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59 lines
3.4 KiB
HTML
<p>You are given an array of network towers <code>towers</code>, where <code>towers[i] = [x<sub>i</sub>, y<sub>i</sub>, q<sub>i</sub>]</code> denotes the <code>i<sup>th</sup></code> network tower with location <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and quality factor <code>q<sub>i</sub></code>. All the coordinates are <strong>integral coordinates</strong> on the X-Y plane, and the distance between the two coordinates is the <strong>Euclidean distance</strong>.</p>
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<p>You are also given an integer <code>radius</code> where a tower is <strong>reachable</strong> if the distance is <strong>less than or equal to</strong> <code>radius</code>. Outside that distance, the signal becomes garbled, and the tower is <strong>not reachable</strong>.</p>
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<p>The signal quality of the <code>i<sup>th</sup></code> tower at a coordinate <code>(x, y)</code> is calculated with the formula <code>⌊q<sub>i</sub> / (1 + d)⌋</code>, where <code>d</code> is the distance between the tower and the coordinate. The <strong>network quality</strong> at a coordinate is the sum of the signal qualities from all the <strong>reachable</strong> towers.</p>
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<p>Return <em>the array </em><code>[c<sub>x</sub>, c<sub>y</sub>]</code><em> representing the <strong>integral</strong> coordinate </em><code>(c<sub>x</sub>, c<sub>y</sub>)</code><em> where the <strong>network quality</strong> is maximum. If there are multiple coordinates with the same <strong>network quality</strong>, return the lexicographically minimum <strong>non-negative</strong> coordinate.</em></p>
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<p><strong>Note:</strong></p>
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<ul>
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<li>A coordinate <code>(x1, y1)</code> is lexicographically smaller than <code>(x2, y2)</code> if either:
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<ul>
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<li><code>x1 < x2</code>, or</li>
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<li><code>x1 == x2</code> and <code>y1 < y2</code>.</li>
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</ul>
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</li>
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<li><code>⌊val⌋</code> is the greatest integer less than or equal to <code>val</code> (the floor function).</li>
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</ul>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/09/22/untitled-diagram.png" style="width: 176px; height: 176px;" />
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<pre>
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<strong>Input:</strong> towers = [[1,2,5],[2,1,7],[3,1,9]], radius = 2
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<strong>Output:</strong> [2,1]
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<strong>Explanation:</strong> At coordinate (2, 1) the total quality is 13.
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- Quality of 7 from (2, 1) results in ⌊7 / (1 + sqrt(0)⌋ = ⌊7⌋ = 7
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- Quality of 5 from (1, 2) results in ⌊5 / (1 + sqrt(2)⌋ = ⌊2.07⌋ = 2
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- Quality of 9 from (3, 1) results in ⌊9 / (1 + sqrt(1)⌋ = ⌊4.5⌋ = 4
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No other coordinate has a higher network quality.</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> towers = [[23,11,21]], radius = 9
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<strong>Output:</strong> [23,11]
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<strong>Explanation:</strong> Since there is only one tower, the network quality is highest right at the tower's location.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> towers = [[1,2,13],[2,1,7],[0,1,9]], radius = 2
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<strong>Output:</strong> [1,2]
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<strong>Explanation:</strong> Coordinate (1, 2) has the highest network quality.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= towers.length <= 50</code></li>
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<li><code>towers[i].length == 3</code></li>
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<li><code>0 <= x<sub>i</sub>, y<sub>i</sub>, q<sub>i</sub> <= 50</code></li>
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<li><code>1 <= radius <= 50</code></li>
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</ul>
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