``1` `<< num_of_bits) ``-` `2``;` `            ``prefix_shift ``=` `1``;` `            `  `            ``while` `(msk):            ` `                ``prefix ``=` `((msk & i) >> ` `                           ``prefix_shift);` `                ``prefix_one_cnt ``=` `0``;` `                ``prefix_zero_cnt ``=` `0``;` `                `  `                ``while` `(prefix):                ` `                    ``if` `(prefix & ``1``):` `                        ``prefix_one_cnt ``+``=` `1` `                    ``else``:` `                        ``prefix_zero_cnt ``+``=` `1` `                    ``prefix ``=` `prefix >> ``1``;` `                `  `                ``if` `(prefix_zero_cnt > ` `                    ``prefix_one_cnt):                ` `                    ``all_prefix_match ``=` `False``;` `                    ``break``;` `                `  `                ``prefix_shift ``+``=` `1` `                ``msk ``=` `msk & (msk << ``1``);` `            `  `            ``if` `(all_prefix_match):            ` `                ``r.append(getBinaryRep(i, ` `                                      ``num_of_bits));          ` `    ``return` `r`   `# Driver code` `if` `__name__ ``=``=` `"__main__"``:` ` `  `    ``n ``=` `4``;` `  `  `    ``# Function call` `    ``results ``=` `NBitBinary(n);` `    ``for` `i ``in` `range` `(``len``(results)):` `        ``print` `(results[i], ` `               ``end ``=` `" "``)` `    ``print` `()` `    `  `# This code is contributed by Chitranayal`

## C#

 `// C# program to print all N-bit binary` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG{` `    `  `// Function to get the binary representation` `// of the number N` `static` `string` `getBinaryRep(``int` `N, ``int` `num_of_bits)` `{` `    ``string` `r = ``""``;` `    ``num_of_bits--;` `    `  `    ``// loop for each bit` `    ``while` `(num_of_bits >= 0) ` `    ``{` `        ``if` `((N & (1 << num_of_bits)) != 0)` `            ``r += ``"1"``;` `        ``else` `            ``r += ``"0"``;` `            `  `        ``num_of_bits--;` `    ``}` `    ``return` `r;` `}` `    `  `static` `List<``string``> NBitBinary(``int` `N)` `{` `    ``List<``string``> r = ``new` `List<``string``>();` `    ``int` `first = 1 << (N - 1);` `    ``int` `last = first * 2;` `    `  `    ``// Generate numbers in the range of (2^N)-1 to 2^(N-1)` `    ``// inclusive` `    ``for``(``int` `i = last - 1; i >= first; --i)` `    ``{` `        ``int` `zero_cnt = 0;` `        ``int` `one_cnt = 0;` `        ``int` `t = i;` `        ``int` `num_of_bits = 0;` `        `  `        ``// longest prefix check` `        ``while` `(t > 0) ` `        ``{` `            ``if` `((t & 1) != 0)` `                ``one_cnt++;` `            ``else` `                ``zero_cnt++;` `                `  `            ``num_of_bits++;` `            ``t = t >> 1;` `        ``}` `    `  `        ``// If counts of 1 is greater than` `        ``// counts of zero` `        ``if` `(one_cnt >= zero_cnt)` `        ``{` `            `  `            ``// Do sub-prefixes check` `            ``bool` `all_prefix_match = ``true``;` `            ``int` `msk = (1 << num_of_bits) - 2;` `            ``int` `prefix_shift = 1;` `            `  `            ``while` `(msk > 0) ` `            ``{` `                ``int` `prefix = (msk & i) >> prefix_shift;` `                ``int` `prefix_one_cnt = 0;` `                ``int` `prefix_zero_cnt = 0;` `                `  `                ``while` `(prefix > 0)` `                ``{` `                    ``if` `((prefix & 1)!=0)` `                        ``prefix_one_cnt++;` `                    ``else` `                        ``prefix_zero_cnt++;` `                        `  `                    ``prefix = prefix >> 1;` `                ``}` `                ``if` `(prefix_zero_cnt > prefix_one_cnt)` `                ``{` `                    ``all_prefix_match = ``false``;` `                    ``break``;` `                ``}` `                ``prefix_shift++;` `                ``msk = msk & (msk << 1);` `            ``}` `            ``if` `(all_prefix_match)` `            ``{` `                ``r.Add(getBinaryRep(i, num_of_bits));` `            ``}` `        ``}` `    ``}` `    ``return` `r;` `}`   `// Driver code` `static` `public` `void` `Main()` `{` `    ``int` `n = 4;` `    `  `    ``// Function call` `    ``List<``string``> results = NBitBinary(n);` `    ``for` `(``int` `i = 0; i < results.Count; ++i)` `        ``Console.Write(results[i] + ``" "``);` `        `  `    ``Console.WriteLine();` `}` `}`   `// This code is contributed by rag2127`

## Javascript

 ``

Output

`1111 1110 1101 1100 1011 1010 `

Time Complexity: O(m*n)
Auxiliary Space: O(n)

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