Merge pull request #590 from tkoeppe/algorithm

[algorithms] Improve typographic consistency of complexity expressions

Author: jwakely

source/algorithms.tex

@@ -2271,9 +2271,8 @@
 
 \pnum
 \complexity
-At most
-\tcode{(last - first) * log(last - first)}
-swaps, but only linear number of swaps if there is enough extra memory.
+At most $N \log(N)$ swaps, where $N = \tcode{last - first}$,
+but only \bigoh{N} swaps if there is enough extra memory.
 Exactly
 \tcode{last - first}
 applications of the predicate.
@@ -2324,7 +2323,7 @@
 \returns An iterator \tcode{mid} such that \tcode{all_of(first, mid, pred)} and \tcode{none_of(mid, last, pred)} are both true.
 
 \pnum
-\complexity \bigoh{log(last - first)} applications of \tcode{pred}.
+\complexity \bigoh{\log(\tcode{last - first})} applications of \tcode{pred}.
 \end{itemdescr}
 
 
@@ -2481,10 +2480,7 @@
 
 \pnum
 \complexity
-\bigoh{N\log(N)}
-(where
-\tcode{$N$ == last - first})
-comparisons.
+\bigoh{N\log(N)} comparisons, where $N = \tcode{last - first}$.
 \end{itemdescr}
 
 \rSec3[stable.sort]{\tcode{stable_sort}}
@@ -2515,11 +2511,9 @@
 
 \pnum
 \complexity
-It does at most $N \log^2(N)$
-(where
-\tcode{$N$ == last - first})
-comparisons; if enough extra memory is available, it is
-$N \log(N)$.
+At most $N \log^2(N)$
+comparisons, where
+$N = \tcode{last - first}$, but only $N \log(N)$ comparisons if there is enough extra memory.
 
 \pnum
 \remarks Stable~(\ref{algorithm.stable}).
@@ -3045,12 +3039,7 @@
 \tcode{(last - first) - 1}
 comparisons.
 If no additional memory is available, an algorithm with complexity
-$N \log(N)$
-(where
-\tcode{N}
-is equal to
-\tcode{last - first})
-may be used.
+$N \log(N)$ may be used, where $N = \tcode{last - first}$.
 
 \pnum
 \remarks Stable~(\ref{algorithm.stable}).
@@ -3381,7 +3370,7 @@
 \pnum
 \complexity
 At most
-\tcode{log(last - first)}
+$\log(\tcode{last - first})$
 comparisons.
 \end{itemdescr}
 
@@ -3422,7 +3411,7 @@
 \pnum
 \complexity
 At most
-\tcode{2 * log(last - first)}
+$2 \log(\tcode{last - first})$
 comparisons.
 \end{itemdescr}
 
@@ -3488,8 +3477,8 @@
 \pnum
 \complexity
 At most $N \log(N)$
-comparisons (where
-\tcode{N == last - first}).
+comparisons, where
+$N = \tcode{last - first}$.
 \end{itemdescr}
 
 \rSec3[is.heap]{\tcode{is_heap}}