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42 lines
2.6 KiB
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42 lines
2.6 KiB
HTML
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<h1>1053. Path of Equal Weight (30)</h1>
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<div id="problemContent">
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<p>Given a non-empty tree with root R, and with weight W<sub>i</sub> assigned to each tree node T<sub>i</sub>. The <b>weight of a path from R to L</b> is defined to be the sum of the weights of all the nodes along the path from R to any leaf node L.</p>
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<p>Now given any weighted tree, you are supposed to find all the paths with their weights equal to a given number. For example, let's consider the tree showed in Figure 1: for each node, the upper number is the node ID which is a two-digit number, and the lower number is the weight of that node. Suppose that the given number is 24, then there exists 4 different paths which have the same given weight: {10 5 2 7}, {10 4 10}, {10 3 3 6 2} and {10 3 3 6 2}, which correspond to the red edges in Figure 1.
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</p>
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<center><img src="http://nos.patest.cn/5b_mj58f84v11w.jpg"/><br/>Figure 1</center>
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<p><b>
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Input Specification:
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</b></p>
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<p>Each input file contains one test case. Each case starts with a line containing 0 < N <= 100, the number of nodes in a tree, M (< N), the number of non-leaf nodes, and 0 < S < 2<sup>30</sup>, the given weight number. The next line contains N positive numbers where W<sub>i</sub> (&lt1000;) corresponds to the tree node T<sub>i</sub>. Then M lines follow, each in the format:</p>
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<pre>
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ID K ID[1] ID[2] ... ID[K]
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</pre>
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<p>where ID is a two-digit number representing a given non-leaf node, K is the number of its children, followed by a sequence of two-digit ID's of its children. For the sake of simplicity, let us fix the root ID to be 00.</p>
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<p><b>
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Output Specification:
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</b></p>
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<p>For each test case, print all the paths with weight S in <b>non-increasing</b> order. Each path occupies a line with printed weights from the root to the leaf in order. All the numbers must be separated by a space with no extra space at the end of the line.
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</p>
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<p>Note: sequence {A<sub>1</sub>, A<sub>2</sub>, ..., A<sub>n</sub>} is said to be <b>greater than</b> sequence {B<sub>1</sub>, B<sub>2</sub>, ..., B<sub>m</sub>} if there exists 1 <= k < min{n, m} such that A<sub>i</sub> = B<sub>i</sub> for i=1, ... k, and A<sub>k+1</sub> > B<sub>k+1</sub>.</p>
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<b>Sample Input:</b><pre>
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20 9 24
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10 2 4 3 5 10 2 18 9 7 2 2 1 3 12 1 8 6 2 2
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00 4 01 02 03 04
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02 1 05
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04 2 06 07
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03 3 11 12 13
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06 1 09
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07 2 08 10
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16 1 15
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13 3 14 16 17
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17 2 18 19
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</pre>
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<b>Sample Output:</b><pre>
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10 5 2 7
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10 4 10
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10 3 3 6 2
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10 3 3 6 2
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</pre>
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</div> |