Problem Link  Students, heights and their IQs
Problem Statement:
In the school morning assembly, there are n students standing in a line, each with a height and IQ level. The task is to find the longest subsequence of students with strictly increasing heights and strictly decreasing IQ levels. A subsequence can be formed by removing some (or no) students.
Approach:
The solution uses dynamic programming to find the longest valid subsequence. We maintain an array DP
where DP[i]
represents the length of the longest subsequence ending at student i
.
 Dynamic Programming Initialization: Initialize the
DP
array with all values set to 1, indicating each student can be a subsequence by themselves.  Building the DP Array: For each student
i
, check previous studentsj
:
Skip if
H[j] >= H[i]
(not strictly increasing) orIQ[j] <= IQ[i]
(not strictly decreasing). 
Update
DP[i]
to be the maximum of its current value or1 + DP[j]
if both conditions are satisfied.

 Finding the Maximum Length: After populating the
DP
array, find the maximum value, representing the longest valid subsequence.
This method efficiently calculates the longest subsequence using relationships between students based on their heights and IQ levels.
Time Complexity:
 O(n²) for each test case, where n is the number of students.
Space Complexity:
 O(n) due to the
DP
array used to store subsequence lengths.