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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/sum-to-100.md

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+---
+id: 5a23c84252665b21eecc8043
+title: Sum to 100
+challengeType: 5
+forumTopicId: 302335
+---
+
+## Description
+
+<section id='description'>
+Find solutions to the  <i>sum to one hundred</i>  puzzle.
+Add (insert) the mathematical operators <b>+</b> or <b>─</b> (plus or minus)  before any of the digits in the decimal numeric string   <b>123456789</b>   such that the resulting mathematical expression adds up to a particular sum   (in this iconic case,  <b>100</b>).
+Example:
+<pre><b>123 + 4 - 5 + 67 - 89   =   100</b></pre>
+</section>
+
+## Instructions
+
+<section id='instructions'>
+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.
+</section>
+
+## Tests
+
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>sumTo100</code> should be a function.
+    testString: assert(typeof sumTo100 == 'function');
+  - text: <code>sumTo100(199)</code> should return an array.
+    testString: assert(Array.isArray(sumTo100(199)));
+  - text: <code>sumTo100(199)</code> should return <code>["-1+2-3+45+67+89", "123-4+5+6+78-9", "123-4+56+7+8+9"]</code>.
+    testString: assert.deepEqual(sumTo100(199), ["-1+2-3+45+67+89", "123-4+5+6+78-9", "123-4+56+7+8+9"]);
+  - text: <code>sumTo100(209)</code> should return <code>["1+234+56+7-89"]</code>.
+    testString: assert.deepEqual(sumTo100(209), ["1+234+56+7-89"]);
+  - text: <code>sumTo100(243)</code> should return <code>["-1-234+567-89", "-12+345+6-7-89", "123+45+6+78-9"]</code>.
+    testString: assert.deepEqual(sumTo100(243), ["-1-234+567-89", "-12+345+6-7-89", "123+45+6+78-9"]);
+  - text: <code>sumTo100(199)</code> should return <code>["-1+2-3+45+67+89", "123-4+5+6+78-9", "123-4+56+7+8+9"]</code>.
+    testString: assert.deepEqual(sumTo100(199), ["-1+2-3+45+67+89", "123-4+5+6+78-9", "123-4+56+7+8+9"]);
+  - text: <code>sumTo100(197)</code> should return <code>["1-2-3+45+67+89", "12+34-5+67+89", "123+4-5+6+78-9"]</code>.
+    testString: assert.deepEqual(sumTo100(197), ["1-2-3+45+67+89", "12+34-5+67+89", "123+4-5+6+78-9"]);
+```
+
+</section>
+
+## Challenge Seed
+
+<section id='challengeSeed'>
+<div id='js-seed'>
+
+```js
+function sumTo100(n) {
+
+}
+```
+
+</div>
+</section>
+
+## Solution
+
+<section id='solution'>
+
+```js
+function sumTo100(n) {
+  var permutationsWithRepetition = function(n, as) {
+    return as.length > 0
+      ? foldl1(curry(cartesianProduct)(as), replicate(n, as))
+      : [];
+  };
+
+  var cartesianProduct = function(xs, ys) {
+    return [].concat.apply(
+      [],
+      xs.map(function(x) {
+        return [].concat.apply(
+          [],
+          ys.map(function(y) {
+            return [[x].concat(y)];
+          })
+        );
+      })
+    );
+  };
+
+  var curry = function(f) {
+    return function(a) {
+      return function(b) {
+        return f(a, b);
+      };
+    };
+  };
+
+  var flip = function(f) {
+    return function(a, b) {
+      return f.apply(null, [b, a]);
+    };
+  };
+
+  var foldl1 = function(f, xs) {
+    return xs.length > 0 ? xs.slice(1).reduce(f, xs[0]) : [];
+  };
+
+  var replicate = function(n, a) {
+    var v = [a],
+      o = [];
+    if (n < 1) return o;
+    while (n > 1) {
+      if (n & 1) o = o.concat(v);
+      n >>= 1;
+      v = v.concat(v);
+    }
+    return o.concat(v);
+  };
+
+  var asSum = function(xs) {
+    var dct = xs.reduceRight(
+      function(a, sign, i) {
+        var d = i + 1; //  zero-based index to [1-9] positions
+        if (sign !== 0) {
+          // Sum increased, digits cleared
+          return {
+            digits: [],
+            n: a.n + sign * parseInt([d].concat(a.digits).join(''), 10)
+          };
+        } else
+          return {
+            // Digits extended, sum unchanged
+            digits: [d].concat(a.digits),
+            n: a.n
+          };
+      },
+      {
+        digits: [],
+        n: 0
+      }
+    );
+    return (
+      dct.n + (dct.digits.length > 0 ? parseInt(dct.digits.join(''), 10) : 0)
+    );
+  };
+
+  var asString = function(xs) {
+    var ns = xs.reduce(function(a, sign, i) {
+      var d = (i + 1).toString();
+      return sign === 0 ? a + d : a + (sign > 0 ? '+' : '-') + d;
+    }, '');
+
+    return ns[0] === '+' ? tail(ns) : ns;
+  };
+
+  var universe = permutationsWithRepetition(9, [0, 1, -1])
+    .filter(function(x) {
+      return x[0] !== 1 && asSum(x) === n;
+    })
+    .map(asString);
+  return universe.sort();
+}
+```
+
+</section>