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Problem18.html
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<html>
<head>
<title>
Project Euler, Problem 18: Maximum Path Sum I
</title>
<link rel="stylesheet" type="text/css" href="eulerStyle.css" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
</head>
<body>
<header>
<svg height="5rem" width="90vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/projectEulerIndex.html">
<text id="euler" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Project Euler
</text>
</a>
</svg>
<br />
<svg height="4rem" width="90vw">
<a href="https://projecteuler.net/problem=18">
<text id="problemID" x="50%" y="50%" text-anchor="middle" dominant-baseline="middle">
Problem 18: Maximum Path Sum I
</text>
</a>
</svg>
</header>
<nav>
<svg height="3rem" width="75vw">
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem17.html">
<text x="0%" y="50%" text-anchor="start" dominant-baseline="middle">
Problem 17
</text>
</a>
<a href="https://dkallen78.github.io/Project-Euler-Files/Problem19.html">
<text x="100%" y="50%" text-anchor="end" dominant-baseline="middle">
Problem 19
</text>
</a>
</svg>
</nav>
<main>
<p>
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.
<br />
<div class="example">
<span class="red">3</span><br />
<span class="red">7</span> 4<br />
2 <span class="red">4</span> 6<br />
8 5 <span class="red">9</span> 3<br />
</div>
<br />
That is,
<math>
<mn>3</mn>
<mo>+</mo>
<mn>7</mn>
<mo>+</mo>
<mn>4</mn>
<mo>+</mo>
<mn>9</mn>
<mo>=</mo>
<mn>23</mn>
</math>.
<br /><br />
Find the maximum total from top to bottom of the triangle below:
<br /><br />
<div class="example">
75<br />
95 64<br />
17 47 82<br />
18 35 87 10<br />
20 04 82 47 65<br />
19 01 23 75 03 34<br />
88 02 77 73 07 63 67<br />
99 65 04 28 06 16 70 92<br />
41 41 26 56 83 40 80 70 33<br />
41 48 72 33 47 32 37 16 94 29<br />
53 71 44 65 25 43 91 52 97 51 14<br />
70 11 33 28 77 73 17 78 39 68 17 57<br />
91 71 52 38 17 14 91 43 58 50 27 29 48<br />
63 66 04 68 89 53 67 30 73 16 69 87 40 31<br />
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23<br />
</div>
<br />
<span class="bold">NOTE:</span> 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)
</p>
<button id="problem" onclick="projectEulerProblem18()">
Find Sum
</button>
<br />
<summary id="notes">
<div id="totalTime"></div>
<p>
I made an array where each element of the array was an array of the numbers
in the rows.
<br /><br />
I then worked my way up from the bottom instead of the top. Starting with
the first number in the second from the last row, I added the larger of
the two numbers beneath it to the number, then I did the same for the rest
of the row. Then I did the same for the next row up until I reached the
top row.
<br /><br />
###,###
</p>
</summary>
</main>
</body>
<script>
function projectEulerProblem18() {
let startTime = new Date();
let triangle = [
[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]
];
let greatestSum = 0;
//
//Works through each row of the triangle adding
//the larger of each pair to the number above it
for (let x = (triangle.length - 2); x >= 0; x--) {
for (let y = 0; y < triangle[x].length; y++) {
if (triangle[(x + 1)][y] > triangle[(x + 1)][(y + 1)]) {
triangle[x][y] += triangle[(x + 1)][y];
} else {
triangle[x][y] += triangle[(x + 1)][(y + 1)];
}
}
}
let endTime = new Date();
let totalTime = endTime - startTime;
document.getElementById("totalTime").innerHTML = totalTime + " ms";
document.getElementById("notes").style.display = "block";
document.getElementById("problem").innerHTML = triangle[0][0];
}
</script>
</html>