Given an integer N, the task is to find the Nth pure number.
A pure number has to satisfy three conditions:
1) It has even number of digits.
2) All digits are either 4 or 5.
3) And the number is a palindrome.
The Pure number series is: 44, 55, 4444, 4554, 5445, 5555, 444444, 445544, 454454, 455554 and so on.
Input: 5 Output: 5445 Explanation: 5445 is the 5th pure number in the series. Input: 19 Output: 45444454 Explanation: 45444454 is the 19th pure number in the series.
Approach: We will assume that 2 numbers make one single block. For each block, there is 2block number of pure numbers. For pure numbers with 1 block, there are 21 pure numbers, for numbers with 2 blocks, there are 22 numbers and so on.
- Pure numbers starting with 4, starts at position 2block – 1 for example, 4444 is at (22 -1 = 3) which means it is at third position in the series.
- Pure numbers starting with 5 starts at position 2block + 2(block-1) -1 for example, 5555 is at (2^2 + 2^1 -1 =5) which means it is at fifth position in the series.
A pure number at a block is essentially sandwiched between two 4’s or 5’s and is a combination of all previous block numbers. To understand it better let’s consider the example below:
- First pure number is 44 and second pure number is 55
- 4444 (“4″+ “44” + “4”) 44 from previous block
- 4554 (“4″+ “55” + “4”) 55 from previous block
- 5445 (“5″+ “44” + “5”) 44 from previous block
- 5555 (“5″+ “55” + “5”) 55 from previous block
This pattern repeats for all the numbers in the series.
Below is the implementation of the above approach:
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