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51 lines
2.1 KiB
HTML
51 lines
2.1 KiB
HTML
<!DOCTYPE html>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<h1>1135. Is It A Red-Black Tree (30)</h1>
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<div id="problemContent">
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<p>There is a kind of balanced binary search tree named <b>red-black tree</b> in the data structure. It has the following 5 properties:</p>
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<p>
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(1) Every node is either red or black.<br/>
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(2) The root is black.<br/>
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(3) Every leaf (NULL) is black.<br/>
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(4) If a node is red, then both its children are black.<br/>
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(5) For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.
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</p>
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<p>For example, the tree in Figure 1 is a red-black tree, while the ones in Figure 2 and 3 are not.</p>
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<center>
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<table>
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<tr>
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<td><center><img src="http://nos.patest.cn/pc_ovw0hp2a4xp.jpg"/></center></td>
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<td><center><img src="http://nos.patest.cn/pc_ovw0huh8oas.jpg"/></center></td>
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<td><center><img src="http://nos.patest.cn/pc_ovw0jb719kh.jpg"/></center></td>
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</tr>
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<tr>
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<td><center>Figure 1</center></td>
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<td><center>Figure 2</center></td>
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<td><center>Figure 3</center></td>
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</tr>
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</table>
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</center>
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<p>For each given binary search tree, you are supposed to tell if it is a legal red-black tree.</p>
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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 several test cases. The first line gives a positive integer K (<=30) which is the total number of cases. For each case, the first line gives a positive integer N (<=30), the total number of nodes in the binary tree. The second line gives the preorder traversal sequence of the tree. While all the keys in a tree are positive integers, we use negative signs to represent red nodes. All the numbers in a line are separated by a space. The sample input cases correspond to the trees shown in Figure 1, 2 and 3.</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 in a line "Yes" if the given tree is a red-black tree, or "No" if not.</p>
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<b>Sample Input:</b><pre>
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3
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9
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7 -2 1 5 -4 -11 8 14 -15
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9
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11 -2 1 -7 5 -4 8 14 -15
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8
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10 -7 5 -6 8 15 -11 17
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</pre>
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<b>Sample Output:</b><pre>
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Yes
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No
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No
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</pre>
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</div> |