diff --git a/curriculum/challenges/_meta/rosetta-code/meta.json b/curriculum/challenges/_meta/rosetta-code/meta.json index a1a1289c25..31f5d6864c 100644 --- a/curriculum/challenges/_meta/rosetta-code/meta.json +++ b/curriculum/challenges/_meta/rosetta-code/meta.json @@ -320,6 +320,22 @@ "5a23c84252665b21eecc7eca", "Kaprekar numbers" ], + [ + "5a23c84252665b21eecc7ed1", + "Knapsack problem/0-1" + ], + [ + "5a23c84252665b21eecc7ed2", + "Knapsack problem/Bounded" + ], + [ + "5a23c84252665b21eecc7ed3", + "Knapsack problem/Continuous" + ], + [ + "5a23c84252665b21eecc7ed4", + "Knapsack problem/Unbounded" + ], [ "5a23c84252665b21eecc7ed5", "Knight's tour" diff --git a/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-0-1.md b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-0-1.md new file mode 100644 index 0000000000..587e3b28de --- /dev/null +++ b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-0-1.md @@ -0,0 +1,160 @@ +--- +id: 5a23c84252665b21eecc7ed1 +title: Knapsack problem/0-1 +challengeType: 5 +--- + +## Description +
+The 0-1 knapsack problem is defined as follows: +You are given an array of objects representing items to be put in a knapsack. The objects have 3 attributes: name, weight, and value. The items need to be selected so that the total weight does not exceed the maximum weight and the value is maximized. +
+ +## Instructions +
+Write a function to solve the knapsack problem. The function is given the array of objects and the maximum weight as parameters. It should return the maximum total value possible. +
+ +## Tests +
+ +``` yml +tests: + - text: knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 100) should return 405. + testString: assert.equal(knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 100), 405, "knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 100) should return 405."); + - text: knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 200) should return 510. + testString: assert.equal(knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 200), 510, "knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 200) should return 510."); + - text: knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 100) should return 145. + testString: assert.equal(knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 100), 145, "knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 100) should return 145."); + - text: knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 200) should return 185. + testString: assert.equal(knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 200), 185, "knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 200) should return 185."); + - text: knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 100) should return 237. + testString: assert.equal(knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 100), 237, "knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 100) should return 237."); + - text: knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 200) should return 317.' + testString: assert.equal(knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 200), 317, "knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 200) should return 317."); +``` + +
+ +## Challenge Seed +
+
+ +```js +function knapsack(items, maxweight) { + // Good luck! +} +``` + +
+
+ +## Solution +
+ +```js +function knapsack(items, maxweight) { + var _ = { + max: function (e) { + var mx = e[0]; + e.forEach(function (f) { + if (mx < f) + mx = f; + }) + return mx; + }, + map: function (array, func) { + return array.map(func) + }, + isUndefined: function (a) { + if (a) { + return false; + } + return true; + }, + range: function (start, end, step) { + var a = [] + var f = f = (i, end) => i < end + if (start > end) + f = (i, end) => i > end + + for (var i = start; f(i, end); i += step) + a.push(i) + return a + } + } + + var valuefn = (e) => e.value + var weightfn = (e) => e.weight + var _epsilon = 0.01; + var _p = _.max(_.map(items, valuefn)); + var _k = _epsilon * _p / items.length; + + var _memo = (function () { + var _mem = {}; + var _key = function (i, w) { + return i + '::' + w; + }; + return { + get: function (i, w) { + return _mem[_key(i, w)]; + }, + put: function (i, w, r) { + _mem[_key(i, w)] = r; + return r; + } + }; + })(); + + var _m = function (i, w) { + + i = Math.round(i); + w = Math.round(w); + + + if (i < 0 || w === 0) { + // empty base case + return { items: [], totalWeight: 0, totalValue: 0 }; + } + + var mm = _memo.get(i, w); + if (!_.isUndefined(mm)) { + return mm; + } + + var item = items[i]; + if (weightfn(item) > w) { + //item does not fit, try the next item + return _memo.put(i, w, _m(i - 1, w)); + } + // this item could fit. + // are we better off excluding it? + var excluded = _m(i - 1, w); + // or including it? + var included = _m(i - 1, w - weightfn(item)); + if (included.totalValue + Math.floor(valuefn(item) / _k) > excluded.totalValue) { + // better off including it + // make a copy of the list + var i1 = included.items.slice(); + i1.push(item); + return _memo.put(i, w, + { + items: i1, + totalWeight: included.totalWeight + weightfn(item), + totalValue: included.totalValue + Math.floor(valuefn(item) / _k) + }); + } + //better off excluding it + return _memo.put(i, w, excluded); + }; + var scaled = _m(items.length - 1, maxweight); + + var val = 0; + scaled.items.forEach(function (e) { + val += e.value + }) + return val; +} +``` + +
diff --git a/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-bounded.md b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-bounded.md new file mode 100644 index 0000000000..2aa35b36a5 --- /dev/null +++ b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-bounded.md @@ -0,0 +1,108 @@ +--- +id: 5a23c84252665b21eecc7ed2 +title: Knapsack problem/Bounded +challengeType: 5 +--- + +## Description +
+The bounded knapsack problem is defined as follows: +You are given an array of objects representing items to be put in a knapsack. The objects have 4 attributes: name, pieces (the number of the particular item), weight, and value. The items need to be selected so that the total weight does not exceed the maximum weight and the value is maximized. Keep in mind that each item can appear between 0 and pieces times. +
+ +## Instructions +
+Write a function to solve the knapsack problem. The function is given the array of objects and the maximum weight as parameters. It should return the maximum total value possible. +
+ +## Tests +
+ +``` yml +tests: + - text: findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300) should return 755. + testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300), 755, "findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300) should return 755."); + - text: findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400) should return 875. + testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400), 875, "findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400) should return 875."); + - text: findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500) should return 1015. + testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500), 1015, "findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500) should return 1015."); + - text: findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600) should return 1120. + testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600), 1120, "findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600) should return 1120."); + - text: findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700) should return 1225. + testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700), 1225, "findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700) should return 1225."); +``` + +
+ +## Challenge Seed +
+
+ +```js +function findBestPack(data, maxweight) { + // Good luck! +} +``` + +
+
+ +## Solution +
+ +```js +function findBestPack(data, maxweight) { + var m = [ + [0] + ]; // maximum pack value found so far + var b = [ + [0] + ]; // best combination found so far + var opts = [0]; // item index for 0 of item 0 + var P = [1]; // item encoding for 0 of item 0 + var choose = 0; + for (var j = 0; j < data.length; j++) { + opts[j + 1] = opts[j] + data[j].pieces; // item index for 0 of item j+1 + P[j + 1] = P[j] * (1 + data[j].pieces); // item encoding for 0 of item j+1 + } + for (var j = 0; j < opts[data.length]; j++) { + m[0][j + 1] = b[0][j + 1] = 0; // best values and combos for empty pack: nothing + } + for (var w = 1; w <= maxweight; w++) { + m[w] = [0]; + b[w] = [0]; + for (var j = 0; j < data.length; j++) { + var N = data[j].pieces; // how many of these can we have? + var base = opts[j]; // what is the item index for 0 of these? + for (var n = 1; n <= N; n++) { + var W = n * data[j].weight; // how much do these items weigh? + var s = w >= W ? 1 : 0; // can we carry this many? + var v = s * n * data[j].value; // how much are they worth? + var I = base + n; // what is the item number for this many? + var wN = w - s * W; // how much other stuff can we be carrying? + var C = n * P[j] + b[wN][base]; // encoded combination + m[w][I] = Math.max(m[w][I - 1], v + m[wN][base]); // best value + choose = b[w][I] = m[w][I] > m[w][I - 1] ? C : b[w][I - 1]; + } + } + } + + var best = []; + for (var j = data.length - 1; j >= 0; j--) { + best[j] = Math.floor(choose / P[j]); + choose -= best[j] * P[j]; + } + + var wgt = 0; + var val = 0; + for (var i = 0; i < best.length; i++) { + if (0 == best[i]) continue; + wgt += best[i] * data[i].weight; + val += best[i] * data[i].value; + } + + return val; +} +``` + +
diff --git a/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-continuous.md b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-continuous.md new file mode 100644 index 0000000000..0c67becb90 --- /dev/null +++ b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-continuous.md @@ -0,0 +1,77 @@ +--- +id: 5a23c84252665b21eecc7ed3 +title: Knapsack problem/Continuous +challengeType: 5 +--- + +## Description +
+A thief burgles a butcher's shop, where he can select from some items. +The thief knows the weights and prices of each items. Because he has a knapsack with a limit on the maximum weight that it can carry, he wants to select the items such that he would have his profit maximized. He may cut the items; the item has a reduced price after cutting that is proportional to the original price by the ratio of masses. That means: half of an item has half the price of the original. +
+ +## Instructions +
+Write a function that takes an array of objects representing the items available in the shop. Each object has 3 attributes: name, weight, and value. The function also takes the maximum weight as a parameter. The function should return the maximum value possible, and the total weight of the selected items should not exceed the maximum weight. +
+ +## Tests +
+ +``` yml +tests: + - text: knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 10) should return 257.875. + testString: assert.equal(knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 10), 257.875, 'knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 10) should return 257.875.'); + - text: knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 12) should return 295.05405405405406. + testString: assert.equal(knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 12), 295.05405405405406, 'knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 12) should return 295.05405405405406.'); + - text: knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 15) should return 349.3783783783784. + testString: assert.equal(knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 15), 349.3783783783784, 'knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 15) should return 349.3783783783784.'); + - text: knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 22) should return 459.5263157894737. + testString: assert.equal(knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 22), 459.5263157894737, 'knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 22) should return 459.5263157894737.'); + - text: knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 24) should return 478.4736842105263. + testString: assert.equal(knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 24), 478.4736842105263, 'knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 24) should return 478.4736842105263.'); +``` + +
+ +## Challenge Seed +
+
+ +```js +function knapContinuous (items, maxweight) { + // Good luck! +} +``` + +
+
+ +## Solution +
+ +```js +function knapContinuous(items, maxweight) { + function item_cmp(a, b) { + const ua = a.unitVal, ub = b.unitVal; + return ua < ub ? 1 : ua > ub ? -1 : 0; + } + items = items.map(({ value, weight }) => ({ unitVal: value / weight, weight })); + items.sort(item_cmp) + + let val = 0; + let wt = 0; + for (let { unitVal, weight } of items) { + var portion = Math.min(maxweight - wt, weight); + wt += portion; + var addVal = portion * unitVal; + val += addVal; + if (wt >= maxweight) { + break; + } + } + return val; +} +``` + +
diff --git a/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-unbounded.md b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-unbounded.md new file mode 100644 index 0000000000..c471852c1f --- /dev/null +++ b/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-unbounded.md @@ -0,0 +1,90 @@ +--- +id: 5a23c84252665b21eecc7ed4 +title: Knapsack problem/Unbounded +challengeType: 5 +--- + +## Description +
+A traveler gets diverted and has to make an unscheduled stop in what turns out to be Shangri-La. Opting to leave, he is allowed to take as much as he likes of the items available there, so long as it will fit in his knapsack, and he can carry it. +He knows that he can carry no more than a particular value of maximum weight in total; and that the capacity of his knapsack has a limited volume. +Looking just above the bar codes on the items he finds their weights and volumes. He digs out his recent copy of a financial paper and gets the value of each item. +He can only take whole units of any item, but there is much more of any item than he could ever carry. +
+ +## Instructions +
+Write a function that takes an array of objects, maximum weight, and maximum volume as parameters. Each object has 4 attributes: name, value, weight, and volume. The function should return the maximum value of items the traveller can take with him. +
+ +## Tests +
+ +``` yml +tests: + - text: knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.25) should return 54500. + testString: assert.equal(knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.25), 54500, 'knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.25) should return 54500.'); + - text: knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 55, 0.25) should return 88400. + testString: assert.equal(knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 55, 0.25), 88400, 'knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 55, 0.25) should return 88400.'); + - text: knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.15) should return 42500. + testString: assert.equal(knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.15), 42500, 'knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 25, 0.15) should return 42500.'); + - text: knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 35, 0.35) should return 75300. + testString: assert.equal(knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 35, 0.35), 75300, 'knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 35, 0.35) should return 75300.'); + - text: knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 15, 0.25) should return 43200. + testString: assert.equal(knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 15, 0.25), 43200, 'knapsackUnbounded([{ name:"panacea", value:3000, weight:0.3, volume:0.025 }, { name:"ichor", value:1800, weight:0.2, volume:0.015 }, { name:"gold", value:2500, weight:2, volume:0.002 }], 15, 0.25) should return 43200.'); +``` + +
+ +## Challenge Seed +
+
+ +```js +function knapsackUnbounded(items, maxweight, maxvolume) { + // Good luck! +} +``` + +
+
+ +## Solution +
+ +```js +function knapsackUnbounded(items, maxweight, maxvolume) { + var n = items.length; + var best_value = 0; + var count = new Array(n) + var best = new Array(n) + function recurseKnapsack(i, value, weight, volume) { + var j, m1, m2, m; + if (i == n) { + if (value > best_value) { + best_value = value; + for (j = 0; j < n; j++) { + best[j] = count[j]; + } + } + return; + } + m1 = Math.floor(weight / items[i].weight); + m2 = Math.floor(volume / items[i].volume); + m = m1 < m2 ? m1 : m2; + for (count[i] = m; count[i] >= 0; count[i]--) { + recurseKnapsack( + i + 1, + value + count[i] * items[i].value, + weight - count[i] * items[i].weight, + volume - count[i] * items[i].volume + ); + } + } + + recurseKnapsack(0, 0, maxweight, maxvolume); + return best_value; +} +``` + +