diff --git a/dynamic-programming/notes.md b/dynamic-programming/notes.md
index c2821f3c1c89f1164bbce957e628bb7004047549..e70b77e912866fe1284bc5fa86bc59f1a2a8311a 100644
--- a/dynamic-programming/notes.md
+++ b/dynamic-programming/notes.md
@@ -115,34 +115,34 @@ Problem: Wrap a paragraph to a line length, minimizing the sum of the squares of
## DAG
* Edges (actions):
- * …
+ * Place an entire line
* Vertices (situations):
- * …
+ * The number of words placed so far
* Edge weights:
- * …
+ * The penalty for the line just placed
* Topological order:
- * …
+ * 0 → 1 → … → `wordCount`
* Goal:
- * …
+ * Find a shortest path from 0 to `wordCount`
## Backpointer Class
* Information for the final result:
- * …
+ * What was the position of the previous line break?
* Information to go back:
- * …
+ * What was the position of the previous line break? (redundant)
* Information to compare quality:
- * …
+ * What was the *total* penalty for the lines placed so far?
## Choosing a Backpointer
* Exhaustive search:
- * Generate ….
- * Check that ….
+ * Generate start-of-line positions (in reverse order) as long as the character count (a running total) does not exceed the line length and the start-of-line position does not go negative.
+ * Check that the backpointer minimizes the *total* penalty (the total penalty of all prior lines plus the penalty of the newly added line).
## Example
-> x x x x xxxx xxxx
+> x x x|x xxxx|xxxx
> 0 1 2 3 4 5 6
Vertex Backpointer
@@ -150,13 +150,13 @@ Problem: Wrap a paragraph to a line length, minimizing the sum of the squares of
Index Previous Index Total Penalty
------ -------------- -------------
0 ⊥ 0
- 1 … …
- 2 … …
- 3 … …
- 4 … …
- 5 … …
- 6 … …
+ 1 0 36
+ 2 0 16
+ 3 0 4
+ 4 0 0
+ 5 3 5
+ 6 5 14
Reversed Path
----
- 6 ← …
+ 6 ← 5 ← 3 ← 0
diff --git a/dynamic-programming/src/features/wrapping/solver.js b/dynamic-programming/src/features/wrapping/solver.js
index 062a7fa11ac32231da84d1930b7350c7e2707993..380f102797d83114548734f0257e61f4d6fff199 100644
--- a/dynamic-programming/src/features/wrapping/solver.js
+++ b/dynamic-programming/src/features/wrapping/solver.js
@@ -12,7 +12,17 @@ class Backpointer {
function chooseBackpointer(wordLengths, lineLength, backpointers) {
const index = backpointers.length;
let best = new Backpointer(undefined, Infinity);
- // TODO: stub
+ for (let start = index - 1, characterCount = wordLengths[start];
+ start >= 0 && characterCount <= lineLength;
+ --start, characterCount += wordLengths[start] + 1) {
+ const candidate = new Backpointer(
+ start,
+ backpointers[start].totalPenalty + penalty(characterCount, lineLength),
+ );
+ if (candidate.totalPenalty < best.totalPenalty) {
+ best = candidate;
+ }
+ }
console.assert(
best.previousIndex !== undefined,
`One of the word lengths ${wordLengths} is too long to fit in a line of length ${lineLength}.`,