"Write a C$++$ program that creates a divided difference table from the given data in a text file and uses that to create the interpolating polynomial. Print the polynomial in both the Newton's form and Lagrange's form. The sample input is:

$1$ VB$191\mathrm{.}502$

$33\mathrm{.}2531\mathrm{.}67$

The sample output of your program should print out the divided difference table and the interpolating polynomial as shown below:

student submitted image, transcription available below

Interpolating polynomial is:

$3+1/2($x$-1)+1/3($x$-1)($x$-3/2)-2($x$-1)($x$-3/2)$x

Simplified polynomial is:$$ f$[]$ f$[...]$ f$[...]$ f$[]311/23/213/41/31/6-2$ O $3-5/3-2/325/3$

$-2$x$^3+5\mathrm{.}334$x$^23\mathrm{.}334$x $+3$ f$[]$ f$[...]$ f$[...]$ f$[]311/23/213/41/31/6-2$ O $3-5/3-2/325/3"$