add special case to binary search definition

jakobkogler · jakobkogler · commit 2044a9996878 · 2023-10-13T20:20:44.000+02:00
diff --git a/src/num_methods/binary_search.md b/src/num_methods/binary_search.md
@@ -79,7 +79,8 @@ $$
 f(0) \leq f(1) \leq \dots \leq f(n-1).
 $$
 
-The binary search, the way it is described above, finds the partition of the array by the predicate $f(M)$, holding the boolean value of $k < A_M$ expression. In other words, binary search finds the unique index $L$ such that $f(L) = 0$ and $f(R)=f(L+1)=1$.
+The binary search, the way it is described above, finds the partition of the array by the predicate $f(M)$, holding the boolean value of $k < A_M$ expression.
+In other words, binary search finds the unique index $L$ such that $f(L) = 0$ and $f(R)=f(L+1)=1$, or gives us $L = n-1$ if $f(0) = \dots = f(n-1) = 0$ or $L = -1$ if $f(0) = \dots = f(n-1) = 1$.
 
 It is possible to use arbitrary monotonous predicate instead of $k < A_M$. It is particularly useful when the computation of $f(k)$ is requires too much time to actually compute it for every possible value.
 
