feat(curriculum): add solution (#42146)

* fix: ensure using in test arrays from background

* feat: add solution

* fix: improve description

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-82-path-sum-three-ways.md

@@ -10,46 +10,51 @@ dashedName: problem-82-path-sum-three-ways
 
 **Note:** This problem is a more challenging version of Problem 81.
 
-The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994.
+The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to `994`.
 
-<div style='text-align: center;'>
-  $\begin{pmatrix}
+  $$\begin{pmatrix}
   131 & 673 & \color{red}{234} & \color{red}{103} & \color{red}{18}\\\\
   \color{red}{201} & \color{red}{96} & \color{red}{342} & 965 & 150\\\\
   630 & 803 & 746 & 422 & 111\\\\
   537 & 699 & 497 & 121 & 956\\\\
   805 & 732 & 524 & 37 & 331
-  \end{pmatrix}$
-</div>
+  \end{pmatrix}$$
 
-Find the minimal path sum from the left column to the right column in `matrix`, a 2D array containing an 80 by 80 matrix.
+Find the minimal path sum from the left column to the right column in `matrix`, a 2D array representing a matrix. The maximum matrix size used in tests will be 80 by 80.
 
 # --hints--
 
-`pathSumThreeWays(testMatrix)` should return a number.
+`pathSumThreeWays(testMatrix1)` should return a number.
 
 ```js
-assert(typeof pathSumThreeWays(testMatrix) === 'number');
+assert(typeof pathSumThreeWays(_testMatrix1) === 'number');
 ```
 
-`pathSumThreeWays(testMatrix)` should return 994.
+`pathSumThreeWays(testMatrix1)` should return `994`.
 
 ```js
-assert.strictEqual(pathSumThreeWays(testMatrix), 994);
+assert.strictEqual(pathSumThreeWays(_testMatrix1), 994);
 ```
 
-`pathSumThreeWays(matrix)` should return 260324.
+`pathSumThreeWays(testMatrix2)` should return `260324`.
 
 ```js
-assert.strictEqual(pathSumThreeWays(matrix), 260324);
+assert.strictEqual(pathSumThreeWays(_testMatrix2), 260324);
 ```
 
 # --seed--
 
-## --before-user-code--
+## --after-user-code--
 
 ```js
-const matrix = [
+const _testMatrix1 = [
+  [131, 673, 234, 103, 18],
+  [201, 96, 342, 965, 150],
+  [630, 803, 746, 422, 111],
+  [537, 699, 497, 121, 956],
+  [805, 732, 524, 37, 331]
+];
+const _testMatrix2 = [
   [4445,2697,5115,718,2209,2212,654,4348,3079,6821,7668,3276,8874,4190,3785,2752,9473,7817,9137,496,7338,3434,7152,4355,4552,7917,7827,2460,2350,691,3514,5880,3145,7633,7199,3783,5066,7487,3285,1084,8985,760,872,8609,8051,1134,9536,5750,9716,9371,7619,5617,275,9721,2997,2698,1887,8825,6372,3014,2113,7122,7050,6775,5948,2758,1219,3539,348,7989,2735,9862,1263,8089,6401,9462,3168,2758,3748,5870],
   [1096,20,1318,7586,5167,2642,1443,5741,7621,7030,5526,4244,2348,4641,9827,2448,6918,5883,3737,300,7116,6531,567,5997,3971,6623,820,6148,3287,1874,7981,8424,7672,7575,6797,6717,1078,5008,4051,8795,5820,346,1851,6463,2117,6058,3407,8211,117,4822,1317,4377,4434,5925,8341,4800,1175,4173,690,8978,7470,1295,3799,8724,3509,9849,618,3320,7068,9633,2384,7175,544,6583,1908,9983,481,4187,9353,9377],
   [9607,7385,521,6084,1364,8983,7623,1585,6935,8551,2574,8267,4781,3834,2764,2084,2669,4656,9343,7709,2203,9328,8004,6192,5856,3555,2260,5118,6504,1839,9227,1259,9451,1388,7909,5733,6968,8519,9973,1663,5315,7571,3035,4325,4283,2304,6438,3815,9213,9806,9536,196,5542,6907,2475,1159,5820,9075,9470,2179,9248,1828,4592,9167,3713,4640,47,3637,309,7344,6955,346,378,9044,8635,7466,5036,9515,6385,9230],
@@ -136,14 +141,14 @@ const matrix = [
 ## --seed-contents--
 
 ```js
-function pathSumThreeWays(arr) {
+function pathSumThreeWays(matrix) {
 
   return true;
 }
 
 // Only change code above this line
 
-const testMatrix = [
+const testMatrix1 = [
   [131, 673, 234, 103, 18],
   [201, 96, 342, 965, 150],
   [630, 803, 746, 422, 111],
@@ -151,11 +156,44 @@ const testMatrix = [
   [805, 732, 524, 37, 331]
 ];
 
-pathSumThreeWays(testMatrix);
+pathSumThreeWays(testMatrix1);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function pathSumThreeWays(matrix) {
+  function makeMinimumMoveFromUpOrRight(row, column) {
+    const curValue = matrix[row][column];
+    if (values[row - 1] > values[row]) {
+      return values[row] + curValue;
+    }
+    return values[row - 1] + curValue;
+  }
+  function isGoingFromDownBetter(row, column) {
+    return values[row] > values[row + 1] + matrix[row][column];
+  }
+
+  const size = matrix.length;
+  const values = [];
+  for (let row = 0; row < size; row++) {
+    values.push(matrix[row][size - 1]);
+  }
+
+  for (let column = size - 2; column >= 0; column--) {
+    values[0] += matrix[0][column];
+
+    for (let row = 1; row < size; row++) {
+      values[row] = makeMinimumMoveFromUpOrRight(row, column);
+    }
+
+    for (let row = size - 2; row >= 0; row--) {
+      if (isGoingFromDownBetter(row, column)) {
+        values[row] = values[row + 1] + matrix[row][column];
+      }
+    }
+  }
+
+  return Math.min(...values);
+}
 ```