George cantor named mathematician gave a proof that set of rational numbers is enumerable. We don’t have to proof it over here rather we have to determine the Nth term in the set of rational numbers.
Input : N = 8 Output : 2/3 Input : N = 15 Output : 1/5 See image for reference of counting.
The set of rational numbers goes like the below image :
Here the first term is 1/1, second term is 1/2, third term is 2/1, fourth term is 3/1, fifth term is 2/2, sixth term is 1/3 so on……
1. View this as a matrix(2-D array) with rows from 1 to n and columns from 1 to n.
2. rows/columns will give the rational numbers.
3. Observe the pattern from the above image it will be clear how to traverse through the matrix i.e diagonally from left to right upwards and then from right to left downwards till we reach the Nth position.
4. There are 4 regular repeating pattern
One going horizontal one times when i = 1
Then moving downwards horizontally untill j = 1
Then moving verticals ones when j = 1
Then moving diagonal upwards until i = 1
5. After each iteration move to next number to keep counting its position using counter k, then compare it with N
N-th term : 1/5
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Improved By : jit_t