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Fix 0/1 Knapsack traceback crash and incorrect item selection #2109

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Fix 0/1 Knapsack traceback crash and incorrect item selection #2109

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30 changes: 9 additions & 21 deletions src/algorithms/sets/knapsack-problem/Knapsack.js
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Original file line number Diff line number Diff line change
Expand Up @@ -122,32 +122,20 @@ export default class Knapsack {

while (itemIndex > 0) {
const currentItem = this.possibleItems[itemIndex];
const prevItem = this.possibleItems[itemIndex - 1];

// 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);

// If the value differs from the row above, the current item was included.
if (knapsackMatrix[itemIndex][weightIndex] !== knapsackMatrix[itemIndex - 1][weightIndex]) {
this.selectedItems.push(currentItem);
weightIndex -= currentItem.weight;
}

itemIndex -= 1;
}

// Check if the first item was also included.
if (knapsackMatrix[0][weightIndex] !== 0) {
this.selectedItems.push(this.possibleItems[0]);
}
}

// Solve unbounded knapsack problem.
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19 changes: 19 additions & 0 deletions src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js
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Original file line number Diff line number Diff line change
Expand Up @@ -44,6 +44,25 @@ describe('Knapsack', () => {
expect(knapsack.selectedItems[1].toString()).toBe('v4 w3 x 1');
});

it('should solve 0/1 knapsack problem with no single-weight-1 item (issue #248)', () => {
const possibleKnapsackItems = [
new KnapsackItem({ value: 3, weight: 2 }),
new KnapsackItem({ value: 4, weight: 3 }),
new KnapsackItem({ value: 5, weight: 4 }),
new KnapsackItem({ value: 7, weight: 5 }),
];

const maxKnapsackWeight = 7;

const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight);

knapsack.solveZeroOneKnapsackProblem();

expect(knapsack.totalValue).toBe(10);
expect(knapsack.totalWeight).toBe(7);
expect(knapsack.selectedItems.length).toBe(2);
});

it('should solve 0/1 knapsack problem with impossible items set', () => {
const possibleKnapsackItems = [
new KnapsackItem({ value: 5, weight: 40 }),
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