From f60de17430b45df353984978ab493e91de3b56b5 Mon Sep 17 00:00:00 2001
From: Daniel Ethridge <danielethridge@icloud.com>
Date: Sat, 4 Sep 2021 22:12:47 -0400
Subject: [PATCH 1/2] Initial reconciliation code

---
 packages/bruh/src/reconcile/index.mjs | 62 +++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 packages/bruh/src/reconcile/index.mjs

diff --git a/packages/bruh/src/reconcile/index.mjs b/packages/bruh/src/reconcile/index.mjs
new file mode 100644
index 0000000..29d849e
--- /dev/null
+++ b/packages/bruh/src/reconcile/index.mjs
@@ -0,0 +1,62 @@
+// Find how to change a source array into a target array, minimizing removals
+export const compare = (source, target) => {
+  // Set every item of a size (a+1)*(b+1) matrix except for
+  // the first row and column, which are both filled with 0
+  const m = Array.from(
+    Array(source.length+1),
+    () => Array(target.length+1).fill(0)
+  )
+
+  for (let i = 1; i <= source.length; i++)
+  for (let j = 1; j <= target.length; j++)
+    m[i][j] =
+      source[i-1] === target[j-1]
+        // If the corresponding array items match,
+        // set the item to be one more than
+        // its upper left diagonal neighbor
+        ? m[i-1][j-1] + 1
+        // If they don't match,
+        // set the item to be the largest of
+        // its top or left neighbors
+        : m[i-1][j] > m[i][j-1]
+            ? m[i-1][j  ]
+            : m[i  ][j-1]
+
+  // Now we trace backwards from the bottom right corner
+  // to the top left corner (we will return the reverse)
+  const changes = []
+
+  let i = source.length
+  let j = target.length
+  while (i > 0 && j > 0) switch (m[i][j]) {
+    // When the left neighbor was this items source,
+    // that corresponds to an insertion
+    case m[i  ][j-1]:
+      changes.push({ insert: target[j-1] })
+      j--
+      break
+
+    // When the top neighbor was this item's source,
+    // that corresponds to a removal
+    case m[i-1][j  ]:
+      changes.push({ remove: source[i-1] })
+      i--
+      break
+
+    // When the upper left diagonal neighbor was
+    // this item's source, the item was unchanged
+    // That means that it is part of the LCS
+    case m[i-1][j-1] + 1:
+      changes.push({ keep: source[i-1] })
+      i--
+      j--
+  }
+
+  // Account for any initial removals or insertions
+  for (; i > 0; i--)
+    changes.push({ remove: source[i-1] })
+  for (; j > 0; j--)
+    changes.push({ insert: target[j-1] })
+
+  return changes.reverse()
+}

From be97d54293bed644476acb35179b036b9520bb46 Mon Sep 17 00:00:00 2001
From: Daniel Ethridge <danielethridge@icloud.com>
Date: Tue, 12 Oct 2021 21:28:17 -0400
Subject: [PATCH 2/2] WIP Wu Manber

---
 packages/bruh/src/reconcile/index.mjs | 63 +++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)

diff --git a/packages/bruh/src/reconcile/index.mjs b/packages/bruh/src/reconcile/index.mjs
index 29d849e..37dc8b6 100644
--- a/packages/bruh/src/reconcile/index.mjs
+++ b/packages/bruh/src/reconcile/index.mjs
@@ -60,3 +60,66 @@ export const compare = (source, target) => {
 
   return changes.reverse()
 }
+
+const compareFast = (source, target) => {
+  const [a, b, insert, remove] =
+    source.length < target.length
+      ? [source, target, "insert", "remove"]
+      : [target, source, "remove", "insert"]
+
+  const Δ = b.length - a.length
+
+  // [-(|a|+1) ... 0 ...  |b|+1]
+  const furthestPoints = Array(1+a.length + 1 + b.length+1).fill(-1)
+  const changes = []
+
+  // diagonal k has vertices (x, y) where k = y - x
+  // there are diagonals ranging from -a.length to b.length
+  // diagonal 0 starts with the source (0, 0)
+  // diagonal Δ ends with the sink (a.length, b.length)
+  const snake = k => {
+    // diagonal below k
+    const yBelow = furthestPoints[k-1] + 1
+    // diagonal above k
+    const yAbove = furthestPoints[k+1]
+
+    let x, y
+    if (yBelow > yAbove) {
+      y = yBelow
+      x = y - k
+      changes[k] = [...changes[k-1] || [], { [insert]: b[y] }]
+    }
+    else {
+      y = yAbove
+      x = y - k
+      changes[k] = [...changes[k+1] || [], { [remove]: a[x] }]
+    }
+
+    while (x < a.length && y < b.length && a[x+1] === b[y+1]) {
+      changes[k].push({ keep: a[x+1] })
+      x++
+      y++
+    }
+
+    furthestPoints[k] = y
+  }
+
+  // p = (d-Δ)/2 where d is the number of insertions and removals
+  // We only need to examine diagonals from 0-p to Δ+p because vertices
+  // outside of the band from the source-p diagonal to sink+p diagonal
+  // by definition cannot have a shorter path than vertices within the p-band
+  for (let p = 0; furthestPoints[Δ] !== b.length; p++) {
+    // Examine diagonals from -p up to Δ-1
+    for (let k = -p;    k < Δ; k++)
+      snake(k)
+
+    // Examine diagonals from Δ + p down to Δ+1
+    for (let k = Δ + p; k > Δ; k--)
+      snake(k)
+
+    // Examine the diagonal at Δ
+    snake(Δ)
+  }
+
+  return changes[Δ].slice(1, -1)
+}