Given a chess board with 4 rows and n columns. On every cell there's an integer. Given 2n discs that part of them, or all of them you can put on a different cell on the board so the total sum is maximal. The only limitation is that 2 discs can't be next to each other vertically or horizontally. How to place the best combination of discs on the board in O(n) using DP ?
Dynamic Programming for sub sum elements in a matrix
275 Views Asked by itorra At
1
There are 1 best solutions below
Related Questions in ALGORITHM
- MCNP 6 - Doubts about cells
- Given partially sorted array of type x<y => first apperance of x comes before first of y, sort in average O(n)
- What is the algorithm behind math.gcd and why it is faster Euclidean algorithm?
- Purpose of last 2 while loops in the merge algorithm of merge sort sorting technique
- Dots and Boxes with apha-beta pruning
- What is the average and worst-case time complexity of my string searching algorithm?
- Building a School Schedule Generator
- TC problem 5-2:how to calculate the probability of the indicator random variable?
- LCA of a binary tree implemented in Python
- Identify the checksum algorithm
- Algorithm for finding a subset of nodes in a weighted connected graph such that the distance between any pair nodes are under a postive number?
- Creating an efficent and time-saving algorithm to find difference between greater than and lesser than combination
- Algorithm to find neighbours of point by distance with no repeats
- Asking code suggestions about data structure and algorithm
- Heap sort with multithreading
Related Questions in DYNAMIC-PROGRAMMING
- Leetcode 1255-recursion and backtracking
- Can dynamic programming help solve this problem?
- How to dynamically switch between two images onclick in Vue.js
- What boilerplate is the best for dynamic form building with reactjs typescript and .Net core microservices
- Is there a optimal solution for Jump Game Problem using C programming
- How to using Dapper to extract data from column dynamically altered table
- I'm facing a problem regarding hexagonal tiles
- 2 City Scheduling DP clarification
- How to find min cost for element selection from a sequence of adjacent pairs
- Dynamically Create Nested Structure
- Dynamic Dependency Injection at The Run Time
- Number of hits in fibonacci using lru_cache
- jit - "Failed in nopython mode pipeline" error, despite not using nopython in numba
- Issue solving DFS Flood Fill problem while iterating through branching options
- Discrepancy in Recursive and Memoized Knapsack Solution
Related Questions in DIVIDE-AND-CONQUER
- Google interview question - check if all subarrays of an array have at least one unique element
- Find max product using divide and conqure in O(n) time
- How to compute the product of a n x n size Toeplitz matrix and a n-length vector in O(nlogn) time using FFT algorithm
- Proof of correctness for algorithm to find the median of the union of two sorted arrays
- Is there an equivalent to divide and conquer when trying to identify multiple items?
- Divide and conquer algorithm problem applied to an n x n-matrix
- How can I adjust my code to use binary search to guess the number I am thinking in my head
- XSLT recursion crashes after 1000 calls - how to transform it to DVC style?
- labeling graph edges
- Restore the original array after merge Sort based on it's steps
- binary search left and right index to find median of two sorted arrays
- Divide and Conquer max profit algorithm
- How to add `n log n` stones to a grid to form a beautiful arrangement using divide-and-conquer? - algorithm idea
- How will the stack be formed by Recursion in the MergeSort function?
- How can I find all the matches of two sorted arrays in O(n) with limitations on number of comparisons?
Related Questions in BOTTOM-UP
- Eliminating Recursion stack space
- bottom up register allocation, reserving register for loads/stores
- Cant initialize a 2d array/matrix to 0
- Recursive query sum leaf values and pass sum to parents. Values stored in another table
- How do you implement the bottom-up and top-down approach in this problem?
- How can I add limited coins to the coin change problem? (Bottom-up - Dynamic programming)
- Count the sum of subsets of size k when the sum is (Greater than or equal to R) or (Lesser than or equal to L)
- Runtime Error when Trying Bottom Up Approach to Implement Fibonacci function in Swift?
- when adding new text it appears on bottom and rest of text goes up
- How to convert the recursive solution to "Moons and Umbrellas" to DP?
- LR-Parsing-Table: What determines next state in reduce-actions?
- Output produced for the given input using the bottom up parsing
- L-attributed grammar and bottom-up parsing
- Parsing table size (bottom-up)
- Find k out of n subset with maximal area
Trending Questions
- UIImageView Frame Doesn't Reflect Constraints
- Is it possible to use adb commands to click on a view by finding its ID?
- How to create a new web character symbol recognizable by html/javascript?
- Why isn't my CSS3 animation smooth in Google Chrome (but very smooth on other browsers)?
- Heap Gives Page Fault
- Connect ffmpeg to Visual Studio 2008
- Both Object- and ValueAnimator jumps when Duration is set above API LvL 24
- How to avoid default initialization of objects in std::vector?
- second argument of the command line arguments in a format other than char** argv or char* argv[]
- How to improve efficiency of algorithm which generates next lexicographic permutation?
- Navigating to the another actvity app getting crash in android
- How to read the particular message format in android and store in sqlite database?
- Resetting inventory status after order is cancelled
- Efficiently compute powers of X in SSE/AVX
- Insert into an external database using ajax and php : POST 500 (Internal Server Error)
Popular # Hahtags
Popular Questions
- How do I undo the most recent local commits in Git?
- How can I remove a specific item from an array in JavaScript?
- How do I delete a Git branch locally and remotely?
- Find all files containing a specific text (string) on Linux?
- How do I revert a Git repository to a previous commit?
- How do I create an HTML button that acts like a link?
- How do I check out a remote Git branch?
- How do I force "git pull" to overwrite local files?
- How do I list all files of a directory?
- How to check whether a string contains a substring in JavaScript?
- How do I redirect to another webpage?
- How can I iterate over rows in a Pandas DataFrame?
- How do I convert a String to an int in Java?
- Does Python have a string 'contains' substring method?
- How do I check if a string contains a specific word?
1st, we cannot possibly use more than 2*n disk as any column could contain at maximum 2 disks.
let's say d[i][mask] - maximum amount obtained after filling columns from 1 to i with disks so that the last column is filled as mask ( mask could be 0000, 0001, 0010, 0100, 0101, 1000, 1001 or 1010 where 1 means disk was placed and 0 means it wasn't)
So d[i][mask1] = max of (d[i-1][mask2] + number obtained from applying mask1 on i-th column), where mask2 could be any mask which doensn't contradict with mask1
Edit 1: You do not need to change anything. When you are on i-th step on certain mask, it only depends on the answers for masks of i-1. And you already have all of them. You just try to update the current d[i][mask] from those which are valid. As I already said d[i][mask] - stores the maximum value which could be obtained filling columns from 1 to i, optimally, so that the last column has disks in form of this mask (doesn't matter masks before the i-th column were filled, because they won't affect next column)