nutes

Question $1$: Model flow of liquid

Max Score: $50\mathrm{.}0$

The problem is an over simplification of the flow of liquid. $-$ A terrain is given as a grid of cells of random elevations. The grid is always odd sized and is always a square. $-$ A liquid is poured at the central cell. Water can flow only north$-$south or east$-$west; not diagnonally. $-$ At the first step, the water level is the same as the central cell. $-$ Water from one cell flows to a neighbouring cell if the level of water is equal to greater than the elevation of the neighbouring cell. $-$ When the water flows to the neighbouring cell, the level of water is maintained. $-$ If the water cannot flow to any new cell, the water level rises. $-$ The simulation stops when the water reaches the end of the domain. $-$ The output consists of the domain represented by $.$ and W representing dry and wet terrain.

Below is an example

Input Format

$7494888977098472650734095922030163928029066690663282412750578767349984317219361315454421112460575572389635170174946593314300620167931780416954275$

Water level and location of water:

$----------$

Current water level: $172$

$.......$

$.......$

$.......$

$...$W$...$

$...$W$...$

$.......$

$.......$

$----------$

Current water level: $172$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.......$

$.......$

$----------$

Current water level: $172$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.......$

$.......$

Cannot flow, increasing water level to $173$

$----------$

Current water level: $173$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.......$

$.......$

Cannot flow, increasing water level to $174$

$----------$

Current water level: $174$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$..$W$....$

$.......$

$----------$

Current water level: $174$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.$WW$....$

$.......$

$----------$

Current water level: $174$

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.$WW$....$

$.$W$.....$

$----------$

Current water level: $174$ Reached edge, exiting. Solution:

Output Format

$.......$

$.......$

$.......$

$...$W$...$

$..$WW$...$

$.$WW$....$

$.$W$.....$

Constraints: First line of the input has dimension n of $($n X n$)$ matrix. Followed by the matrix itself as shown below in the sample input. we want this output..................W$................$

$...............$W$.$WWW$...............$

$..............$WWWWWWW$..............$

$..............$WWWWWW$...............$

$.............$WWW$..$WWWW$.............$

$...........$W$.$WWWWWWW$.$WWW$...........$

$..........$WWWWW$.$WWWWWWWWW$..........$

$.........$WWWWW$.$WWWWWWWWW$.$W$.........$

$.........$WWWWW$.$WWWWWWWW$.$WWW$........$

$.......$W$..$WWWWWWWWWWWWWWWWWW$.......$

$......$WWW$.$WWWWWWW$.$WWW$..$WWWWWW$......$

$.....$WWWW$...$WWWWWWW$.$WWW$.$WW$.$WWW$.....$

$........$WWWWW$.$W$.$WWWWWWWW$.$WWWWWW$....$

$...$W$.$WWWWWWWWWWWW$.$WWWWWWWWW$.$WW$.....$

$..$WWWWWWWWW$.$WWW$.$WWWWW$.$WWWW$.$WWWW$....$

$.$WWWWWWWWW$.$WW$.$WWWWWWWWW$.$WWWWW$......$

$...$WWW$..$WWWWWW$..$WWWWW$..$W$.$W$..$WWW$....$

$..$WWWWWWWWWWWWWWWWWWWW$.$WW$..$WWWWW$...$

$..$WWW$.$WWWWW$.$WWW$.$WWWWWW$.$WWWWW$.$WW$....$

$.$WWWW$..$WWWWWWWWWWWWWWWWWW$.$WWWWWW$...$

$..$WWWW$.$WWWW$.$WWW$.$WWWWWW$..$W$.$W$.$WWW$....$

$...$WWWWWWWWWWWWWWWWW$.$WWWWWWWWW$.....$

$....$WWWW$..$WWWWW$.$W$.$WWW$.$WWWWWW$.$WW$....$

$.....$WWWWWWWWWWW$.$WWWWWWWW$.$WWWW$.....$

$......$WWWWWWWWWWWWWWWWWWWWWWW$......$

$.......$WWWW$.$WW$.$WWW$.$WW$..$WWWWW$.......$

$........$WWWWWW$.$WW$...$WWWW$.$WW$........$

$.........$WW$.$