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51 lines
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51 lines
3.1 KiB
HTML
<p>You are given an array of variable pairs <code>equations</code> and an array of real numbers <code>values</code>, where <code>equations[i] = [A<sub>i</sub>, B<sub>i</sub>]</code> and <code>values[i]</code> represent the equation <code>A<sub>i</sub> / B<sub>i</sub> = values[i]</code>. Each <code>A<sub>i</sub></code> or <code>B<sub>i</sub></code> is a string that represents a single variable.</p>
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<p>You are also given some <code>queries</code>, where <code>queries[j] = [C<sub>j</sub>, D<sub>j</sub>]</code> represents the <code>j<sup>th</sup></code> query where you must find the answer for <code>C<sub>j</sub> / D<sub>j</sub> = ?</code>.</p>
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<p>Return <em>the answers to all queries</em>. If a single answer cannot be determined, return <code>-1.0</code>.</p>
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<p><strong>Note:</strong> The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.</p>
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<p><strong>Note: </strong>The variables that do not occur in the list of equations are undefined, so the answer cannot be determined for them.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> equations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
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<strong>Output:</strong> [6.00000,0.50000,-1.00000,1.00000,-1.00000]
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<strong>Explanation:</strong>
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Given: <em>a / b = 2.0</em>, <em>b / c = 3.0</em>
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queries are: <em>a / c = ?</em>, <em>b / a = ?</em>, <em>a / e = ?</em>, <em>a / a = ?</em>, <em>x / x = ? </em>
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return: [6.0, 0.5, -1.0, 1.0, -1.0 ]
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note: x is undefined => -1.0</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]
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<strong>Output:</strong> [3.75000,0.40000,5.00000,0.20000]
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
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<strong>Output:</strong> [0.50000,2.00000,-1.00000,-1.00000]
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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 <= equations.length <= 20</code></li>
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<li><code>equations[i].length == 2</code></li>
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<li><code>1 <= A<sub>i</sub>.length, B<sub>i</sub>.length <= 5</code></li>
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<li><code>values.length == equations.length</code></li>
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<li><code>0.0 < values[i] <= 20.0</code></li>
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<li><code>1 <= queries.length <= 20</code></li>
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<li><code>queries[i].length == 2</code></li>
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<li><code>1 <= C<sub>j</sub>.length, D<sub>j</sub>.length <= 5</code></li>
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<li><code>A<sub>i</sub>, B<sub>i</sub>, C<sub>j</sub>, D<sub>j</sub></code> consist of lower case English letters and digits.</li>
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</ul>
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