Saturday, October 10, 2015

THE ALGORITHM GIVEN BY NARAYANA PANDIT (1325-1400 AD)

IS USED IN THE COMMAND next_permutation IN C++ PROGRAMMING LANGUAGE.
 
Nārāyana Pandit was the first who gave a non-recursive algorithm for expansion of partitions of a number. He demonstrated his algorithm which is based on finding the next permutation in lexicographical order. In this algorithm, one has to start by sorting the sequence in increasing order to get its lexicographically minimal solution and repeat advancing to the next permutation as long as one is found. 
 
The algorithm applied by Nārāyana Pandit is:
Step 1 : Find largest index k such a[k] < a[k+1] that ;
Step 2 : Find largest index 1 such that a[k] < a[1]
Step 3 : Swap a[k] and a[1]
Step 4 : Reverse the range a[k+1] to a[n-1]


Two examples given by Narayana Pandit are shown in images enclosed.
-Vedveer Arya ,Indian History Real Truth

No comments:

Post a Comment