# HackerRank Min Max Riddle Interview preparation kit solution

In this HackerRank Min Max Riddle Interview preparation kit problem you have Given an integer array of size n, find the maximum of the minimum(s) of every window size in the array. The window size varies from 1 to n.

## Problem solution in Python programming.

```#!/bin/python3

import math
import os
import random
import re
import sys

# Complete the riddle function below.
def riddle(arr):
n = len(arr)
max_mins = [None]*n
stack = [] # will store (num, index)
for i in range(n):
#print('stack', stack)
#print('max_mins', max_mins)
# remember to "push back"
_m = i
while len(stack) > 0 and stack[-1][0] > arr[i]:
_v, _i = stack.pop(-1)
w = i - _i
for _w in range(w): # note that it's zero indexed and shifted down
if max_mins[_w] is None:
max_mins[_w] = _v
else:
max_mins[_w] = max(max_mins[_w], _v)
_m = _i # get the smallest index at which we could start
stack.append((arr[i],_m))

# these were the minima for all this time
while len(stack) > 0:
#print('stack', stack)
#print('max_mins', max_mins)
_v, _i = stack.pop(-1)
w = n - _i
for _w in range(w):
if max_mins[_w] is None:
max_mins[_w] = _v
else:
max_mins[_w] = max(max_mins[_w], _v)
return max_mins

if __name__ == '__main__':
fptr = open(os.environ['OUTPUT_PATH'], 'w')

n = int(input())

arr = list(map(int, input().rstrip().split()))

res = riddle(arr)

fptr.write(' '.join(map(str, res)))
fptr.write('\n')

fptr.close()```

## Problem solution in C++ programming.

```#include <bits/stdc++.h>
using namespace std;

int main()
{
int n,i;
cin>>n;

int a[n];
for(i=0;i<n;++i) {
cin>>a[i];
}

stack<int> s;
int left[n],right[n],ans[n+1],len;

for(i=0;i<n;++i) {
left[i]=-1,right[i]=n;
}

for(i=0;i<n;++i) {
while(!s.empty() && a[s.top()] >= a[i]) {
s.pop();
}
if(!s.empty()) {
left[i]=s.top();
}
s.push(i);
}

while(!s.empty()) {
s.pop();
}

for(i=n-1;i>=0;--i) {
while(!s.empty() && a[s.top()] >= a[i]) {
s.pop();
}
if(!s.empty()) {
right[i]=s.top();
}
s.push(i);
}

memset(ans, 0, sizeof ans);
for(i=0;i<n;++i) {
len = right[i]-left[i]-1;
ans[len]=max(ans[len], a[i]);
}

for(i=n-1;i>=1;--i) {
ans[i]=max(ans[i], ans[i+1]);
}

for(i=1;i<=n;++i) {
cout<<ans[i]<<" ";
}
cout<<endl;
return 0;
}```