Given a matrix of size N X N, the task is to find maximum sum of this Matrix where each value picked is from a unique column for every row.
Input: matrix = [[3, 4, 4, 4], [1, 3, 4, 4], [3, 2, 3, 4], [4, 4, 4, 4]] Output: 16 Explanation: Selecting (0, 1) from row 1 = 4 Selecting (1, 2) from row 2 = 4 Selecting (2, 3) from row 3 = 4 Selecting (3, 0) from row 4 = 4 Therefore, max sum = 4 + 4 + 4 + 4 = 16 Input: matrix = [[0, 1, 0, 1], [3, 0, 0, 2], [1, 0, 2, 0], [0, 2, 0, 0]] Output: 8 Explanation: Selecting (0, 3) from row 1 = 1 Selecting (1, 0) from row 2 = 3 Selecting (2, 2) from row 3 = 2 Selecting (3, 1) from row 4 = 2 Therefore, max sum = 1 + 3 + 2 + 2 = 8
- Genrate a numeric string of size N containing numbers from 1 to N
- Find the permutation of this string (N!).
- Now pairing is done between the permutations, such that each N! pairing has a unique column for every row.
- Then calculate the sum of values for all the pairs.
Below is the implementation of the above approach:
Time complexity: O(K), where K = N!
Auxiliary Space complexity: O(K), where K = N!
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