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id	challengeType	title	forumTopicId
5900f37e1000cf542c50fe91	5	Problem 18: Maximum path sum I	301815

Description

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3
7 4
2 4 6
8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: 75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

Instructions

Tests

tests:
  - text: <code>maximumPathSumI(testTriangle)</code> should return 23.
    testString: assert.strictEqual(maximumPathSumI(testTriangle), 23);
  - text: <code>maximumPathSumI(numTriangle)</code> should return 1074.
    testString: assert.strictEqual(maximumPathSumI(numTriangle), 1074);

Challenge Seed

function maximumPathSumI(triangle) {
  // Good luck!
  return true;
}

const testTriangle = [[3, 0, 0, 0],
                      [7, 4, 0, 0],
                      [2, 4, 6, 0],
                      [8, 5, 9, 3]];

maximumPathSumI(testTriangle);

Before Test

const numTriangle = [[75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [95, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17, 47, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18, 35, 87, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [20, 4, 82, 47, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [19, 1, 23, 75, 3, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0], [88, 2, 77, 73, 7, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0], [99, 65, 4, 28, 6, 16, 70, 92, 0, 0, 0, 0, 0, 0, 0], [41, 41, 26, 56, 83, 40, 80, 70, 33, 0, 0, 0, 0, 0, 0], [41, 48, 72, 33, 47, 32, 37, 16, 94, 29, 0, 0, 0, 0, 0], [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14, 0, 0, 0, 0], [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57, 0, 0, 0], [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48, 0, 0], [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31, 0], [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]];

Solution

const testTriangle = [[3, 0, 0, 0],
  [7, 4, 0, 0],
  [2, 4, 6, 0],
  [8, 5, 9, 3]];

function maximumPathSumI(triangle) {
  let maxSum = triangle.slice();

  for (let i = triangle.length - 1; i > 0; i--) {
    let currentRow = maxSum[i];
    let previousRow = maxSum[i - 1];
    const temp = [];
    for (let j = 0; j < i; j++) {
      temp.push(Math.max((currentRow[j] + previousRow[j]), (currentRow[j + 1] + previousRow[j])));
    }
    maxSum[i - 1] = temp;
    maxSum.pop();
  }
  return maxSum[0][0];
}

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