Linda comments -> mods

Author: lee-naish

src/algorithms/explanations/PRIMExp.md

@@ -33,7 +33,8 @@ These are:
 
 
 - "Finalised" nodes, for which the shortest or least costly path back to the start node has already
-been finalised, that is the final parent node has been determined and is recorded;
+been finalised (see below for further explanation of this),
+that is the final parent node has been determined and is recorded;
 
 - "Frontier" nodes, that are not finalised but are connected to a finalised node by a single edge; and
 
@@ -53,6 +54,14 @@ been finalised
 have their costs recomputed. Other algorithms use other data structures to keep track 
 of the frontier nodes.
 
+Saying the finalised nodes have "the least costly path" back to the start
+node may be a little misleading: Prim's algorithm uses the length of just
+*the first edge of the path* as the cost. At each step, Prim's algorithm
+chooses the node with the least *incremental* cost increase for the tree
+being constructed. Throughout the execution, if finalised has size *N*,
+it contains the smallest tree with *N* nodes that includes the start node.
+The paths from each node back to the start are generally not the shortest.
+
 In the presentation here, we do not give details of how the priority
 queue is implemented, but just emphasise it is a collection of nodes
 with associated costs and the node with the minimum cost is selected each

src/algorithms/pseudocode/msort_arr_nat.js

@@ -58,8 +58,8 @@ MergeAll
 FirstRun
     mid <- left \\B mid
     while mid < size and A[mid] <= A[mid+1] \\B FirstRunWhile
-    \\Expl{ Scan until we find an element that is less than the previous
-        element (or we reach the end).
+    \\Expl{ Scan until we find the end of the run: the next element is less
+        than the current element (or we reach the end).
     \\Expl}
     \\In{
         mid <- mid + 1 \\B mid++
@@ -70,8 +70,8 @@ FirstRun
 SecondRun
     right <- mid + 1 \\B right
     while right < size and A[right] <= A[right+1] \\B SecondRunWhile
-    \\Expl{ Scan until we find an element that is less than the previous
-        element (or we reach the end).
+    \\Expl{ Scan until we find the end of the run: the next element is less
+        than the current element (or we reach the end).
     \\Expl}
     \\In{
         right <- right + 1 \\B right++