From 3c7e32370cb26098d6108292b7dbc482281e4fef Mon Sep 17 00:00:00 2001
From: Dmitry Naimark <dmitrynaimark@gmail.com>
Date: Thu, 25 Apr 2019 12:37:21 +0300
Subject: [PATCH] Add test for Knapsack 0/1 problem and fix "tracing" part of
 this algorithm.

---
 .../sets/knapsack-problem/Knapsack.js         | 36 +++++++------------
 .../__test__/Knapsack.test.js                 | 20 +++++++++++
 2 files changed, 33 insertions(+), 23 deletions(-)

diff --git a/src/algorithms/sets/knapsack-problem/Knapsack.js b/src/algorithms/sets/knapsack-problem/Knapsack.js
index d93e51a3..1500f4c2 100644
--- a/src/algorithms/sets/knapsack-problem/Knapsack.js
+++ b/src/algorithms/sets/knapsack-problem/Knapsack.js
@@ -120,30 +120,20 @@ export default class Knapsack {
     let itemIndex = this.possibleItems.length - 1;
     let weightIndex = this.weightLimit;
 
-    while (itemIndex > 0) {
-      const currentItem = this.possibleItems[itemIndex];
-      const prevItem = this.possibleItems[itemIndex - 1];
-
+    while (itemIndex >= 0) {
       // Check if matrix value came from top (from previous item).
-      // In this case this would mean that we need to include previous item
-      // to the list of selected items.
-      if (
-        knapsackMatrix[itemIndex][weightIndex]
-        && knapsackMatrix[itemIndex][weightIndex] === knapsackMatrix[itemIndex - 1][weightIndex]
-      ) {
-        // Check if there are several items with the same weight but with the different values.
-        // We need to add highest item in the matrix that is possible to get the highest value.
-        const prevSumValue = knapsackMatrix[itemIndex - 1][weightIndex];
-        const prevPrevSumValue = knapsackMatrix[itemIndex - 2][weightIndex];
-        if (
-          !prevSumValue
-          || (prevSumValue && prevPrevSumValue !== prevSumValue)
-        ) {
-          this.selectedItems.push(prevItem);
-        }
-      } else if (knapsackMatrix[itemIndex - 1][weightIndex - currentItem.weight]) {
-        this.selectedItems.push(prevItem);
-        weightIndex -= currentItem.weight;
+      // In this case this would mean that we need to include the topmost item with the
+      // same max possible value and the same weight to the list of selected items.
+      while (knapsackMatrix[itemIndex - 1] !== undefined
+        && knapsackMatrix[itemIndex][weightIndex] === knapsackMatrix[itemIndex - 1][weightIndex]) {
+        itemIndex -= 1;
+      }
+
+      // If max possible value in the cell is not zero(and not undefined).
+      if (knapsackMatrix[itemIndex][weightIndex]) {
+        // Add item to knapsack and decrease remaining weight capacity by item's weight.
+        this.selectedItems.push(this.possibleItems[itemIndex]);
+        weightIndex -= this.possibleItems[itemIndex].weight;
       }
 
       itemIndex -= 1;
diff --git a/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js b/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js
index d322445a..9b1c7dbf 100644
--- a/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js
+++ b/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js
@@ -44,6 +44,26 @@ describe('Knapsack', () => {
     expect(knapsack.selectedItems[1].toString()).toBe('v4 w3 x 1');
   });
 
+  it('should solve 0/1 knapsack problem 2', () => {
+    const possibleKnapsackItems = [
+      new KnapsackItem({ value: 5, weight: 3 }),
+      new KnapsackItem({ value: 3, weight: 2 }),
+      new KnapsackItem({ value: 4, weight: 1 }),
+    ];
+
+    const maxKnapsackWeight = 5;
+
+    const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight);
+
+    knapsack.solveZeroOneKnapsackProblem();
+
+    expect(knapsack.totalValue).toBe(9);
+    expect(knapsack.totalWeight).toBe(4);
+    expect(knapsack.selectedItems.length).toBe(2);
+    expect(knapsack.selectedItems[0].toString()).toBe('v5 w3 x 1');
+    expect(knapsack.selectedItems[1].toString()).toBe('v4 w1 x 1');
+  });
+
   it('should solve 0/1 knapsack problem with impossible items set', () => {
     const possibleKnapsackItems = [
       new KnapsackItem({ value: 5, weight: 40 }),