Given a number N, we have to find the minimum number of palindromes required to express N as a sum of them.
Input : N = 11
Output : 1
Explanation: 11 is itself a palindrome.
Input : N = 65
Output : 3
Explanation: 65 can be expressed as a sum of three palindromes (55, 9, 1).
In the previous post, we discussed a dynamic programming approach to this problem which had a time and space complexity of O(N3/2).
Cilleruelo, Luca, and Baxter proved in a 2016 research paper that every number can be expressed as the sum of maximum three palindromes in any base b >= 5 (this lower bound was later improved to 3). For the proof of this theorem, please refer to the original paper. We can make the use of this theorem by safely assuming the answer to be three if the number N is not itself a palindrome and cannot be expressed as the sum of two palindromes.
Below is the implementation of the above approach:
Time Complexity: O(√(N)log N).
- Minimum number of palindromes required to express N as a sum | Set 1
- Minimum number of given powers of 2 required to represent a number
- Minimum number of operations required to reduce N to 1
- Minimum number operations required to convert n to m | Set-2
- Minimum number of changes required to make the given array an AP
- Minimum number of given operation required to convert n to m
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- Minimum number of operations required to sum to binary string S
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- Minimum number of single digit primes required whose sum is equal to N
- Minimum number of given operations required to reduce the array to 0 element
- Minimum number of given operations required to make two strings equal
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Improved By : rituraj_jain