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Separation logic assertions describe "states" consisting of a store and a heap, roughly corresponding to the state of local (or stack-allocated) variables and dynamically-allocated objects in common programming languages such as C and Java. A store is a function mapping variables to values.
For example, the quicksort algorithm can be implemented so that it never requires more than nested recursive calls to sort items. Stack overflow may be difficult to avoid when using recursive procedures since many compilers assume that the recursion stack is a contiguous area of memory, and some allocate a fixed amount of space for it.
Jeff Dean and Sanjay Ghemawat wanted to create a system resembling the Bigtable tablet stack that had minimal dependencies and would be suitable for open sourcing, and also would be suitable for use in Chrome for the IndexedDB implementation. They wrote LevelDB starting in early 2011, with the same general design as the Bigtable tablet stack ...
Copy the nth item on the stack (given by the argument) onto the top of the stack** n+1 [Space] [LF][Tab]-Swap the top two items on the stack 2 [Space] [LF][LF]-Discard the top item on the stack 1 [Space] [Tab][LF] Number n: Slide n items off the stack, keeping the top item** may be less than n+1, but at least 1 item (top of the stack) is required
The sequence of pushes and pops performed by Knuth's sorting algorithm as it sorts a stack-sortable permutation form a Dyck language: reinterpreting a push as a left parenthesis and a pop as a right parenthesis produces a string of balanced parentheses. Moreover, every Dyck string comes from a stack-sortable permutation in this way, and every ...
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However, quicksort requires O(log n) stack space pointers to keep track of the subarrays in its divide and conquer strategy. Consequently, quicksort needs O (log 2 n ) additional space. Although this non-constant space technically takes quicksort out of the in-place category, quicksort and other algorithms needing only O (log n ) additional ...
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