181 lines
3.8 KiB
Markdown
181 lines
3.8 KiB
Markdown
---
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id: 5a23c84252665b21eecc8043
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title: Sum to 100
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challengeType: 5
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forumTopicId: 302335
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dashedName: sum-to-100
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---
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# --description--
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Find solutions to the *sum to one hundred* puzzle.
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Add (insert) the mathematical operators **+** or **─** (plus or minus) before any of the digits in the decimal numeric string **123456789** such that the resulting mathematical expression adds up to a particular sum (in this iconic case, **100**).
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Example:
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<pre><b>123 + 4 - 5 + 67 - 89 = 100</b></pre>
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# --instructions--
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Write a function that takes a number as parameter. The function should return an array containing all solutions for the given number. The solutions should be strings representing the expressions. For example: "1+23-456+78-9". Sort the array before returning it.
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# --hints--
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`sumTo100` should be a function.
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```js
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assert(typeof sumTo100 == 'function');
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```
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`sumTo100(199)` should return an array.
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```js
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assert(Array.isArray(sumTo100(199)));
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```
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`sumTo100(199)` should return `["-1+2-3+45+67+89", "123-4+5+6+78-9", "123-4+56+7+8+9"]`.
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```js
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assert.deepEqual(sumTo100(199), [
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'-1+2-3+45+67+89',
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'123-4+5+6+78-9',
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'123-4+56+7+8+9'
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]);
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```
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`sumTo100(209)` should return `["1+234+56+7-89"]`.
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```js
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assert.deepEqual(sumTo100(209), ['1+234+56+7-89']);
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```
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`sumTo100(243)` should return `["-1-234+567-89", "-12+345+6-7-89", "123+45+6+78-9"]`.
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```js
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assert.deepEqual(sumTo100(243), [
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'-1-234+567-89',
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'-12+345+6-7-89',
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'123+45+6+78-9'
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]);
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```
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`sumTo100(197)` should return `["1-2-3+45+67+89", "12+34-5+67+89", "123+4-5+6+78-9"]`.
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```js
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assert.deepEqual(sumTo100(197), [
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'1-2-3+45+67+89',
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'12+34-5+67+89',
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'123+4-5+6+78-9'
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]);
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```
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# --seed--
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## --seed-contents--
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```js
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function sumTo100(n) {
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}
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```
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# --solutions--
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```js
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function sumTo100(n) {
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var permutationsWithRepetition = function(n, as) {
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return as.length > 0
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? foldl1(curry(cartesianProduct)(as), replicate(n, as))
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: [];
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};
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var cartesianProduct = function(xs, ys) {
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return [].concat.apply(
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[],
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xs.map(function(x) {
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return [].concat.apply(
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[],
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ys.map(function(y) {
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return [[x].concat(y)];
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})
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);
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})
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);
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};
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var curry = function(f) {
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return function(a) {
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return function(b) {
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return f(a, b);
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};
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};
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};
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var flip = function(f) {
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return function(a, b) {
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return f.apply(null, [b, a]);
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};
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};
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var foldl1 = function(f, xs) {
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return xs.length > 0 ? xs.slice(1).reduce(f, xs[0]) : [];
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};
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var replicate = function(n, a) {
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var v = [a],
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o = [];
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if (n < 1) return o;
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while (n > 1) {
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if (n & 1) o = o.concat(v);
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n >>= 1;
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v = v.concat(v);
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}
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return o.concat(v);
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};
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var asSum = function(xs) {
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var dct = xs.reduceRight(
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function(a, sign, i) {
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var d = i + 1; // zero-based index to [1-9] positions
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if (sign !== 0) {
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// Sum increased, digits cleared
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return {
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digits: [],
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n: a.n + sign * parseInt([d].concat(a.digits).join(''), 10)
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};
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} else
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return {
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// Digits extended, sum unchanged
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digits: [d].concat(a.digits),
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n: a.n
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};
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},
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{
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digits: [],
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n: 0
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}
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);
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return (
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dct.n + (dct.digits.length > 0 ? parseInt(dct.digits.join(''), 10) : 0)
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);
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};
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var asString = function(xs) {
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var ns = xs.reduce(function(a, sign, i) {
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var d = (i + 1).toString();
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return sign === 0 ? a + d : a + (sign > 0 ? '+' : '-') + d;
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}, '');
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return ns[0] === '+' ? tail(ns) : ns;
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};
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var universe = permutationsWithRepetition(9, [0, 1, -1])
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.filter(function(x) {
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return x[0] !== 1 && asSum(x) === n;
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})
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.map(asString);
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return universe.sort();
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}
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```
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