Please solve the solution in C$++$ code & also see the image.

$$ Problem $2$: Given a set of n rectangles on x$-$axis, remove the hidden lines to mark the boundary only.

$**$Follow:

Input is sorted in non$-$descending order of startX

Input:

$<3,7,10>$

$<5,9,12>$

$<12,20,5>$

$<13,15,15>$

$<19,22,8>$

$**$Hidden Line Removal: Output

Follow:

Output is sorted in ascending order of X

$<3,10>$

$<5,12>$

$<9,0>$

$<12,5>$

$<13,15>$

$<15,5>$

$<19,8>$

$<22,0>$

$**$Hidden Line Removal: Sweep Line Algorithm

Follow:

Input is sorted in non$-$decreasing order of startX

$<3,10,$ s$>$

$<7,10,$ e$>$

$<5,12,$ s$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<20,5,$ e$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Follow:

Input is sorted in non$-$decreasing order of startX

Sort X$-$coordinates

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$Hidden Line Removal: Algorithm

Maximum Height $=0$ Heap $=\{0\}$

Scan the points from left to right, and insert$/$delete heights into$/$from Max$-$Heap as follows:

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=10$ Heap $=\{10,0\}$ Point $=(3,10)$

Start points are inserted into the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$Hidden Line Removal: Algorithm

Maximum Height $=12$ Heap $=\{12,10,0\}$ Point $=(5,12)$

Start points are inserted into the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=12$ Heap $=\{12,0\}$

End points are deleted from the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=0$ Heap $=\{0\}$ Point $=(9,0)$

End points are deleted from the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=5$ Heap $=\{5,0\}$ Point $=(12,5)$

Start points are inserted into the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=15$ Heap $=\{15,5,0\}$ Point $=(13,15)$

Start points are inserted into the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$Hidden Line Removal: Algorithm

Maximum Height $=5$ Heap $=\{5,0\}$ Point $=(15,5)$

End points are deleted from the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$

$<13,15,$ s$>$

$<15,15,$ e$>$

$<19,8,$ s$>$

$<20,5,$ e$>$

$<22,8,$ e$>$

$**$ Hidden Line Removal: Algorithm

Maximum Height $=8$ Heap $=\{8,5,0\}$ Point $=(19,8)$

Start points are inserted into the heap. If the maximum height changes, then the point belongs to the boundary

$<3,10,$ s$>$

$<5,12,$ s$>$

$<7,10,$ e$>$

$<9,12,$ e$>$

$<12,5,$ s$>$