Suppose we have three positive numbers say n, lower, and upper. We have to find a list whose length is n and that is strictly increasing and then strictly decreasing and all the numbers are in range [lower and upper] (both inclusive). And each increasing and decreasing parts should be non-empty. We have to find the lexicographically largest such list possible, if this is not possible, then return empty list.
So, if the input is like n = 5 lower = 3 upper = 7, then the output will be [6, 7, 6, 5, 4], if we look closely, the [7, 6, 5, 4, 3] is not valid because the strictly increasing part should be non-empty.
To solve this, we will follow these steps −
if n > 2 * (upper - lower) + 1, then
return empty list
c := upper - lower
d := 1
if c < n, then
d := n - c - 1
if d is same as 0, then
d := 1
f := a new list from range from (upper - d) to (upper - 1)
g := a new list from range (upper - n + d - 1) down to upper
concatenate f and g and return
Example
Let us see the following implementation to get better understanding
def solve(n, lower, upper):
if n > 2 * (upper - lower) + 1:
return []
c = upper - lower
d = 1
if c < n:
d = n - c - 1
if d == 0:
d = 1
f = list(range(upper - d, upper))
g = list(range(upper, upper - n + d, -1))
return f + g
n = 5
lower = 3
upper = 7
print(solve(n, lower, upper))Input
5, 3, 7
Output
[6, 7, 6, 5, 4]