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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

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 <bits/stdc++.h>
    using namespace std;
      
    // Function to calculate weight at (xFind, yFind)
    int findWeight(vector<vector<int> >& 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][0]]
                += operations[i][2];
      
            // Updating column
            col[operations[i][0]]
                += operations[i][2];
        }
      
        // Find weight at (xi, yj) using
        // w = arrX[i] + arrY[j]
        int result = row[xFind] + col[yFind];
      
        return result;
    }
      
    // Driver code
    int main()
    {
        vector<vector<int> > 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:  O(m) where m is the number of operations




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