 ## Category: Maximum sum path in a matrix

Given an NxM N rows and M columns integer matrix with non-negative values What is the maximum sum from going top left 0, 0 to bottom right N-1, M-1? My example below includes both versions, and the first version will print the path too. Just go from source node to destination node and calculate the distance for each path,basically dfs will find out all the paths and all you need to do is to keep the minimum.

Sorry but bfs won't work as each node doesn't have equal weight. One should not disqualify the whole path based on the current adjacent cell values. The remainder of "disqualified path" may overweight the remainder of the "winning path". It's gotta be recursive. The easiest way is just BFS your way through a known size matrix. You can do this by thinking of the matrix as a series of diagonals.

First, its 0,0. One step away you can get 1,0 0,1. Two steps, you can get 2,0 0,2 1,1. Three steps, you get 3,0 2,1 1,2 0,3 etc, notice how it forms a diagonal across the matrix. At each step, you can calculate the max for each square on the diagonal according to the previous step. Eventually, you'll hit the destination and you can just read off the max value. The hidden trick in this question is the range of values. This can be done using DP in O mn and with O 1 i. Used DP CareerCup's interview videos give you a real-life look at technical interviews.

### Maximum sum path in a matrix from top to bottom in C++

In these unscripted videos, watch how other candidates handle tough questions and how the interviewer thinks about their performance. Most engineers make critical mistakes on their resumes -- we can fix your resume with our custom resume review service. And, we use fellow engineers as our resume reviewers, so you can be sure that we "get" what you're saying. Our Mock Interviews will be conducted "in character" just like a real interview, and can focus on whatever topics you want. All our interviewers have worked for Microsoft, Google or Amazon, you know you'll get a true-to-life experience. Samsung Interview Question for Java Developers. Comment hidden because of low score.

Click to expand. O mn time and O 1 space. Samsung interview question - Anonymous July 26, Flag Reply. I think minimum extra space required is o mn - rajdeeps. Add a Comment Add a Comment.Given an element array of integers,and an integer,determine the maximum value of the sum of any of its subarrays modulo.

For example, Assume and. The following table lists all subarrays and their moduli:. The maximum modulus is. Complete the maximumSum function in the editor below. It should return a long integer that represents the maximum value of. The first line contains an integerthe number of queries to perform.

The next pairs of lines are as follows:. For each query, return the maximum value of as a long integer. The subarrays of array and their respective sums modulo are ranked in order of length and sum in the following list:. The maximum value for for any subarray is. We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies. Practice Compete Jobs Leaderboard.

We define the following: A subarray of array of length is a contiguous segment from through where. The sum of an array is the sum of its elements. Input Format. The next pairs of lines are as follows: The first line contains two space-separated integers and longthe length of and the modulo divisor.

The second line contains space-separated long integers.

Output Format. Sample Input. Sample Output. The subarrays of array and their respective sums modulo are ranked in order of length and sum in the following list: and and The maximum value for for any subarray is.Given a matrix of n rows and n coloumsconsisting of integersfind the submatrix with maximum sum among all submatrices. Example case 1. Fetching successful submissions. Program should read from standard input and write to standard output.

## Maximum path sum in matrix in C++

After you submit a solution you can see your results by clicking on the [My Submissions] tab on the problem page. Below are the possible results:. CodeChef was created as a platform to help programmers make it big in the world of algorithmscomputer programmingand programming contests. At CodeChef we work hard to revive the geek in you by hosting a programming contest at the start of the month and two smaller programming challenges at the middle and end of the month.

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Put yourself up for recognition and win great prizes. We use cookies to improve your experience and for analytical purposes. Read our Privacy Policy and Terms to know more. You consent to our cookies if you continue to use our website. Maximum Sum Submatrix. Input First line consists of two integers n and m. Next n lines each consists of m integers. CodeChef is a non-profit competitive programming community.

In order to report copyright violations of any kind, send in an email to copyright codechef. The time now is: Your IP: CodeChef - A Platform for Aspiring Programmers CodeChef was created as a platform to help programmers make it big in the world of algorithmscomputer programmingand programming contests.Given an m x n matrix filled with non-negative integers, use dynamic programming techniques to find the maximum sum along a path from the top-left of the grid to the bottom-right.

Return this maximum sum. The direction of movement is limited to right and down. That won't work for large sized matrices - just consider the size of the recursion tree for a x matrix! Dynamic Programming should afford a better solution.

Need a hand? Try out these hints, one at a time. Log in to see all hints. Quick hint to get things rolling. Consider the following constraints : 1 The direction of movement is limited to down and right 2 The Matrix contains non-negative integers We can conclude that each step in the path can be found by looking at the previous steps and picking the step that results in a maximal value. Also, since the direction of movement is heavily constrained, this problem has an Optimal Substructure.

Create an m x n matrix that will keep the record of the maximum sum obtained at each cell in the grid. Fill the first row and column of this matrix and use this information to traverse the cells and fill each cell. Final hint! You should be able to code the problem on viewing this. The interview prep tool you'll fall in love with! Log in to Run your code against the test cases and check the answer.I came across this problem recently that required solving for the maximum-sum path in a triangle array.

To copy the above triangle array:. As can be seen, there are 15 levels to this tree including the top most node. Therefore, there are 2 14 possible routes to scan in order to check for the maximum sum using brute force. However, doing the same using brute force on a triangle array of levels would take several billion years to solve using a computer that checks through say, 10 12 routes per second. For instance, for the level problem:.

Solving such a problem would require a powerful approach — and surely enough, there is an algorithm that solves the level problem in a fraction of a second. Now for the Python code. I first store the level triangle array in a text file, euler This code is the key to solving problems 18 and 67 of Project Euler. Problem 18 Ans: Problem 67 Ans: You are commenting using your WordPress.

Email required Address never made public. Name required. Post to Cancel.Starting from the top of a pyramid of numbers like this, you can walk down going one step on the right or on the left, until you reach the bottom row:.

One of such walks is 55 - 94 - 30 - You can compute the total of the numbers you have seen in such walk, in this case it's Your problem is to find the maximum total among all possible paths from the top to the bottom row of the triangle. In the little example above it's This task is derived from the Euler Problem This being Fortran, why not a brute-force scan of all possible paths? This is eased by noting that from a given position, only two numbers are accessible, and always two numbers.

Just like binary digits. So, for three levels, the choices would be,or somesuch. Since however the pinnacle of the pyramid is always chosen, there is no choice there so the digits would be, A triangular array can be defined in some languages, and in some circumstances a square array is used with a lower triangle and upper triangle partition, but here, a simple linear array is in order, with some attention to subscript usage.

The first layer has one number, the second has two, the third has three, The more refined method that determines the maximum sum without ascertaining the path through working upwards from the base employs a FOR ALL statement in adding the maximum of the two possible descendants to each brick in the current layer, employing array BEST that starts off with all the values of the bottom layer.

For input, free-format is convenient. Bad input still is a problem, and can lead to puzzles. If say when N values are to be read but an input line is short of numbers, then additional lines will be read and confusion is likely. So, read the file's record into a text variable and then extract the expected N values from that.

Should a problem arise, then the troublesome record can be shown. First, we pad all short rows with trailing zeros so that all rows are the same length. This eliminates some ambiguity and simplifies the expression of both the data and the code. Second, starting with the last row, for each pair of numbers we find the largest of the two resulting in a list slightly shorter than before, so of course we pad it with a trailing zero and add that row to the previous row.

After repeating this through all the rows, the first value of the resulting row is the maximum we were looking for.Suppose each cell in the matrix has a value assigned. Find the path from the top row to the bottom row following the aforementioned condition such that the maximum sum is obtained.

Algorithm: The idea is to find maximum sum or all paths starting with every cell of first row and finally return maximum of all values in first row. We use Dynamic Programming as results of many subproblems are needed again and again.

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Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. Writing code in comment? Please use ide. Maximum sum path in a matrix from top to bottom Count of subsets with sum equal to X Split the given string into Primes : Digit DP Count of numbers in range which are divisible by M and have digit D at odd places Median of sliding window in an array Eggs dropping puzzle Set 2 Count number of ways to arrange first N numbers Minimum increment or decrement required to sort the array Top-down Approach Maximum sum path in a Matrix Find the numbers from 1 to N that contains exactly k non-zero digits Minimum window size containing atleast P primes in every window of given range Maximum size of square such that all submatrices of that size have sum less than K Count the numbers with N digits and whose suffix is divisible by K Count maximum occurrence of subsequence in string such that indices in subsequence is in A.

Python3 implementation to find. Driver program to test above. This code is contributed by sahilshelangia. MinValue, max. Recommended Posts: Maximum sum path in a matrix from top to bottom and back Lexicographically largest prime path from top-left to bottom-right in a matrix Maximum points from top left of matrix to bottom right and return back Maximum sum path in a Matrix Maximum path sum in matrix Maximum decimal value path in a binary matrix Find maximum path length in a binary matrix Paths from entry to exit in matrix and maximum path sum Maximum weight path ending at any element of last row in a matrix Find maximum path sum in a 2D matrix when exactly two left moves are allowed Minimum Cost Path with Left, Right, Bottom and Up moves allowed Print all possible paths from top left to bottom right of a mXn matrix Count all possible paths from top left to bottom right of a mXn matrix Print all palindromic paths from top left to bottom right in a matrix Minimum cost to reach from the top-left to the bottom-right corner of a matrix.