# Find the weight at (Xi, Yi) after M operations in a Matrix

Given n x n points on cartesian plane, the task is to find the weight at (xi, yj) after m operation. xi, yj, w denotes the operation of adding weight w at all the points on the lines x = xi and y = yj.

Examples:

Input: n = 3, m = 2
0 0 1
1 1 2
x = 1, y = 0
Output: 3
Explanation: Initially, weights are
0 0 0
0 0 0
0 0 0
After 1st operation
2 1 1
1 0 0
1 0 0
After 2nd operation
2 3 1
3 4 2
1 0 0
Clearly, weight at (x1, y0) is 3

Input: n = 2, m = 2
0 1 1
1 0 2
x = 1, y = 1
Output: 3

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

Naive Approach:
Consider a 2-d array arr[n][n] = {0} and perform the given operations and then, retrieve the weight at (xi, yj). This approach will take O(n*m) time.

Efficient Approach:

• Consider the arrays arrX[n] = arrY[n] = {0}.
• Redefine the operation xi, yj, w as
```arrX[i] += w
and
arrY[j] += w
```
• Find weight at (xi, yj) using
`w = arrX[i] + arrY[j]`
• Below is the implementation of the above approach:

 `// C++ program to find the ` `// weight at xi and yi ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate weight at (xFind, yFind) ` `int` `findWeight(vector >& operations, ` `               ``int` `n, ``int` `m, ` `               ``int` `xFind, ``int` `yFind) ` `{ ` `    ``int` `row[n] = { 0 }; ` `    ``int` `col[n] = { 0 }; ` ` `  `    ``// Loop to perform operations ` `    ``for` `(``int` `i = 0; i < m; i++) { ` ` `  `        ``// Updating row ` `        ``row[operations[i]] ` `            ``+= operations[i]; ` ` `  `        ``// Updating column ` `        ``col[operations[i]] ` `            ``+= operations[i]; ` `    ``} ` ` `  `    ``// Find weight at (xi, yj) using ` `    ``// w = arrX[i] + arrY[j] ` `    ``int` `result = row[xFind] + col[yFind]; ` ` `  `    ``return` `result; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``vector > operations ` `        ``= { ` `            ``{ 0, 0, 1 }, ` `            ``{ 1, 1, 2 } ` `          ``}; ` `    ``int` `n = 3, ` `        ``m = operations.size(), ` `        ``xFind = 1, ` `        ``yFind = 0; ` `    ``cout << findWeight(operations, ` `                       ``n, m, xFind, ` `                       ``yFind); ` `    ``return` `0; ` `} `

Output:

`3`

Time Complexity: where m is the number of operations

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