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aa:lab:sol:8 [2025/12/01 19:14] mihnea.gheorghe rezolvare exercițiu Python |
aa:lab:sol:8 [2025/12/04 12:08] (current) mihnea.gheorghe fix notation consistency |
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| \begin{aligned} | \begin{aligned} | ||
| \mathrm{isBST}(\mathrm{Nil}) | \mathrm{isBST}(\mathrm{Nil}) | ||
| - | &\overset{(\text{BST})}{=} \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, \infty) \\ | + | &\overset{(\text{BST})}{=} \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, +\infty) \\ |
| &\overset{(\text{BST1})}{=} \text{true}, \forall x \in \mathbb{E} | &\overset{(\text{BST1})}{=} \text{true}, \forall x \in \mathbb{E} | ||
| \end{aligned} | \end{aligned} | ||
| Line 146: | Line 146: | ||
| \begin{aligned} | \begin{aligned} | ||
| \mathrm{isBST}(\mathrm{Node}(x, \mathrm{Nil}, \mathrm{Nil})) | \mathrm{isBST}(\mathrm{Node}(x, \mathrm{Nil}, \mathrm{Nil})) | ||
| - | &\overset{(\text{BST})}{=} \mathrm{isBSTBetween}(\mathrm{Node}(x, \mathrm{Nil}, \mathrm{Nil}), -\infty, \infty) \\ | + | &\overset{(\text{BST})}{=} \mathrm{isBSTBetween}(\mathrm{Node}(x, \mathrm{Nil}, \mathrm{Nil}), -\infty, +\infty) \\ |
| - | &\overset{(\text{BST2})}{=} (-\infty \le x \le \infty) | + | &\overset{(\text{BST2})}{=} (-\infty \le x \le +\infty) |
| \;\land\; | \;\land\; | ||
| \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, x) | \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, x) | ||
| \;\land\; | \;\land\; | ||
| - | \mathrm{isBSTBetween}(\mathrm{Nil}, x, \infty) \\ | + | \mathrm{isBSTBetween}(\mathrm{Nil}, x, +\infty) \\ |
| &\overset{(\overline{\mathbb{E}})}{=} \text{true} \;\land\; | &\overset{(\overline{\mathbb{E}})}{=} \text{true} \;\land\; | ||
| \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, x) | \mathrm{isBSTBetween}(\mathrm{Nil}, -\infty, x) | ||
| \;\land\; | \;\land\; | ||
| - | \mathrm{isBSTBetween}(\mathrm{Nil}, x, \infty) \\ | + | \mathrm{isBSTBetween}(\mathrm{Nil}, x, +\infty) \\ |
| &\overset{(\text{BST1})}{=} \text{true}, \forall x \in \mathbb{E} | &\overset{(\text{BST1})}{=} \text{true}, \forall x \in \mathbb{E} | ||
| \end{aligned} | \end{aligned} | ||
| Line 169: | Line 169: | ||
| \( | \( | ||
| \overset{(\text{BST})}{\Leftrightarrow} | \overset{(\text{BST})}{\Leftrightarrow} | ||
| - | \mathrm{isBSTBetween}(t, -\infty, \infty) | + | \mathrm{isBSTBetween}(t, -\infty, +\infty) |
| \overset{(\text{BST2})}{\Leftrightarrow} | \overset{(\text{BST2})}{\Leftrightarrow} | ||
| - | (lo \le y \le hi) \;\land\; | + | (-\infty \le y \le +\infty) \;\land\; |
| - | \mathrm{isBSTBetween}(l, lo, y) \;\land\; | + | \mathrm{isBSTBetween}(l, -\infty, y) \;\land\; |
| - | \mathrm{isBSTBetween}(r, y, hi) \ | + | \mathrm{isBSTBetween}(r, y, +\infty) \ |
| (\text{II}) | (\text{II}) | ||
| \) | \) | ||