# Check whether bits are in alternate pattern in the given range | Set-2

Given a non-negative number and two values and . The problem is to check whether or not N has an alternate pattern in its binary representation in the range L to R.

Here, alternate pattern means that the set and unset bits occur in alternate order. The bits are numbered from right to left, i.e., the least significant bit is considered to be at first position.

Examples:

```Input : N = 18, L = 1, R = 3
Output : Yes
(18)10 = (10010)2
The bits in the range 1 to 3 in the
binary representation of 18 are in
alternate order.

Input : N = 22, L = 2, R = 4
Output : No
(22)10 = (10110)2
The bits in the range 2 to 4 in the
binary representation of 22 are not in
alternate order.
```

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

Simple Approach: It has been discussed in this post which has a worst case time complexity of O(log2n).

Efficient Approach: Following are the steps:

1. Declare two variables num and left_shift.
2. Check if rth bit is set or not in n. Refer this post. If set then, assign num = n and left_shift = r, Else set the (r+1)th bit in n and assign it to num. Refer this post. Also assign left_shift = r + 1.
3. Perform num = num & ((1 << left_shift) – 1).
4. Perform num = num >> (l – 1).
5. Finally check whether bits are in alternate pattern in num or not. Refer this post.

The entire idea of the above approach is to create a number num in which bits are in same pattern as in the given range of n and then check whether bits are in alternate pattern in num or not.

## C++

 `// C++ implementation to check whether bits are in ` `// alternate pattern in the given range ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// function to check whether rightmost ` `// kth bit is set or not in 'n' ` `bool` `isKthBitSet(unsigned ``int` `n, ` `                 ``unsigned ``int` `k) ` `{ ` `    ``if` `((n >> (k - 1)) & 1) ` `        ``return` `true``; ` `    ``return` `false``; ` `} ` ` `  `// function to set the rightmost kth bit in 'n' ` `unsigned ``int` `setKthBit(unsigned ``int` `n, ` `                       ``unsigned ``int` `k) ` `{ ` `    ``// kth bit of n is being set by this operation ` `    ``return` `((1 << (k - 1)) | n); ` `} ` ` `  `// function to check if all the bits are set or not ` `// in the binary representation of 'n' ` `bool` `allBitsAreSet(unsigned ``int` `n) ` `{ ` `    ``// if true, then all bits are set ` `    ``if` `(((n + 1) & n) == 0) ` `        ``return` `true``; ` ` `  `    ``// else all bits are not set ` `    ``return` `false``; ` `} ` ` `  `// function to check if a number ` `// has bits in alternate pattern ` `bool` `bitsAreInAltOrder(unsigned ``int` `n) ` `{ ` `    ``unsigned ``int` `num = n ^ (n >> 1); ` ` `  `    ``// to check if all bits are set ` `    ``// in 'num' ` `    ``return` `allBitsAreSet(num); ` `} ` ` `  `// function to check whether bits are in ` `// alternate pattern in the given range ` `bool` `bitsAreInAltPatrnInGivenRange(unsigned ``int` `n, ` `                                   ``unsigned ``int` `l, ` `                                   ``unsigned ``int` `r) ` `{ ` `    ``unsigned ``int` `num, left_shift; ` ` `  `    ``// preparing a number 'num' and 'left_shift' ` `    ``// which can be further used for the check ` `    ``// of alternate pattern in the given range ` `    ``if` `(isKthBitSet(n, r)) { ` `        ``num = n; ` `        ``left_shift = r; ` `    ``} ` `    ``else` `{ ` `        ``num = setKthBit(n, (r + 1)); ` `        ``left_shift = r + 1; ` `    ``} ` ` `  `    ``// unset all the bits which are left to the ` `    ``// rth bit of (r+1)th bit ` `    ``num = num & ((1 << left_shift) - 1); ` ` `  `    ``// right shift 'num' by (l-1) bits ` `    ``num = num >> (l - 1); ` ` `  `    ``return` `bitsAreInAltOrder(num); ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``unsigned ``int` `n = 18; ` `    ``unsigned ``int` `l = 1, r = 3; ` `    ``if` `(bitsAreInAltPatrnInGivenRange(n, l, r)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Java implementation to check whether bits are in ` `// alternate pattern in the given range ` `class` `GFG  ` `{ ` ` `  `// function to check whether rightmost ` `// kth bit is set or not in 'n' ` `static` `boolean` `isKthBitSet(``int` `n, ` `                            ``int` `k) ` `{ ` `    ``if` `((n >> (k - ``1``)) == ``1``) ` `        ``return` `true``; ` `    ``return` `false``; ` `} ` ` `  `// function to set the rightmost kth bit in 'n' ` `static` `int` `setKthBit(``int` `n, ` `                    ``int` `k) ` `{ ` `    ``// kth bit of n is being set by this operation ` `    ``return` `((``1` `<< (k - ``1``)) | n); ` `} ` ` `  `// function to check if all the bits are set or not ` `// in the binary representation of 'n' ` `static` `boolean` `allBitsAreSet(``int` `n) ` `{ ` `    ``// if true, then all bits are set ` `    ``if` `(((n + ``1``) & n) == ``0``) ` `        ``return` `true``; ` ` `  `    ``// else all bits are not set ` `    ``return` `false``; ` `} ` ` `  `// function to check if a number ` `// has bits in alternate pattern ` `static` `boolean` `bitsAreInAltOrder(``int` `n) ` `{ ` `    ``int` `num = n ^ (n >> ``1``); ` ` `  `    ``// to check if all bits are set ` `    ``// in 'num' ` `    ``return` `allBitsAreSet(num); ` `} ` ` `  `// function to check whether bits are in ` `// alternate pattern in the given range ` `static` `boolean` `bitsAreInAltPatrnInGivenRange(``int` `n, ` `                                ``int` `l, ``int` `r) ` `{ ` `    ``int` `num, left_shift; ` ` `  `    ``// preparing a number 'num' and 'left_shift' ` `    ``// which can be further used for the check ` `    ``// of alternate pattern in the given range ` `    ``if` `(isKthBitSet(n, r))  ` `    ``{ ` `        ``num = n; ` `        ``left_shift = r; ` `    ``} ` `    ``else` `    ``{ ` `        ``num = setKthBit(n, (r + ``1``)); ` `        ``left_shift = r + ``1``; ` `    ``} ` ` `  `    ``// unset all the bits which are left to the ` `    ``// rth bit of (r+1)th bit ` `    ``num = num & ((``1` `<< left_shift) - ``1``); ` ` `  `    ``// right shift 'num' by (l-1) bits ` `    ``num = num >> (l - ``1``); ` ` `  `    ``return` `bitsAreInAltOrder(num); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``18``; ` `    ``int` `l = ``1``, r = ``3``; ` `    ``if` `(bitsAreInAltPatrnInGivenRange(n, l, r)) ` `        ``System.out.println(``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

## Python3

 `# Python 3 implementation to check  ` `# whether bits are in alternate pattern ` `# in the given range ` ` `  `# function to check whether rightmost ` `# kth bit is set or not in 'n' ` `def` `isKthBitSet(n, k): ` `    ``if``((n >> (k ``-` `1``)) & ``1``): ` `        ``return` `True` `    ``return` `False` ` `  `# function to set the rightmost kth bit in 'n' ` `def` `setKthBit(n, k): ` `     `  `    ``# kth bit of n is being set ` `    ``# by this operation ` `    ``return` `((``1` `<< (k ``-` `1``)) | n) ` ` `  `# function to check if all the bits are set or not ` `# in the binary representation of 'n' ` `def` `allBitsAreSet(n): ` `     `  `    ``# if true, then all bits are set ` `    ``if` `(((n ``+` `1``) & n) ``=``=` `0``): ` `        ``return` `True` ` `  `    ``# else all bits are not set ` `    ``return` `False` ` `  `# function to check if a number ` `# has bits in alternate pattern ` `def` `bitsAreInAltOrder(n): ` `    ``num ``=` `n ^ (n >> ``1``) ` ` `  `    ``# to check if all bits are set ` `    ``# in 'num' ` `    ``return` `allBitsAreSet(num) ` ` `  `# function to check whether bits are in ` `# alternate pattern in the given range ` `def` `bitsAreInAltPatrnInGivenRange(n, l, r): ` `     `  `    ``# preparing a number 'num' and 'left_shift' ` `    ``# which can be further used for the check ` `    ``# of alternate pattern in the given range ` `    ``if` `(isKthBitSet(n, r)): ` `        ``num ``=` `n ` `        ``left_shift ``=` `r ` ` `  `    ``else``: ` `        ``num ``=` `setKthBit(n, (r ``+` `1``)) ` `        ``left_shift ``=` `r ``+` `1` `     `  `    ``# unset all the bits which are left to the ` `    ``# rth bit of (r+1)th bit ` `    ``num ``=` `num & ((``1` `<< left_shift) ``-` `1``) ` ` `  `    ``# right shift 'num' by (l-1) bits ` `    ``num ``=` `num >> (l ``-` `1``) ` ` `  `    ``return` `bitsAreInAltOrder(num) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `18` `    ``l ``=` `1` `    ``r ``=` `3` `    ``if` `(bitsAreInAltPatrnInGivenRange(n, l, r)): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation to check whether bits are in  ` `// alternate pattern in the given range  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` ` `  `// function to check whether rightmost  ` `// kth bit is set or not in 'n'  ` `static` `bool` `isKthBitSet(``int` `n,  ` `                            ``int` `k)  ` `{  ` `    ``if` `((n >> (k - 1)) == 1)  ` `        ``return` `true``;  ` `    ``return` `false``;  ` `}  ` ` `  `// function to set the rightmost kth bit in 'n'  ` `static` `int` `setKthBit(``int` `n,  ` `                    ``int` `k)  ` `{  ` `    ``// kth bit of n is being set by this operation  ` `    ``return` `((1 << (k - 1)) | n);  ` `}  ` ` `  `// function to check if all the bits are set or not  ` `// in the binary representation of 'n'  ` `static` `bool` `allBitsAreSet(``int` `n)  ` `{  ` `    ``// if true, then all bits are set  ` `    ``if` `(((n + 1) & n) == 0)  ` `        ``return` `true``;  ` ` `  `    ``// else all bits are not set  ` `    ``return` `false``;  ` `}  ` ` `  `// function to check if a number  ` `// has bits in alternate pattern  ` `static` `bool` `bitsAreInAltOrder(``int` `n)  ` `{  ` `    ``int` `num = n ^ (n >> 1);  ` ` `  `    ``// to check if all bits are set  ` `    ``// in 'num'  ` `    ``return` `allBitsAreSet(num);  ` `}  ` ` `  `// function to check whether bits are in  ` `// alternate pattern in the given range  ` `static` `bool` `bitsAreInAltPatrnInGivenRange(``int` `n,  ` `                                ``int` `l, ``int` `r)  ` `{  ` `    ``int` `num, left_shift;  ` ` `  `    ``// preparing a number 'num' and 'left_shift'  ` `    ``// which can be further used for the check  ` `    ``// of alternate pattern in the given range  ` `    ``if` `(isKthBitSet(n, r))  ` `    ``{  ` `        ``num = n;  ` `        ``left_shift = r;  ` `    ``}  ` `    ``else` `    ``{  ` `        ``num = setKthBit(n, (r + 1));  ` `        ``left_shift = r + 1;  ` `    ``}  ` ` `  `    ``// unset all the bits which are left to the  ` `    ``// rth bit of (r+1)th bit  ` `    ``num = num & ((1 << left_shift) - 1);  ` ` `  `    ``// right shift 'num' by (l-1) bits  ` `    ``num = num >> (l - 1);  ` ` `  `    ``return` `bitsAreInAltOrder(num);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main()  ` `{  ` `    ``int` `n = 18;  ` `    ``int` `l = 1, r = 3;  ` `    ``if` `(bitsAreInAltPatrnInGivenRange(n, l, r))  ` `        ``Console.WriteLine(``"Yes"``);  ` `    ``else` `        ``Console.WriteLine(``"No"``);  ` `}  ` `}  ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

```Yes
```

Time Complexity: O(1).

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