Given an integer N, the task is to find the smallest integer X such that it has no odd position set and X ≥ N.
Note: The positioning of bits is assumed from the right side and the first bit is assumed to be 0th bit.
Input: N = 9
16’s binary representation is 10000, which has its 4th bit
set which is the smallest number possible satisfying the given condition.
Input: N = 5
Input: N = 19
Approach: The problem can be solved using a greedy approach and some bit properties. The property that if smaller powers of two are taken exactly once and added up they can never exceed a higher power of two (e.g., (1 + 2 + 4) < 8). The following greedy approach is used to solve the above problem:
- Initially count the number of bits.
- Get the leftmost index of the set bit.
- If the leftmost set bit is at an odd index, then answer will always be (1 << (leftmost_bit_index + 1)).
- Else, greedily form a number by setting all the even bits from 0 to leftmost_bit_index. Now greedily remove a power of two from right to check if we get a number which satisfies the given conditions.
- If the above condition does not give us our number, then we simply set the next leftmost even bit and return the answer.
Below is the implementation of the above approach:
- Find smallest number n such that n XOR n+1 equals to given k.
- Smallest number greater than or equal to N divisible by K
- Smallest Special Prime which is greater than or equal to a given number
- Smallest divisor D of N such that gcd(D, M) is greater than 1
- Smallest power of 4 greater than or equal to N
- Smallest integer greater than n such that it consists of digit m exactly k times
- Minimum number of squares whose sum equals to given number n
- Number of Co-prime pairs from 1 to N with product equals to N
- Check whether all the rotations of a given number is greater than or equal to the given number or not
- Find the smallest number whose digits multiply to a given number n
- Least Greater number with same digit sum
- Largest number not greater than N all the digits of which are odd
- Find next greater number with same set of digits
- Perfect cube greater than a given number
- Largest even digit number not greater than N
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