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Maximum sum path in a Matrix

Given a matrix of integers, the task is to find a path from the top-left corner to the bottom-right corner of the matrix that maximizes the sum of the elements along the path. The path can only move down or right.

Code Solution

// C Program
// Maximum sum path in a Matrix
#include <stdio.h>
#include <limits.h>

#define R 3 
#define C 4 

// Find the path sum of (0,0) to Matrix (R-1,C-1) 
void path_sum(int matrix[R][C],int *output,int i ,int j,int count,int k,int sum)
{

  if(count==k && *output < sum)
  {
    // When get a new result
    *output = sum;
  }
  else if(i < R && j < C)
  {
    //Recursive execute method with new parameters
    path_sum(matrix,output,i+1,j,count+1,k,sum+matrix[i][j]);
    path_sum(matrix,output,i,j+1,count+1,k,sum+matrix[i][j]);
  }
}

// Handles the request to find max path sum in a matrix
void max_path_sum(int matrix[R][C])
{
    // Set initially min value
    int output = INT_MIN;

    // Calculate max path sum
    path_sum(matrix,&output,0,0,0,R+C-1,0);

    // Display find result
    printf(" %d \n",output);
}

int main()
{
    int matrix[R][C] =
    {
        {4, 6, -2 , 2 },
        {3, -1, 5 , 3 },
        {1, 7,  4,  6 }
    };
    // 4 -> 6 -> -1 -> 7 -> 4 -> 6
    max_path_sum(matrix);

  return 0;
}

Output

 26
/*
    Java program 
    Maximum sum path in a Matrix
*/
// Define TreeNode
public class MyMatrix
{
    public int output;
    // Find the path sum of (0,0) to Matrix (R-1,C-1) 
    public void path_sum(int[][] matrix, 
  	int i, int j, 
  	int count, int k, 
  	int sum, 
  	int rows, int cols)
    {
        if (count == k && this.output < sum)
        {
            // When get a new result
            this.output = sum;
        }
        else if (i < rows && j < cols)
        {
            //Recursive execute method with new parameters
            path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j],rows,cols);
            path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j],rows,cols);
        }
    }
    // Handles the request to find max path sum in a matrix
    public void max_path_sum(int[][] matrix)
    {
        int r = matrix.length;
        int c = matrix[0].length;
        // Set initially min value
        this.output = Integer.MIN_VALUE;
        // Calculate max path sum
        path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
        // Display find result
        System.out.print("  " + this.output + " \n");
    }
    public static void main(String[] args)
    {
        MyMatrix obj = new MyMatrix();
        int[][] matrix =
        {
            {
                4 , 6 , -2 , 2
            }, 
            {
                3 , -1 , 5 , 3
            }, 
            {
                1 , 7 , 4 , 6
            }
        };
        // 4->6->-1->7->4->6
        obj.max_path_sum(matrix);
    }
}

Output

  26
// Include header file
#include <iostream>
#include<limits.h>
#define R 3 
#define C 4 
using namespace std;
/*
    C++ program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix
{
	public: int output;
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	void path_sum(int matrix[R][C], int i, int j, int count, int k, int sum)
	{
		if (count == k && this->output < sum)
		{
			//  When get a new result
			this->output = sum;
		}
		else if (i < R && j < C)
		{
			// Recursive execute method with new parameters
			this->path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j]);
			this->path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j]);
		}
	}
	//  Handles the request to find max path sum in a matrix
	void max_path_sum(int matrix[R][C])
	{

		//  Set initially min value
		this->output = INT_MIN;
		//  Calculate max path sum
		this->path_sum(matrix, 0, 0, 0, R + C - 1, 0);
		//  Display find result
		cout << "  " << this->output << " \n";
	}
};
int main()
{
	MyMatrix obj = MyMatrix();
	int matrix[R][C] = {
		{
			4 , 6 , -2 , 2
		} , {
			3 , -1 , 5 , 3
		} , {
			1 , 7 , 4 , 6
		}
	};
	//  4->6->-1->7->4->6
	obj.max_path_sum(matrix);
	return 0;
}

Output

  26
// Include namespace system
using System;
/*
    C# program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
public class MyMatrix
{
	public int output;
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	public void path_sum(int[,] matrix, int i, int j, int count, int k, int sum, int rows, int cols)
	{
		if (count == k && this.output < sum)
		{
			//  When get a new result
			this.output = sum;
		}
		else if (i < rows && j < cols)
		{
			// Recursive execute method with new parameters
			path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i,j], rows, cols);
			path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i,j], rows, cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	public void max_path_sum(int[,] matrix)
	{
		int r = matrix.GetLength(0);
		int c = matrix.GetLength(1);
		//  Set initially min value
		this.output = int.MinValue;
		//  Calculate max path sum
		path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
		//  Display find result
		Console.Write("  " + this.output + " \n");
	}
	public static void Main(String[] args)
	{
		MyMatrix obj = new MyMatrix();
		int[,] matrix = {
			{
				4 , 6 , -2 , 2
			} , {
				3 , -1 , 5 , 3
			} , {
				1 , 7 , 4 , 6
			}
		};
		//  4->6->-1->7->4->6
		obj.max_path_sum(matrix);
	}
}

Output

  26
<?php
/*
    Php program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix
{
	public $output;
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	public	function path_sum( & $matrix, $i, $j, $count, $k, $sum, $rows, $cols)
	{
		if ($count == $k && $this->output < $sum)
		{
			//  When get a new result
			$this->output = $sum;
		}
		else if ($i < $rows && $j < $cols)
		{
			// Recursive execute method with new parameters
			$this->path_sum($matrix, $i + 1, $j, $count + 1, $k, $sum + $matrix[$i][$j], $rows, $cols);
			$this->path_sum($matrix, $i, $j + 1, $count + 1, $k, $sum + $matrix[$i][$j], $rows, $cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	public	function max_path_sum( & $matrix)
	{
		$r = count($matrix);
		$c = count($matrix[0]);
		//  Set initially min value
		$this->output = -PHP_INT_MAX;
		//  Calculate max path sum
		$this->path_sum($matrix, 0, 0, 0, $r + $c - 1, 0, $r, $c);
		//  Display find result
		echo "  ". $this->output ." \n";
	}
}

function main()
{
	$obj = new MyMatrix();
	$matrix = array(
      array(4, 6, -2, 2), 
      array(3, -1, 5, 3), 
      array(1, 7, 4, 6)
    );
	//  4->6->-1->7->4->6
	$obj->max_path_sum($matrix);
}
main();

Output

  26
/*
    Node Js program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix
{
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	path_sum(matrix, i, j, count, k, sum, rows, cols)
	{
		if (count == k && this.output < sum)
		{
			//  When get a new result
			this.output = sum;
		}
		else if (i < rows && j < cols)
		{
			// Recursive execute method with new parameters
			this.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j], rows, cols);
			this.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j], rows, cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	max_path_sum(matrix)
	{
		var r = matrix.length;
		var c = matrix[0].length;
		//  Set initially min value
		this.output = -Number.MAX_VALUE;
		//  Calculate max path sum
		this.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
		//  Display find result
		process.stdout.write("  " + this.output + " \n");
	}
}

function main()
{
	var obj = new MyMatrix();
	var matrix = [
		[4, 6, -2, 2] , [3, -1, 5, 3] , [1, 7, 4, 6]
	];
	//  4->6->-1->7->4->6
	obj.max_path_sum(matrix);
}
main();

Output

  26
import sys

#  Python 3 program 
#  Maximum sum path in a Matrix

#  Define TreeNode
class MyMatrix :
	
	#  Find the path sum of (0,0) to Matrix (R-1,C-1) 
	def path_sum(self, matrix, i, j, count, k, sum, rows, cols) :
		if (count == k and self.output < sum) :
			#  When get a new result
			self.output = sum
		
		elif(i < rows and j < cols) :
			# Recursive execute method with new parameters
			self.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j], rows, cols)
			self.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j], rows, cols)
		
	
	#  Handles the request to find max path sum in a matrix
	def max_path_sum(self, matrix) :
		r = len(matrix)
		c = len(matrix[0])
		#  Set initially min value
		self.output = -sys.maxsize
		#  Calculate max path sum
		self.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c)
		#  Display find result
		print("  ", self.output ," \n", end = "")
	

def main() :
	obj = MyMatrix()
	matrix = [
		[4, 6, -2, 2] , 
        [3, -1, 5, 3] , 
        [1, 7, 4, 6]
	]
	#  4->6->-1->7->4->6
	obj.max_path_sum(matrix)

if __name__ == "__main__": main()

Output

   26
#  Ruby program 
#  Maximum sum path in a Matrix

#  Define TreeNode
class MyMatrix  
	# Define the accessor and reader of class MyMatrix  
	attr_reader :output
	attr_accessor :output
 
	
	#  Find the path sum of (0,0) to Matrix (R-1,C-1) 
	def path_sum(matrix, i, j, count, k, sum, rows, cols) 
		if (count == k && self.output < sum) 
			#  When get a new result
			self.output = sum
		elsif(i < rows && j < cols) 
			# Recursive execute method with new parameters
			self.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j], rows, cols)
			self.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j], rows, cols)
		end

	end

	#  Handles the request to find max path sum in a matrix
	def max_path_sum(matrix) 
		r = matrix.length
		c = matrix[0].length
		#  Set initially min value
		self.output = -(2 ** (0. size * 8 - 2))
		#  Calculate max path sum
		self.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c)
		#  Display find result
		print("  ", self.output ," \n")
	end

end

def main() 
	obj = MyMatrix.new()
	matrix = [
		[4, 6, -2, 2] , 
        [3, -1, 5, 3] , 
        [1, 7, 4, 6]
	]
	#  4->6->-1->7->4->6
	obj.max_path_sum(matrix)
end

main()

Output

  26 

/*
    Scala program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix(var output: Int)
{
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	def path_sum(matrix: Array[Array[Int]], 
      i: Int, j: Int, count: Int, k: Int, 
        sum: Int, rows: Int, cols: Int): Unit = {
		if (count == k && this.output < sum)
		{
			//  When get a new result
			this.output = sum;
		}
		else if (i < rows && j < cols)
		{
			// Recursive execute method with new parameters
			this.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix(i)(j), rows, cols);
			this.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix(i)(j), rows, cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	def max_path_sum(matrix: Array[Array[Int]]): Unit = {
		var r: Int = matrix.length;
		var c: Int = matrix(0).length;
		//  Set initially min value
		this.output = Int.MinValue;
		//  Calculate max path sum
		this.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
		//  Display find result
		print("  " + this.output + " \n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MyMatrix = new MyMatrix(0);
		var matrix: Array[Array[Int]] = 
          Array(Array(4, 6, -2, 2), 
                Array(3, -1, 5, 3), 
                Array(1, 7, 4, 6));
		//  4->6->-1->7->4->6
		obj.max_path_sum(matrix);
	}
}

Output

  26
/*
    Swift 4 program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix
{
	var output: Int;
	init()
	{
		self.output = 0;
	}
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	func path_sum(_ matrix: [[Int]], _ i: Int, _ j: Int, _ count: Int, _ k: Int, _ sum: Int, _ rows: Int, _ cols: Int)
	{
		if (count == k && self.output < sum)
		{
			//  When get a new result
			self.output = sum;
		}
		else if (i < rows && j < cols)
		{
			// Recursive execute method with new parameters
			self.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j], rows, cols);
			self.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j], rows, cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	func max_path_sum(_ matrix: [
		[Int]
	])
	{
		let r: Int = matrix.count;
		let c: Int = matrix[0].count;
		//  Set initially min value
		self.output = Int.min;
		//  Calculate max path sum
		self.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
		//  Display find result
		print("  ", self.output ," \n", terminator: "");
	}
}
func main()
{
	let obj: MyMatrix = MyMatrix();
	let matrix: [
		[Int]
	] = [
		[4, 6, -2, 2] , [3, -1, 5, 3] , [1, 7, 4, 6]
	];
	//  4->6->-1->7->4->6
	obj.max_path_sum(matrix);
}
main();

Output

   26
/*
    Kotlin program 
    Maximum sum path in a Matrix
*/
//  Define TreeNode
class MyMatrix
{
	var output: Int;
	constructor()
	{
		this.output = 0;
	}
	//  Find the path sum of (0,0) to Matrix (R-1,C-1)
	fun path_sum(matrix: Array < Array < Int >> , i: Int, j: Int, count: Int, k: Int, sum: Int, rows: Int, cols: Int): Unit
	{
		if (count == k && this.output < sum)
		{
			//  When get a new result
			this.output = sum;
		}
		else if (i < rows && j < cols)
		{
			// Recursive execute method with new parameters
			this.path_sum(matrix, i + 1, j, count + 1, k, sum + matrix[i][j], rows, cols);
			this.path_sum(matrix, i, j + 1, count + 1, k, sum + matrix[i][j], rows, cols);
		}
	}
	//  Handles the request to find max path sum in a matrix
	fun max_path_sum(matrix: Array<Array<Int>> ): Unit
	{
		var r: Int = matrix.count();
		var c: Int = matrix[0].count();
		//  Set initially min value
		this.output = Int.MIN_VALUE;
		//  Calculate max path sum
		this.path_sum(matrix, 0, 0, 0, r + c - 1, 0, r, c);
		//  Display find result
		print("  " + this.output + " \n");
	}
}
fun main(args: Array < String > ): Unit
{
	var obj: MyMatrix = MyMatrix();
	var matrix: Array <Array<Int>> = 
      arrayOf(arrayOf(4, 6, -2, 2), 
              arrayOf(3, -1, 5, 3), 
              arrayOf(1, 7, 4, 6));
	//  4->6->-1->7->4->6
	obj.max_path_sum(matrix);
}

Output

  26
Last updated on by Kalkicode




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