Path in Matrix

PROBLEM :
Given a N X N  matrix Matrix[N][N] of positive integers.  There are only three possible moves from a cell Matrix[r][c].

1. Matrix[r+1][c]
2. Matrix[r+1][c-1]
3. Matrix[r+1][c+1]

Starting from any column in row 0, return the largest sum of any of the paths up to row N-1.

Input:
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N denoting the order of matrix. Next line contains N*N integers denoting the elements of the matrix in row-major form.

Output:
Output the largest sum of any of the paths starting from any cell of row 0 to any cell of row N-1. Print the output of each test case in a new line.

Constraints:
1<=T<=20
2<=N<=20
1<=Matrix[i][j]<=1000 (for all 1<=i<=N && 1<=j<=N)

Example:
Input:
1
2
348 391 618 193

Output:
1009

Explanation: In the sample test case, the path leading to maximum possible sum is 391->618.  (391 + 618 = 1009)

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SIMPLE c++ IMPLEMENTATION :
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#include<iostream>
using namespace std;
#include<limits.h>
#define max 20
int Path_in_Matrix(int [max][max],int ) ;
int max_of1(int ,int ) ;
int max_of2(int ,int ,int ) ;

int main()
 {
int t,no,i,j ;
int mat[max][max] ;
cin>>t ;
while(t--)
{
   cin>>no ;
   for(i=0;i<no;i++)
       for(j=0;j<no;j++)
           cin>>mat[i][j] ;
         
   cout<<Path_in_Matrix(mat,no)<<endl ;
}
return 0;
}

int Path_in_Matrix(int mat[max][max],int no)
{
    int i,j,big ;
    big=INT_MIN ;
   
    for(i=1;i<no;i++)
    {
        for(j=0;j<no;j++)
        {
            if(j==0)
                mat[i][j]+=max_of1(mat[i-1][j],mat[i-1][j+1]) ;
            else if(j==no-1)
                mat[i][j]+=max_of1(mat[i-1][j],mat[i-1][j-1]) ;
            else
                mat[i][j]+=max_of2(mat[i-1][j],mat[i-1][j+1],mat[i-1][j-1]) ;
        }
    }
   
    for(i=0;i<no;i++)
        big=big>mat[no-1][i]?big:mat[no-1][i] ;
   
    return big ;
}

int max_of1(int a,int b)
{
    return a>b?a:b ;
}

int max_of2(int a,int b,int c)
{
    int temp ;
    temp=a>b?a:b ;
    return temp>c?temp:c ;
}

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