feat(interview-prep): Converting and transfering Rosetta problems (#35770)
* feat(interview-prep): Converting and transfering Rosetta problemspull/37479/head
Bhanu Pratap Singh Rathore
Kristofer Koishigawa
parent
b6470f93dc
commit
ca63f90070
|
|
@ -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"
|
||||
|
|
|
|||
|
|
@ -0,0 +1,160 @@
|
|||
---
|
||||
id: 5a23c84252665b21eecc7ed1
|
||||
title: Knapsack problem/0-1
|
||||
challengeType: 5
|
||||
---
|
||||
|
||||
## Description
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Tests
|
||||
<section id='tests'>
|
||||
|
||||
``` yml
|
||||
tests:
|
||||
- text: <code>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)</code> should return <code>405</code>.
|
||||
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, "<code>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)</code> should return <code>405</code>.");
|
||||
- text: <code>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)</code> should return <code>510</code>.
|
||||
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, "<code>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)</code> should return <code>510</code>.");
|
||||
- text: <code>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)</code> should return <code>145</code>.
|
||||
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, "<code>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)</code> should return <code>145</code>.");
|
||||
- text: <code>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)</code> should return <code>185</code>.
|
||||
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, "<code>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)</code> should return <code>185</code>.");
|
||||
- text: <code>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)</code> should return <code>237</code>.
|
||||
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, "<code>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)</code> should return <code>237</code>.");
|
||||
- text: <code>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)</code> should return <code>317</code>.'
|
||||
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, "<code>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)</code> should return <code>317</code>.");
|
||||
```
|
||||
|
||||
</section>
|
||||
|
||||
## Challenge Seed
|
||||
<section id='challengeSeed'>
|
||||
<div id='js-seed'>
|
||||
|
||||
```js
|
||||
function knapsack(items, maxweight) {
|
||||
// Good luck!
|
||||
}
|
||||
```
|
||||
|
||||
</div>
|
||||
</section>
|
||||
|
||||
## Solution
|
||||
<section id='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;
|
||||
}
|
||||
```
|
||||
|
||||
</section>
|
||||
|
|
@ -0,0 +1,108 @@
|
|||
---
|
||||
id: 5a23c84252665b21eecc7ed2
|
||||
title: Knapsack problem/Bounded
|
||||
challengeType: 5
|
||||
---
|
||||
|
||||
## Description
|
||||
<section id='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 <code>pieces</code> times.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Tests
|
||||
<section id='tests'>
|
||||
|
||||
``` yml
|
||||
tests:
|
||||
- text: <code>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)</code> should return <code>755</code>.
|
||||
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, "<code>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)</code> should return <code>755</code>.");
|
||||
- text: <code>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)</code> should return <code>875</code>.
|
||||
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, "<code>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)</code> should return <code>875</code>.");
|
||||
- text: <code>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)</code> should return <code>1015</code>.
|
||||
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, "<code>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)</code> should return <code>1015</code>.");
|
||||
- text: <code>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)</code> should return <code>1120</code>.
|
||||
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, "<code>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)</code> should return <code>1120</code>.");
|
||||
- text: <code>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)</code> should return <code>1225</code>.
|
||||
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, "<code>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)</code> should return <code>1225</code>.");
|
||||
```
|
||||
|
||||
</section>
|
||||
|
||||
## Challenge Seed
|
||||
<section id='challengeSeed'>
|
||||
<div id='js-seed'>
|
||||
|
||||
```js
|
||||
function findBestPack(data, maxweight) {
|
||||
// Good luck!
|
||||
}
|
||||
```
|
||||
|
||||
</div>
|
||||
</section>
|
||||
|
||||
## Solution
|
||||
<section id='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;
|
||||
}
|
||||
```
|
||||
|
||||
</section>
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
---
|
||||
id: 5a23c84252665b21eecc7ed3
|
||||
title: Knapsack problem/Continuous
|
||||
challengeType: 5
|
||||
---
|
||||
|
||||
## Description
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Tests
|
||||
<section id='tests'>
|
||||
|
||||
``` yml
|
||||
tests:
|
||||
- text: <code>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)</code> should return <code>257.875</code>.
|
||||
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, '<code>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)</code> should return <code>257.875</code>.');
|
||||
- text: <code>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)</code> should return <code>295.05405405405406</code>.
|
||||
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, '<code>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)</code> should return <code>295.05405405405406</code>.');
|
||||
- text: <code>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)</code> should return <code>349.3783783783784</code>.
|
||||
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, '<code>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)</code> should return <code>349.3783783783784</code>.');
|
||||
- text: <code>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)</code> should return <code>459.5263157894737</code>.
|
||||
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, '<code>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)</code> should return <code>459.5263157894737</code>.');
|
||||
- text: <code>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)</code> should return <code>478.4736842105263</code>.
|
||||
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, '<code>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)</code> should return <code>478.4736842105263</code>.');
|
||||
```
|
||||
|
||||
</section>
|
||||
|
||||
## Challenge Seed
|
||||
<section id='challengeSeed'>
|
||||
<div id='js-seed'>
|
||||
|
||||
```js
|
||||
function knapContinuous (items, maxweight) {
|
||||
// Good luck!
|
||||
}
|
||||
```
|
||||
|
||||
</div>
|
||||
</section>
|
||||
|
||||
## Solution
|
||||
<section id='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;
|
||||
}
|
||||
```
|
||||
|
||||
</section>
|
||||
|
|
@ -0,0 +1,90 @@
|
|||
---
|
||||
id: 5a23c84252665b21eecc7ed4
|
||||
title: Knapsack problem/Unbounded
|
||||
challengeType: 5
|
||||
---
|
||||
|
||||
## Description
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Instructions
|
||||
<section id='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.
|
||||
</section>
|
||||
|
||||
## Tests
|
||||
<section id='tests'>
|
||||
|
||||
``` yml
|
||||
tests:
|
||||
- text: <code>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)</code> should return <code>54500</code>.
|
||||
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, '<code>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)</code> should return <code>54500</code>.');
|
||||
- text: <code>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)</code> should return <code>88400</code>.
|
||||
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, '<code>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)</code> should return <code>88400</code>.');
|
||||
- text: <code>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)</code> should return <code>42500</code>.
|
||||
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, '<code>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)</code> should return <code>42500</code>.');
|
||||
- text: <code>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)</code> should return <code>75300</code>.
|
||||
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, '<code>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)</code> should return <code>75300</code>.');
|
||||
- text: <code>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)</code> should return <code>43200</code>.
|
||||
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, '<code>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)</code> should return <code>43200</code>.');
|
||||
```
|
||||
|
||||
</section>
|
||||
|
||||
## Challenge Seed
|
||||
<section id='challengeSeed'>
|
||||
<div id='js-seed'>
|
||||
|
||||
```js
|
||||
function knapsackUnbounded(items, maxweight, maxvolume) {
|
||||
// Good luck!
|
||||
}
|
||||
```
|
||||
|
||||
</div>
|
||||
</section>
|
||||
|
||||
## Solution
|
||||
<section id='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;
|
||||
}
|
||||
```
|
||||
|
||||
</section>
|
||||
Loading…
Reference in New Issue