# Sum of all minimum frequency elements in Matrix

Given a NxM matrix of integers containing duplicate elements. The task is to find the sum of all minimum occurring elements in the given matrix. That is the sum of all such elements whose frequency is even in the matrix.

Examples:

```Input : mat[] = {{1, 1, 2},
{2, 3, 3},
{4, 5, 3}}
Output : 9
The min occurring elements are 4, 5 and they
occurs only 1 time.
Therefore, sum = 4+5 = 9

Input : mat[] = {{10, 20},
{40, 40}}
Output : 30
```

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

Approach:

• Traverse the matrix and use a map in C++ to store the frequency of elements of the matrix such that the key of map is the matrix element and value is its frequency in the matrix.
• Then traverse the map to find the minimum frequency.
• Finally, traverse the map to find the frequency of elements and check if it matches with the minimum frequency obtained in previous step, if yes, then add this element it’s frequency times to sum.

Below is the implementation of the above approach:

## C++

 `// C++ program to find sum of all min ` `// frequency elements in a Matrix ` ` `  `#include ` `using` `namespace` `std; ` ` `  `#define N 3 // Rows ` `#define M 3 // Columns ` ` `  `// Function to find sum of all min ` `// frequency elements in a Matrix ` `int` `sumMinOccurring(``int` `arr[N][M]) ` `{ ` `    ``// Store frequencies of elements ` `    ``// in matrix ` `    ``map<``int``, ``int``> mp; ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``for` `(``int` `j = 0; j < M; j++) { ` `            ``mp[arr[i][j]]++; ` `        ``} ` `    ``} ` ` `  `    ``// Find minimum frequency ` `    ``int` `sum = 0; ` `    ``int` `minFreq = INT_MAX; ` `    ``for` `(``auto` `itr = mp.begin(); itr != mp.end(); itr++) { ` `        ``if` `(itr->second < minFreq) ` `            ``minFreq = itr->second; ` `    ``} ` ` `  `    ``// Sum of minimum frequency elements ` `    ``for` `(``auto` `itr = mp.begin(); itr != mp.end(); itr++) { ` `        ``if` `(itr->second == minFreq) { ` `            ``sum += (itr->first) * (itr->second); ` `        ``} ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``int` `mat[N][M] = { { 1, 2, 3 }, ` `                      ``{ 1, 3, 2 }, ` `                      ``{ 1, 5, 6 } }; ` ` `  `    ``cout << sumMinOccurring(mat) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find sum of all min  ` `// frequency elements in a Matrix  ` `import` `java.util.HashMap; ` `import` `java.util.Iterator; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `N = ``3``; ``// Rows ` `    ``static` `int` `M = ``3``; ``// Columns ` ` `  `    ``// Function to find sum of all min ` `    ``// frequency elements in a Matrix ` `    ``public` `static` `int` `sumMinOccuring(``int``[][] arr)  ` `    ``{ ` ` `  `        ``// Store frequencies of elements ` `        ``// in matrix ` `        ``HashMap mp = ``new` `HashMap<>(); ` `        ``for` `(``int` `i = ``0``; i < N; i++)  ` `        ``{ ` `            ``for` `(``int` `j = ``0``; j < M; j++) ` `            ``{ ` `                ``if` `(mp.containsKey(arr[i][j])) ` `                ``{ ` `                    ``int` `x = mp.get(arr[i][j]); ` `                    ``mp.put(arr[i][j], x + ``1``); ` `                ``}  ` `                ``else` `                    ``mp.put(arr[i][j], ``1``); ` `            ``} ` `        ``} ` ` `  `        ``// Find minimum frequency ` `        ``int` `sum = ``0``; ` `        ``int` `minFreq = Integer.MAX_VALUE; ` `        ``for` `(HashMap.Entry entry : mp.entrySet()) ` `        ``{ ` `            ``if` `(entry.getValue() < minFreq) ` `                ``minFreq = entry.getValue(); ` `        ``} ` ` `  `        ``// Sum of minimum frequency elements ` `        ``for` `(HashMap.Entry entry : mp.entrySet())  ` `        ``{ ` `            ``if` `(entry.getValue() == minFreq) ` `                ``sum += entry.getKey() * entry.getValue(); ` `        ``} ` ` `  `        ``return` `sum; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int``[][] mat = { { ``1``, ``2``, ``3` `},  ` `                        ``{ ``1``, ``3``, ``2` `},  ` `                        ``{ ``1``, ``5``, ``6` `} }; ` ` `  `        ``System.out.println(sumMinOccuring(mat)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// sanjeev2552 `

## Python3

 `# Python3 program to find sum of all min  ` `# frequency elements in a Matrix  ` ` `  `import` `sys ` `import` `math ` ` `  `# Store frequencies of elements  ` `# in matrix ` `def` `sumMinOccuring(mat): ` `    ``n,m``=``len``(mat),``len``(mat[``0``]) ` `    ``_map``=``{} ` `    ``for` `i ``in` `range``(n): ` `        ``for` `j ``in` `range``(m): ` `            ``d``=``mat[i][j] ` `            ``if` `d ``in` `_map: ` `                ``_map[d]``=``_map.get(d)``+``1` `            ``else``: ` `                ``_map[d]``=``1` ` `  `    ``# Find minimum frequency ` `    ``_sum,minFreq``=``0``,sys.maxsize ` `    ``for` `i ``in` `_map: ` `        ``minFreq``=``min``(minFreq,_map.get(i)) ` `     `  `    ``# Sum of minimum frequency elements ` `    ``for` `i ``in` `range``(n): ` `        ``for` `j ``in` `range``(m): ` `            ``if` `_map.get(mat[i][j])``=``=``minFreq: ` `                ``_sum``+``=``mat[i][j] ` `     `  `    ``return` `_sum ` `  `  `# Driver Code ` `if` `__name__``=``=``'__main__'``: ` `    ``mat``=``[[``1``,``2``,``3``],[``1``,``3``,``2``],[``1``,``5``,``6``]] ` `    ``print``(sumMinOccuring(mat)) ` ` `  ` `  `# This code is Contributed by Vikash Kumar 37 `

## C#

 `// C# program to find sum of all min  ` `// frequency elements in a Matrix  ` `using` `System;  ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `N = 3; ``// Rows ` `    ``static` `int` `M = 3; ``// Columns ` ` `  `    ``// Function to find sum of all min ` `    ``// frequency elements in a Matrix ` `    ``public` `static` `int` `sumMinOccuring(``int``[,] arr)  ` `    ``{ ` ` `  `        ``// Store frequencies of elements ` `        ``// in matrix ` `        ``Dictionary<``int``,  ` `                   ``int``> mp = ``new` `Dictionary<``int``, ` `                                            ``int``>(); ` `        ``for` `(``int` `i = 0; i < N; i++)  ` `        ``{ ` `            ``for` `(``int` `j = 0; j < M; j++) ` `            ``{ ` `                ``if` `(mp.ContainsKey(arr[i, j])) ` `                ``{ ` `                    ``int` `x = mp[arr[i, j]]; ` `                    ``mp[arr[i, j]] = x + 1; ` `                ``}  ` `                ``else` `                    ``mp[arr[i, j]] = 1; ` `            ``} ` `        ``} ` ` `  `        ``// Find minimum frequency ` `        ``int` `sum = 0; ` `        ``int` `minFreq = 10000009; ` `        ``foreach``(KeyValuePair<``int``, ``int``> ele1 ``in` `mp) ` `        ``{ ` `            ``if``(ele1.Value < minFreq) ` `                ``minFreq = ele1.Value; ` `        ``} ` ` `  `        ``// Sum of minimum frequency elements ` `        ``foreach``(KeyValuePair<``int``, ``int``> ele1 ``in` `mp) ` `        ``{ ` `            ``if` `(ele1.Value == minFreq) ` `                ``sum += ele1.Key * ele1.Value; ` `        ``} ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[,] mat = ``new` `int``[3, 3] {{ 1, 2, 3 },  ` `                                    ``{ 1, 3, 2 },  ` `                                    ``{ 1, 5, 6 }}; ` ` `  `        ``Console.Write(sumMinOccuring(mat)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Mohit kumar `

Output:

```11
```

Time Complexity : O(M x N)
Auxiliary Space : O(M x N)

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