# Find column with maximum sum in a Matrix

Given a N*N matrix. The task is to find the index of column with maximum sum. That is the column whose sum of elements are maximum.

Examples:

```Input : mat[][] = {
{ 1, 2, 3, 4, 5 },
{ 5, 3, 1, 4, 2 },
{ 5, 6, 7, 8, 9 },
{ 0, 6, 3, 4, 12 },
{ 9, 7, 12, 4, 3 },
};
Output : Column 5 has max sum 31

Input : mat[][] = {
{ 1, 2, 3 },
{ 4, 2, 1 },
{ 5, 6, 7 },
};
Output : Column 3 has max sum 11
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is to traverse the matrix column-wise and find the sum of elements in each column and check for every column if current sum is greater than the maximum sum obtained till the current column and update the maximum_sum accordingly.

Below is the implementation of the above approach:

## C++

 `// C++ program to find column with ` `// max sum in a matrix ` `#include ` `using` `namespace` `std; ` ` `  `#define N 5 // No of rows and column ` ` `  `// Function to find the column with max sum ` `pair<``int``, ``int``> colMaxSum(``int` `mat[N][N]) ` `{ ` `    ``// Variable to store index of column ` `    ``// with maximum ` `    ``int` `idx = -1; ` ` `  `    ``// Variable to store max sum ` `    ``int` `maxSum = INT_MIN; ` ` `  `    ``// Traverse matrix column wise ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``int` `sum = 0; ` ` `  `        ``// calculate sum of column ` `        ``for` `(``int` `j = 0; j < N; j++) { ` `            ``sum += mat[j][i]; ` `        ``} ` ` `  `        ``// Update maxSum if it is less than ` `        ``// current sum ` `        ``if` `(sum > maxSum) { ` `            ``maxSum = sum; ` ` `  `            ``// store index ` `            ``idx = i; ` `        ``} ` `    ``} ` ` `  `    ``pair<``int``, ``int``> res; ` ` `  `    ``res = make_pair(idx, maxSum); ` ` `  `    ``// return result ` `    ``return` `res; ` `} ` ` `  `// driver code ` `int` `main() ` `{ ` ` `  `    ``int` `mat[N][N] = { ` `        ``{ 1, 2, 3, 4, 5 }, ` `        ``{ 5, 3, 1, 4, 2 }, ` `        ``{ 5, 6, 7, 8, 9 }, ` `        ``{ 0, 6, 3, 4, 12 }, ` `        ``{ 9, 7, 12, 4, 3 }, ` `    ``}; ` ` `  `    ``pair<``int``, ``int``> ans = colMaxSum(mat); ` ` `  `    ``cout << ``"Column "` `<< ans.first + 1 << ``" has max sum "` `         ``<< ans.second; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find column  ` `// with max sum in a matrix  ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` `// No of rows and column  ` `static` `final` `int` `N = ``5``;  ` ` `  `// structure for pair ` `static` `class` `Pair ` `{ ` `    ``int` `first , second; ` `     `  `    ``Pair(``int` `f, ``int` `s) ` `    ``{ ` `        ``first = f; ` `        ``second = s; ` `    ``} ` `} ` ` `  `// Function to find the column ` `// with max sum  ` `static` `Pair colMaxSum(``int` `mat[][])  ` `{  ` `    ``// Variable to store index of ` `    ``// column with maximum  ` `    ``int` `idx = -``1``;  ` ` `  `    ``// Variable to store max sum  ` `    ``int` `maxSum = Integer.MIN_VALUE;  ` ` `  `    ``// Traverse matrix column wise  ` `    ``for` `(``int` `i = ``0``; i < N; i++) ` `    ``{  ` `        ``int` `sum = ``0``;  ` ` `  `        ``// calculate sum of column  ` `        ``for` `(``int` `j = ``0``; j < N; j++) ` `        ``{  ` `            ``sum += mat[j][i];  ` `        ``}  ` ` `  `        ``// Update maxSum if it is  ` `        ``// less than current sum  ` `        ``if` `(sum > maxSum)  ` `        ``{  ` `            ``maxSum = sum;  ` ` `  `            ``// store index  ` `            ``idx = i;  ` `        ``}  ` `    ``}  ` ` `  `    ``Pair res;  ` ` `  `    ``res = ``new` `Pair(idx, maxSum);  ` ` `  `    ``// return result  ` `    ``return` `res;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``int` `mat[][] = { { ``1``, ``2``, ``3``, ``4``, ``5` `},  ` `                    ``{ ``5``, ``3``, ``1``, ``4``, ``2` `},  ` `                    ``{ ``5``, ``6``, ``7``, ``8``, ``9` `},  ` `                    ``{ ``0``, ``6``, ``3``, ``4``, ``12` `},  ` `                    ``{ ``9``, ``7``, ``12``, ``4``, ``3` `}};  ` ` `  `    ``Pair ans = colMaxSum(mat);  ` ` `  `    ``System.out.println(``"Column "` `+ (``int``)(ans.first + ``1``) + ` `                           ``" has max sum "` `+ ans.second);  ` `}  ` `} ` ` `  `// This code is contributed ` `// by Arnab Kundu `

## Python3

 `# Python3 program to find column with ` `# max Sum in a matrix ` ` `  `N ``=` `5` ` `  `# Function to find the column with max Sum ` `def` `colMaxSum(mat): ` `     `  `    ``# Variable to store index of column ` `    ``# with maximum ` `    ``idx ``=` `-``1` ` `  `    ``# Variable to store max Sum ` `    ``maxSum ``=` `-``10``*``*``9` ` `  `    ``# Traverse matrix column wise ` `    ``for` `i ``in` `range``(N): ` ` `  `        ``Sum` `=` `0` ` `  `        ``# calculate Sum of column ` `        ``for` `j ``in` `range``(N): ` `            ``Sum` `+``=` `mat[j][i] ` ` `  `        ``# Update maxSum if it is less  ` `        ``# than current Sum ` `        ``if` `(``Sum` `> maxSum): ` `            ``maxSum ``=` `Sum` ` `  `            ``# store index ` `            ``idx ``=` `i ` `         `  `    ``# return result ` `    ``return` `idx, maxSum ` ` `  `# Driver Code ` ` `  `mat ``=` `[[ ``1``, ``2``, ``3``, ``4``, ``5` `], ` `       ``[ ``5``, ``3``, ``1``, ``4``, ``2` `], ` `       ``[ ``5``, ``6``, ``7``, ``8``, ``9` `], ` `       ``[ ``0``, ``6``, ``3``, ``4``, ``12` `], ` `       ``[ ``9``, ``7``, ``12``, ``4``, ``3` `]] ` ` `  `ans, ans0 ``=` `colMaxSum(mat) ` ` `  `print``(``"Column"``, ans ``+` `1``,     ` `      ``"has max Sum"``, ans0) ` ` `  `# This code is contributed by ` `# Mohit kumar 29 `

## C#

 `// C# program to find column  ` `// with max sum in a matrix  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// No of rows and column  ` `static` `readonly` `int` `N = 5;  ` ` `  `// structure for pair ` `public` `class` `Pair ` `{ ` `    ``public` `int` `first , second; ` `     `  `    ``public` `Pair(``int` `f, ``int` `s) ` `    ``{ ` `        ``first = f; ` `        ``second = s; ` `    ``} ` `} ` ` `  `// Function to find the column ` `// with max sum  ` `static` `Pair colMaxSum(``int` `[,]mat)  ` `{  ` `    ``// Variable to store index of ` `    ``// column with maximum  ` `    ``int` `idx = -1;  ` ` `  `    ``// Variable to store max sum  ` `    ``int` `maxSum = ``int``.MinValue;  ` ` `  `    ``// Traverse matrix column wise  ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{  ` `        ``int` `sum = 0;  ` ` `  `        ``// calculate sum of column  ` `        ``for` `(``int` `j = 0; j < N; j++) ` `        ``{  ` `            ``sum += mat[j, i];  ` `        ``}  ` ` `  `        ``// Update maxSum if it is  ` `        ``// less than current sum  ` `        ``if` `(sum > maxSum)  ` `        ``{  ` `            ``maxSum = sum;  ` ` `  `            ``// store index  ` `            ``idx = i;  ` `        ``}  ` `    ``}  ` ` `  `    ``Pair res;  ` ` `  `    ``res = ``new` `Pair(idx, maxSum);  ` ` `  `    ``// return result  ` `    ``return` `res;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(String []args) ` `{  ` `    ``int` `[,]mat = { { 1, 2, 3, 4, 5 },  ` `                    ``{ 5, 3, 1, 4, 2 },  ` `                    ``{ 5, 6, 7, 8, 9 },  ` `                    ``{ 0, 6, 3, 4, 12 },  ` `                    ``{ 9, 7, 12, 4, 3 }};  ` ` `  `    ``Pair ans = colMaxSum(mat);  ` ` `  `    ``Console.WriteLine(``"Column "` `+ (``int``)(ans.first + 1) + ` `                        ``" has max sum "` `+ ans.second);  ` `}  ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

Output:

```Column 5 has max sum 31
```

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