Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Maximum path sum in matrix in C++
In this problem, we are given a 2D matrix of size M*N. Our task is to create a program that will find the maximum path sum in the matrix.
Here, the maximum path sum in the matrix is defined as the sum of all elements for one row to the last row. The allowed moves for traversing the path are downward move and diagonal move. The start and endpoints can be any element of the first and last row of the matrix respectively.
Let's take an example to understand the problem
Input −
matrix [][] = 3 5 9 1 7 2 4 8 6
Output − 24
Explanation − The maximum path will be 9 → 7 → 8.
To solve the problem, we will start from the top of the array and find the largest element of the first row, and store into maxSum. Then on traversing the matrix and find the max values that occur in the path. If the new values are greater update maxSum otherwise don't update. And once the whole matrix is traversed and the path is created return the maxSum.
Example
Program to find the maximum path sum in matrix −
#include <iostream>
#define N 3
#define M 3
using namespace std;
int maxPathSum(int mat[][M]){
for (int i = 1; i < N; i++) {
for (int j = 0; j < M; j++) {
if (j > 0 && j < M - 1)
mat[i][j] += max(mat[i - 1][j], max(mat[i - 1][j - 1],mat[i - 1][j + 1]));
else if (j > 0)
mat[i][j] += max(mat[i - 1][j],
mat[i - 1][j - 1]);
else if (j < M - 1)
mat[i][j] += max(mat[i - 1][j],
mat[i - 1][j + 1]);
}
}
int maxSum = mat[N-1][0];
for (int j = 1; j < M; j++)
maxSum = max(mat[N-1][j], maxSum);
return maxSum;
}
int main(){
int matrix[N][M] = {
{3, 5, 9 },
{1, 7, 2},
{4, 8, 6}};
cout<<"The maximum path sum of matrix is : "<<maxPathSum(matrix);
return 0;
}Output
The maximum path sum of matrix is : 24
598 Views
