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 samples $.$ I will be attaching a python code which passes $6$ test cases. Please debug it for $10$ test cases. $3$ test cases are not passing due to return status import numpy as np

n $=$ int$($input$())$

levels $=$ np$.$full$(($n$,$n$),0)$

visited $=$ np$.$full$(($n$,$n$),$ False$)$

for $\_$ in range$($n$)$:

levels$[\_]=$np$.$array$($list$($map$($int$,$ input$().$split$())))$

center $=$ n$//2$

stack $=[($center$,$center$)]$

bound $=$ set$()$

found$\_$wall $=$ False

def is$\_$valid$($row$,$col$)$:

if row$<=0$ or row$>=$n or col$<0$ or col$>=$n:

return False

return True

count$=0$

def water$($level$)$:

global stack, levels, bound, found$\_$wall, count

#print$($stack$)$

#print$("$working$",$ count$)$

count$+=1$

temp $=[]$

while stack:

row, col $=$ stack.pop$()$

if levels$[$row$][$col$]<=$level:

levels$[$row$][$col$]=-1$

visited$[$row$][$col$]=$True

if row$==0$ or row$==$n$-1$ or col$==0$ or col$==$n$-1$:

found$\_$wall$=$True

else:

bound.add$(($row$,$col$))$

if levels$[$row$][$col$]==-1$:

if is$\_$valid$($row$+1,$col$)$ and not visited$[$row$+1][$col$]$:

temp.append$(($row$+1,$col$))$

if is$\_$valid$($row$-1,$col$)$ and not visited$[$row$-1][$col$]$:

temp.append$(($row$-1,$col$))$

if is$\_$valid$($row$,$col$-1)$ and not visited$[$row$][$col$-1]$:

temp.append$(($row$,$col$-1))$

if is$\_$valid$($row$,$col$+1)$ and not visited$[$row$][$col$+1]$:

temp.append$(($row$,$col$+1))$

stack $=$ temp

if stack and not found$\_$wall:

water$($level$)$

water$($levels$[$center$,$center$])$

def if$\_$found$()$:

global bound,stack

if found$\_$wall:

return water$($level$)$

else:

lst $=[]$

for row,col in bound:

lst$.$append$($levels$[$row$][$col$])$

level $=$ min$($lst$)$

stack $=$ list$($bound$)$

bound $=$ set$()$

water$($level$)$

if$\_$found$()$

if$\_$found$()$

for i in range$($n$)$:

for j in range$($n$)$:

if levels$[$i$][$j$]==-1$:

print$("$W$",$end$="")$

else:

print$(".",$end$="")$

print$()$