Add knapsack problem.

Author: trekhleb

README.md

@@ -80,6 +80,7 @@
 ### Algorithms by Paradigm
 
 * **Greedy**
+  * [Unbound Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
 * **Divide and Conquer**
   * [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)
@@ -95,7 +96,7 @@
   * [Longest Common Substring](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
   * [Longest Increasing subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
   * [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence)
-  * [Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
+  * [0/1 Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
   * Maximum subarray
   * Maximum sum path
   * Integer Partition

src/algorithms/sets/knapsack-problem/Knapsack.js

@@ -9,16 +9,9 @@ export default class Knapsack {
     this.selectedItems = [];
     this.weightLimit = weightLimit;
     this.possibleItems = possibleItems;
-    // We do two sorts because in case of equal weights but different values
-    // we need to take the most valuable items first.
-    this.sortPossibleItemsByValue();
-    this.sortPossibleItemsByWeight();
   }
 
   sortPossibleItemsByWeight() {
-    // Sort possible items by their weight.
-    // We need them to be sorted in order to solve knapsack problem using
-    // Dynamic Programming approach.
     this.possibleItems = new MergeSort({
       /**
        * @var KnapsackItem itemA
@@ -35,9 +28,6 @@ export default class Knapsack {
   }
 
   sortPossibleItemsByValue() {
-    // Sort possible items by their weight.
-    // We need them to be sorted in order to solve knapsack problem using
-    // Dynamic Programming approach.
     this.possibleItems = new MergeSort({
       /**
        * @var KnapsackItem itemA
@@ -53,8 +43,30 @@ export default class Knapsack {
     }).sort(this.possibleItems);
   }
 
-  // Solve 0/1 knapsack problem using dynamic programming.
+  sortPossibleItemsByValuePerWeightRatio() {
+    this.possibleItems = new MergeSort({
+      /**
+       * @var KnapsackItem itemA
+       * @var KnapsackItem itemB
+       */
+      compareCallback: (itemA, itemB) => {
+        if (itemA.valuePerWeightRatio === itemB.valuePerWeightRatio) {
+          return 0;
+        }
+
+        return itemA.valuePerWeightRatio > itemB.valuePerWeightRatio ? -1 : 1;
+      },
+    }).sort(this.possibleItems);
+  }
+
+  // Solve 0/1 knapsack problem
+  // Dynamic Programming approach.
   solveZeroOneKnapsackProblem() {
+    // We do two sorts because in case of equal weights but different values
+    // we need to take the most valuable items first.
+    this.sortPossibleItemsByValue();
+    this.sortPossibleItemsByWeight();
+
     this.selectedItems = [];
 
     // Create knapsack values matrix.
@@ -138,6 +150,29 @@ export default class Knapsack {
     }
   }
 
+
+  // Solve unbounded knapsack problem.
+  // Greedy approach.
+  solveUnboundedKnapsackProblem() {
+    this.sortPossibleItemsByValue();
+    this.sortPossibleItemsByValuePerWeightRatio();
+
+    for (let itemIndex = 0; itemIndex < this.possibleItems.length; itemIndex += 1) {
+      if (this.totalWeight < this.weightLimit) {
+        const currentItem = this.possibleItems[itemIndex];
+
+        // Detect how much of current items we can push to knapsack.
+        const availableWeight = this.weightLimit - this.totalWeight;
+        const maxPossibleItemsCount = Math.floor(availableWeight / currentItem.weight);
+
+        if (maxPossibleItemsCount) {
+          currentItem.quantity = maxPossibleItemsCount;
+          this.selectedItems.push(currentItem);
+        }
+      }
+    }
+  }
+
   get totalValue() {
     /** @var {KnapsackItem} item */
     return this.selectedItems.reduce((accumulator, item) => {

src/algorithms/sets/knapsack-problem/KnapsackItem.js

@@ -21,6 +21,12 @@ export default class KnapsackItem {
     return this.weight * this.quantity;
   }
 
+  // This coefficient shows how valuable the 1 unit of weight is
+  // for current item.
+  get valuePerWeightRatio() {
+    return this.value / this.weight;
+  }
+
   toString() {
     return `v${this.value} w${this.weight} x ${this.quantity}`;
   }

src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js

@@ -86,4 +86,27 @@ describe('Knapsack', () => {
     expect(knapsack.selectedItems[1].toString()).toBe('v5 w1 x 1');
     expect(knapsack.selectedItems[2].toString()).toBe('v7 w1 x 1');
   });
+
+  it('should solve unbound knapsack problem', () => {
+    const possibleKnapsackItems = [
+      new KnapsackItem({ value: 84, weight: 7 }), // v/w ratio is 12
+      new KnapsackItem({ value: 5, weight: 2 }), // v/w ratio is 2.5
+      new KnapsackItem({ value: 12, weight: 3 }), // v/w ratio is 4
+      new KnapsackItem({ value: 10, weight: 1 }), // v/w ratio is 10
+      new KnapsackItem({ value: 20, weight: 2 }), // v/w ratio is 10
+    ];
+
+    const maxKnapsackWeight = 17;
+
+    const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight);
+
+    knapsack.solveUnboundedKnapsackProblem();
+
+    expect(knapsack.totalValue).toBe(84 + 84 + 20 + 10);
+    expect(knapsack.totalWeight).toBe(17);
+    expect(knapsack.selectedItems.length).toBe(3);
+    expect(knapsack.selectedItems[0].toString()).toBe('v84 w7 x 2');
+    expect(knapsack.selectedItems[1].toString()).toBe('v20 w2 x 1');
+    expect(knapsack.selectedItems[2].toString()).toBe('v10 w1 x 1');
+  });
 });

src/algorithms/sets/knapsack-problem/__test__/KnapsackItem.test.js

@@ -2,31 +2,34 @@ import KnapsackItem from '../KnapsackItem';
 
 describe('KnapsackItem', () => {
   it('should create knapsack item and count its total weight and value', () => {
-    const item1 = new KnapsackItem({ value: 3, weight: 2 });
+    const knapsackItem = new KnapsackItem({ value: 3, weight: 2 });
 
-    expect(item1.value).toBe(3);
-    expect(item1.weight).toBe(2);
-    expect(item1.quantity).toBe(1);
-    expect(item1.toString()).toBe('v3 w2 x 1');
-    expect(item1.totalValue).toBe(3);
-    expect(item1.totalWeight).toBe(2);
+    expect(knapsackItem.value).toBe(3);
+    expect(knapsackItem.weight).toBe(2);
+    expect(knapsackItem.quantity).toBe(1);
+    expect(knapsackItem.valuePerWeightRatio).toBe(1.5);
+    expect(knapsackItem.toString()).toBe('v3 w2 x 1');
+    expect(knapsackItem.totalValue).toBe(3);
+    expect(knapsackItem.totalWeight).toBe(2);
 
-    item1.quantity = 0;
+    knapsackItem.quantity = 0;
 
-    expect(item1.value).toBe(3);
-    expect(item1.weight).toBe(2);
-    expect(item1.quantity).toBe(0);
-    expect(item1.toString()).toBe('v3 w2 x 0');
-    expect(item1.totalValue).toBe(0);
-    expect(item1.totalWeight).toBe(0);
+    expect(knapsackItem.value).toBe(3);
+    expect(knapsackItem.weight).toBe(2);
+    expect(knapsackItem.quantity).toBe(0);
+    expect(knapsackItem.valuePerWeightRatio).toBe(1.5);
+    expect(knapsackItem.toString()).toBe('v3 w2 x 0');
+    expect(knapsackItem.totalValue).toBe(0);
+    expect(knapsackItem.totalWeight).toBe(0);
 
-    item1.quantity = 2;
+    knapsackItem.quantity = 2;
 
-    expect(item1.value).toBe(3);
-    expect(item1.weight).toBe(2);
-    expect(item1.quantity).toBe(2);
-    expect(item1.toString()).toBe('v3 w2 x 2');
-    expect(item1.totalValue).toBe(6);
-    expect(item1.totalWeight).toBe(4);
+    expect(knapsackItem.value).toBe(3);
+    expect(knapsackItem.weight).toBe(2);
+    expect(knapsackItem.quantity).toBe(2);
+    expect(knapsackItem.valuePerWeightRatio).toBe(1.5);
+    expect(knapsackItem.toString()).toBe('v3 w2 x 2');
+    expect(knapsackItem.totalValue).toBe(6);
+    expect(knapsackItem.totalWeight).toBe(4);
   });
 });