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

• Difficulty Level : Hard
• Last Updated : 12 Dec, 2019

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:

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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++

 `// 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;``}`

## Python3

 `# Python3 program to find the``# weight at xi and yi`` ` `# Function to calculate weight at (xFind, yFind)``def` `findWeight(operations, n, m, xFind, yFind) :`` ` `    ``row ``=` `[ ``0` `] ``*` `n``    ``col ``=` `[ ``0` `] ``*` `n``  ` `    ``# Loop to perform operations``    ``for` `i ``in` `range``(m) :``  ` `        ``# Updating row``        ``row[operations[i][``0``]]``+``=` `operations[i][``2``]``  ` `        ``# Updating column``        ``col[operations[i][``0``]]``+``=` `operations[i][``2``]``  ` `    ``# Find weight at (xi, yj) using``    ``# w = arrX[i] + arrY[j]``    ``result ``=` `row[xFind] ``+` `col[yFind]``  ` `    ``return` `result``  ` `# Driver code``operations ``=` `[[ ``0``, ``0``, ``1` `],[ ``1``, ``1``, ``2` `]]``n ``=` `2``m ``=` `len``(operations)``xFind ``=` `1``yFind ``=` `0``print``(findWeight(operations,n, m, xFind, yFind))`` ` `# This code is contributed by divyamohan123`

Output:
`3`

Time Complexity: where m is the number of operations

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