Given a number N, the task is to find the largest number less than or equal to the given number N such that on rearranging its digits it can become prime.
Input : N = 99 Output : 98 Explanation : We can rearrange the digits of 98 to 89 and 89 is a prime number. Input : N = 84896 Output : 84896 Explanation : We can rearrange the digits of 84896 to 46889 which is a prime number.
Below is the algorithm to find such a largest number num <= N such that digits of num can be rearranged to get a prime number:
Preprocessing Step: Generate a list of all the prime numbers less than or equal to given number N. This can be done efficiently using the sieve of Eratosthenes.
Main Steps: The main idea is to check all numbers from N to 1, if any of the number can be reshuffled to form a prime. The first such number found will be the answer.
To do this, run a loop from N to 1 and for every number:
- Extract the digits of the given number and store it in a vector.
- Sort this vector to get the smallest number which can be formed using these digits.
- For each permutation of this vector, we would form a number and check whether the formed number is prime or not. Here we make use of the Preprocessing step.
- If it is prime then we stop the loop and this is our answer.
Below is the implementation of the above approach:
- Largest number not greater than N all the digits of which are odd
- Largest number with prime digits
- Smallest number by rearranging digits of a given number
- Kth prime number greater than N
- Find the Largest number with given number of digits and sum of digits
- Largest even digit number not greater than N
- Find next greater number with same set of digits
- Next greater Number than N with the same quantity of digits A and B
- Nearest greater number by interchanging the digits
- Largest number with maximum trailing nines which is less than N and greater than N-D
- Smallest Special Prime which is greater than or equal to a given number
- Largest number in [2, 3, .. n] which is co-prime with numbers in [2, 3, .. m]
- Largest number that divides x and is co-prime with y
- Largest number with the given set of N digits that is divisible by 2, 3 and 5
- Recursive sum of digits of a number is prime or not
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Improved By : SURENDRA_GANGWAR