|
|
@@ -6,11 +6,7 @@
|
|
|
#include "shapes.hpp"
|
|
|
#include "heap.hpp"
|
|
|
|
|
|
-
|
|
|
-The Optimized Insert Protocol
|
|
|
-Takes in the additive share of the value to be inserted
|
|
|
-And adds the the value into the heap while keeping the heap property intact
|
|
|
-
|
|
|
+
|
|
|
The heap datastructure is stored in an array with the starting index as 1 (and not 0)
|
|
|
For nodes stored in index i of the array, the parent is stored at i/2 and
|
|
|
The left and right children are stored at 2i and 2i + 1
|
|
|
@@ -29,20 +25,24 @@ All the unused array indicies have MAX_INT stored in them
|
|
|
*/
|
|
|
|
|
|
|
|
|
+The Optimized Insert Protocol
|
|
|
+Takes in the additive share of the value to be inserted
|
|
|
+and adds the the value into the heap while keeping the heap property intact
|
|
|
+
|
|
|
_Protocol 4_ from PRAC: Round-Efficient 3-Party MPC for Dynamic Data Structures
|
|
|
Consider the following insertion path with: x0 < x1 < x2 < NewElement < x3 < x4
|
|
|
|
|
|
- x0 x0 x0
|
|
|
- / \ / \ / \
|
|
|
- x1 x1 x1
|
|
|
- \ \ \
|
|
|
- x2 x2 x2
|
|
|
- \ \ \
|
|
|
- x3 ( ) NewElement
|
|
|
- \ \ \
|
|
|
- x4 x3 x3
|
|
|
- \ \ \
|
|
|
- ( ) x4 x4
|
|
|
+ x0 x0 x0
|
|
|
+ / \ / \ / \
|
|
|
+ x1 x1 x1
|
|
|
+ / / /
|
|
|
+ x2 x2 x2
|
|
|
+ \ \ \
|
|
|
+ x3 ( ) NewElement
|
|
|
+ \ \ \
|
|
|
+ x4 x3 x3
|
|
|
+ / / /
|
|
|
+ ( ) x4 x4
|
|
|
|
|
|
(Path with new element) (binary search to determine (After insertion)
|
|
|
the point where New Element
|
