The BinaryPlace(L, x) function performs a binary placement of x in L, where L is assumed to be sorted.  It returns the greatest index n such that L[n] precedes x. If x precedes all elements in a list L, then the value $0$ is returned.

In this form of the calling sequence, x must be of type numeric or string and L should contain values of the same type in ascending order.

BinaryPlace also accepts a Vector or one-dimensional Array as its first argument. If x precedes all elements in an Array, then the value that is returned is the lowerbound of the Array minus one. Since Vectors, like lists, always have a lowerbound of 1, the value returned for a Vector in this case is $0$.

If L is a list, then the returned value $n$ is such that $\left[\mathrm{op}\left(1..n\,L\right)\,x\,\mathrm{op}\left(n+1..\mathrm{-1}\,L\right)\right]$ is still a sorted list. If L is a Vector or Array, then the returned value $n$ is such that $\left[\mathrm{op}\left(\mathrm{convert}\left(L_{..n}\,\mathrm{list}\right)\right)\,x\,\mathrm{op}\left(\mathrm{convert}\left(L_{n+1..}\,\mathrm{list}\right)\right)\right]$ is sorted.

If three or more arguments are specified in the calling sequence, then $f\left(x,y,\mathrm{opt1},\mathrm{opt2},...\right)$ must return true if x precedes y.

$\mathrm{with}\left(\mathrm{ListTools}\right)\:$

$L≔\left[1\,5\,7\,8\,10\right]\:$

$n≔\mathrm{BinaryPlace}\left(L\,6\right)$

$n≔2$

$\left[\mathrm{op}\left(1..n\,L\right)\,6\,\mathrm{op}\left(n+1..-1\,L\right)\right]$

$\left[1\,5\,6\,7\,8\,10\right]$

$\mathrm{BinaryPlace}\left(\left[''mac''\,''made''\,''magpie''\,''mail''\right]\,''magic''\right)$

$2$

$\mathrm{BinaryPlace}\left(\left[0\,{\sin \left(1\right)}^2\,1\right]\,\exp \left(-\frac{1}{10}\right)\,\mathrm{verify}\,\mathrm{less\_than}\right)$

$2$

$\mathrm{BinaryPlace}\left(\left[\left\{4\right\}\,\left\{1\,2\,4\right\}\,\left\{1\,2\,3\,4\right\}\right]\,\left\{2\,4\right\}\,\mathrm{`subset`}\right)$

$1$

$A≔\mathrm{Array}\left(-2..5\,\left[173\,157\,101\,21\,17\,-3\,-33\,-62\right]\right)$

$\mathrm{BinaryPlace}\left(A\,0\,\mathrm{`>`}\right)$

$2$

$\mathrm{convert}\left(A\left[..2\right]\,'\mathrm{list}'\right)$

$\left[173\,157\,101\,21\,17\right]$

$\mathrm{convert}\left(A\left[3..\right]\,'\mathrm{list}'\right)$

$\left[\mathrm{-3}\,\mathrm{-33}\,\mathrm{-62}\right]$

The ListTools[BinaryPlace] command was updated in Maple 18.

The L parameter was updated in Maple 18.