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aa:lab:sol:9 [2025/12/08 10:44] dmihai created |
aa:lab:sol:9 [2025/12/08 22:35] (current) dmihai |
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| - | t' = \mathrm{rotate-right}(t) = \mathrm{Node}(y, t1, \mathrm{Node}(x,t2,t3)) | + | t' = \mathrm{rotate\text{-}right}(t) = \mathrm{Node}(y, t1, \mathrm{Node}(x,t2,t3)) |
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| P2. \forall a \in \mathrm{elems}(t1),\ a < y \\ | P2. \forall a \in \mathrm{elems}(t1),\ a < y \\ | ||
| - | P3. \forall a \in \mathrm{Node}(x,t2,t3),\ a \ge y \\ | + | P3. \forall a \in \mathrm{elems}(\mathrm{Node}(x,t2,t3)),\ a \ge y \\ |
| \) | \) | ||
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| \( | \( | ||
| - | \mathrm{rotate-left}(\mathrm{Node}(x,t1,\mathrm{Node}(y,t2,t3))) \\ | + | \mathrm{rotate\text{-}left}(\mathrm{Node}(x,t1,\mathrm{Node}(y,t2,t3))) \\ |
| \quad\quad = \mathrm{Node}(y, \mathrm{Node}(x, t1, t2), t3) | \quad\quad = \mathrm{Node}(y, \mathrm{Node}(x, t1, t2), t3) | ||
| \) | \) | ||
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| \( | \( | ||
| - | \mathrm{rotate-right-left}(\mathrm{Node}(x, t1, \mathrm{Node}(y, \mathrm{Node}(z, t2, t3), t4))) \\ | + | \mathrm{rotate\text{-}right\text{-}left}(\mathrm{Node}(x, t1, \mathrm{Node}(y, \mathrm{Node}(z, t2, t3), t4))) \\ |
| \quad\quad = \mathrm{Node}(z, \mathrm{Node}(x, t1, t2), \mathrm{Node}(y, t3, t4)) | \quad\quad = \mathrm{Node}(z, \mathrm{Node}(x, t1, t2), \mathrm{Node}(y, t3, t4)) | ||
| \) | \) | ||