# Check if the binary representation of a number has equal number of 0s and 1s in blocks

Given an integer N, the task is to check if its equivalent binary number has the equal frequency of consecutive blocks of 0 and 1. Note that 0 and a number with all 1s are not considered to have number of blocks of 0s and 1s.

Examples:

Input: N = 5
Output: Yes
Equivalent binary number of 5 is 101.
The first block is of 1 with length 1, the second block is of 0 with length 1
and the third block is of 1 is also of length 1. So, all blocks of 0 and 1 have an equal frequency which is 1.

Input: N = 51
Output: Yes
Equivalent binary number of 51 is 110011.

Input: 8
Output: No

Input: 7
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Simple Approach: First convert the integer to its equivalent binary number. Traverse binary string from left to right, for each block of 1 or 0, find its length and add it in a set. If length of set is 1, print “Yes” else print “No”.

 `# Python implementation of the above  ` `# approach  ` `   `  `# Function to check ` `def` `hasEqualBlockFrequency(N): ` `   `  `    ``# Converting integer to its equivalent  ` `    ``# binary number ` `    ``S ``=` `bin``(N).replace(``"0b"``, "") ` `    ``p ``=` `set``() ` `    ``c ``=` `1` ` `  `    ``for` `i ``in` `range``(``len``(S)``-``1``): ` ` `  `        ``# If adjacent character are same  ` `        ``# then increase counter ` `        ``if` `(S[i] ``=``=` `S[i ``+` `1``]): ` `            ``c ``+``=` `1` ` `  `        ``else``: ` `            ``p.add(c) ` `            ``c ``=` `1` ` `  `        ``p.add(c) ` ` `  `    ``if` `(``len``(p) ``=``=` `1``): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# Driver code ` `N ``=` `5` `hasEqualBlockFrequency(N) `

Output:

```Yes
```

Optimized Solution : We traverse from last bit. We first count number of same bits in the last block. We then traverse through all bits, for every block, we count number of same bits and if this count is not same as first count, we return false. If all blocks have same count, we return true.

## C++

 `// C++ program to check if a number has ` `// same counts of 0s and 1s in every ` `// block. ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// function to convert decimal to binary ` `bool` `isEqualBlock(``int` `n) ` `{ ` `    ``// Count same bits in last block ` `    ``int` `first_bit = n % 2; ` `    ``int` `first_count = 1; ` `    ``n = n / 2; ` `    ``while` `(n % 2 == first_bit && n > 0) { ` `        ``n = n / 2; ` `        ``first_count++; ` `    ``} ` ` `  `    ``// If n is 0 or it has all 1s, ` `    ``// then it is not considered to ` `    ``// have equal number of 0s and ` `    ``// 1s in blocks. ` `    ``if` `(n == 0) ` `        ``return` `false``; ` ` `  `    ``// Count same bits in all remaining blocks. ` `    ``while` `(n > 0) { ` ` `  `        ``int` `first_bit = n % 2; ` `        ``int` `curr_count = 1; ` `        ``n = n / 2; ` `        ``while` `(n % 2 == first_bit) { ` `            ``n = n / 2; ` `            ``curr_count++; ` `        ``} ` ` `  `        ``if` `(curr_count != first_count) ` `            ``return` `false``; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver program to test above function ` `int` `main() ` `{ ` `    ``int` `n = 51; ` `    ``if` `(isEqualBlock(n)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to check if a number has ` `// same counts of 0s and 1s in every ` `// block. ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` ` `  `// function to convert decimal to binary ` `static` `boolean` `isEqualBlock(``int` `n) ` `{ ` `    ``// Count same bits in last block ` `    ``int` `first_bit = n % ``2``; ` `    ``int` `first_count = ``1``; ` `    ``n = n / ``2``; ` `    ``while` `(n % ``2` `== first_bit && n > ``0``)  ` `    ``{ ` `        ``n = n / ``2``; ` `        ``first_count++; ` `    ``} ` ` `  `    ``// If n is 0 or it has all 1s, ` `    ``// then it is not considered to ` `    ``// have equal number of 0s and ` `    ``// 1s in blocks. ` `    ``if` `(n == ``0``) ` `        ``return` `false``; ` ` `  `    ``// Count same bits in all remaining blocks. ` `    ``while` `(n > ``0``)  ` `    ``{ ` ` `  `        ``first_bit = n % ``2``; ` `        ``int` `curr_count = ``1``; ` `        ``n = n / ``2``; ` `        ``while` `(n % ``2` `== first_bit)  ` `        ``{ ` `            ``n = n / ``2``; ` `            ``curr_count++; ` `        ``} ` ` `  `        ``if` `(curr_count != first_count) ` `            ``return` `false``; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `n = ``51``; ` `    ``if` `(isEqualBlock(n)) ` `        ``System.out.println( ``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `} ` ` `  `// This code is contributed by inder_mca `

## Python3

 `# Python3 program to check if a number has  ` `# same counts of 0s and 1s in every block.  ` ` `  `# Function to convert decimal to binary  ` `def` `isEqualBlock(n):  ` ` `  `    ``# Count same bits in last block  ` `    ``first_bit ``=` `n ``%` `2` `    ``first_count ``=` `1` `    ``n ``=` `n ``/``/` `2` `    ``while` `n ``%` `2` `=``=` `first_bit ``and` `n > ``0``:  ` `        ``n ``=` `n ``/``/` `2` `        ``first_count ``+``=` `1` ` `  `    ``# If n is 0 or it has all 1s,  ` `    ``# then it is not considered to  ` `    ``# have equal number of 0s and  ` `    ``# 1s in blocks.  ` `    ``if` `n ``=``=` `0``: ` `        ``return` `False` ` `  `    ``# Count same bits in all remaining blocks.  ` `    ``while` `n > ``0``:  ` ` `  `        ``first_bit ``=` `n ``%` `2` `        ``curr_count ``=` `1` `        ``n ``=` `n ``/``/` `2` `        ``while` `n ``%` `2` `=``=` `first_bit:  ` `            ``n ``=` `n ``/``/` `2` `            ``curr_count ``+``=` `1` `         `  `        ``if` `curr_count !``=` `first_count:  ` `            ``return` `False` `     `  `    ``return` `True` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``:  ` ` `  `    ``n ``=` `51` `    ``if` `isEqualBlock(n):  ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``)  ` `     `  `# This code is contributed by  ` `# Rituraj Jain `

## C#

 `// C# program to check if a number has  ` `// same counts of 0s and 1s in every  ` `// block.  ` ` `  `using` `System; ` ` `  `class` `GFG  ` `{  ` ` `  `    ``// function to convert decimal to binary  ` `    ``static` `bool` `isEqualBlock(``int` `n)  ` `    ``{  ` `        ``// Count same bits in last block  ` `        ``int` `first_bit = n % 2;  ` `        ``int` `first_count = 1;  ` `        ``n = n / 2;  ` `        ``while` `(n % 2 == first_bit && n > 0)  ` `        ``{  ` `            ``n = n / 2;  ` `            ``first_count++;  ` `        ``}  ` `     `  `        ``// If n is 0 or it has all 1s,  ` `        ``// then it is not considered to  ` `        ``// have equal number of 0s and  ` `        ``// 1s in blocks.  ` `        ``if` `(n == 0)  ` `            ``return` `false``;  ` `     `  `        ``// Count same bits in all remaining blocks.  ` `        ``while` `(n > 0)  ` `        ``{  ` `     `  `            ``first_bit = n % 2;  ` `            ``int` `curr_count = 1;  ` `            ``n = n / 2;  ` `             `  `            ``while` `(n % 2 == first_bit)  ` `            ``{  ` `                ``n = n / 2;  ` `                ``curr_count++;  ` `            ``}  ` `             `  `            ``if` `(curr_count != first_count)  ` `                ``return` `false``;  ` `        ``}  ` `        ``return` `true``;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main ()  ` `    ``{  ` `        ``int` `n = 51;  ` `         `  `        ``if` `(isEqualBlock(n))  ` `            ``Console.WriteLine( ``"Yes"``);  ` `        ``else` `            ``Console.WriteLine(``"No"``);  ` `    ``}  ` `}  ` ` `  `// This code is contributed by Ryuga `

## PHP

 ` 0)  ` `    ``{ ` `        ``\$n` `= (int)(``\$n` `/ 2); ` `        ``\$first_count``++; ` `    ``} ` ` `  `    ``// If n is 0 or it has all 1s, then  ` `    ``// it is not considered to have equal  ` `    ``// number of 0s and 1s in blocks. ` `    ``if` `(``\$n` `== 0) ` `        ``return` `false; ` ` `  `    ``// Count same bits in all remaining blocks. ` `    ``while` `(``\$n` `> 0)  ` `    ``{ ` `        ``\$first_bit` `= ``\$n` `% 2; ` `        ``\$curr_count` `= 1; ` `        ``\$n` `= (int)(``\$n` `/ 2); ` `        ``while` `(``\$n` `% 2 == ``\$first_bit``)  ` `        ``{ ` `            ``\$n` `= (int)(``\$n` `/ 2); ` `            ``\$curr_count``++; ` `        ``} ` ` `  `        ``if` `(``\$curr_count` `!= ``\$first_count``) ` `            ``return` `false; ` `    ``} ` ` `  `    ``return` `true; ` `} ` ` `  `// Driver Code ` `\$n` `= 51; ` `if` `(isEqualBlock(``\$n``)) ` `    ``echo` `"Yes"``; ` `else` `    ``echo` `"No"``; ` ` `  `// This code is contributed by ` `// Shivi_Aggarwal  ` `?> `

Output:

```Yes
```

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