K Inverse Pairs Array | Recursion | Memoization | Bottom Up | Optimal Bottom Up | Leetcode 629
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This is the 83rd Video of our Playlist "Dynamic Programming : Popular Interview Problems".
In this video we will try to solve a very good DP problem - K Inverse Pairs Array (Leetcode 629)
I will explain the intuition so easily that you will never forget and start seeing this as cakewalk EASYYY.
We will do live coding after explanation and see if we are able to pass all the test cases.
Also, please note that my Github solution link below contains both C++ as well as JAVA code.
Problem Name : K Inverse Pairs Array | Recursion | Memoization | Bottom Up | Optimal Bottom Up | Leetcode 629
Company Tags : GOOGLE
My solutions on Github(C++ & JAVA) : https://github.com/MAZHARMIK/Interview_DS_Algo/blob/master/DP/K%20Inverse%20Pairs%20Array.cpp
Leetcode Link : https://leetcode.com/problems/k-inverse-pairs-array/description/
My DP Concepts Playlist : https://youtu.be/7eLMOE1jnls
My Graph Concepts Playlist : https://youtu.be/5JGiZnr6B5w
My GitHub Repo for interview preparation : https://github.com/MAZHARMIK/Interview_DS_Algo
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Approach-1 Summary : The Solution uses dynamic programming to optimize the solution by memoizing previously computed values in the 2D array 't'. The solve function calculates the total number of arrays of length 'n' with exactly 'k' inversions, and it recursively considers different cases while updating the memoization table. The kInversePairs function initializes the memoization array 't' with -1 values and then calls the solve function to obtain the final result for the given parameters 'n' and 'k'. The modulo operation is applied at each step to prevent integer overflow, given by the constant 'M = 1e9+7'.
Approach-2 Summary : The solution uses a bottom-up dynamic programming approach and a 2D vector 't' to store intermediate results. The outer loop iterates through array lengths from 0 to 'n', and the inner loops calculate the number of arrays with exactly 'k' inversions for each array length. The triple nested loop considers different cases for inversions and updates the memoization table accordingly. The final result is obtained from the bottom-right corner of the 't' table, representing the total number of arrays of length 'n' with exactly 'k' inversions. The modulo operation is applied at each step to prevent integer overflow, given by the constant 'M = 1e9+7'.
Approach-3 Summary : The solution uses a bottom-up dynamic programming approach and a 2D vector 't' to store intermediate results. The outer loop iterates through array lengths from 0 to 'n', and the inner loops calculate the number of arrays with exactly 'k' inversions for each array length. The cumulative sum approach is used to efficiently compute the values, where cumSum represents the cumulative sum of the previous row's values up to index 'j'. The modulo operation is applied at each step to prevent integer overflow, given by the constant 'M = 1e9+7'. The final result is obtained from the bottom-right corner of the 't' table, representing the total number of arrays of length 'n' with exactly 'k' inversions.
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✨ Timelines✨
00:00 - Introduction
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