There is a question in permutation chapter in my maths class where for a given word we need to find its position in dictionary order. This means to permute the letter of the given word to all possible arrangements (may/may not be meaningful), arrange them in dictionary order and to find the rank of the given word in such arrangement.
For given word BCA, if we start arranging in dictionary order, we get:
1. ABC
2. ACB
3. BAC
4. BCA
5. CAB
6. CBA
These are the only possible arrangements and are in dictionary order. The position of BCA in such arrangement is 4. Which is the solution of the given problem.
My first task is to write a program that can give me the position of a given word if permutated and arranged in dictionary order.
After I've accomplished this, for a given position I want to be able to return the word that would appear at that position in such an arrangement.
After this has been accomplished, I want to be able to pass my program a file containing a list of words and output a file containing the word in one column, rank in another column and for the output to be arranged in the order of the rank in ascending order. For example:
Input File:
Random
Tango
Number
Zenith
Delhi
Mother
Father
Failure
Output File:
Delhi 5
Tango 99
Father 261
Mother 309
Number 469
Random 614
Zenith 616
Failure 1476
While doing my homework I noticed most answers were really big requiring a lots of multiplication and lot more steps to reach the answer, except for the word "Delhi".Such words are very ill suited for my entrance exam. They should not give us such question, considering that we only have 30 sec - 1 min for each question. But then how would they find more words like Delhi if they had to?
This gave me the idea for this problem. I want to know if there are more such words which rank lower in such an arrangement. And if there are, what are they?