P1-DaC-Scheduler

Brute Force (Round Robin)

Using the round robin algorithm to permute all the teams, but the pivot (usually the first) iterating through the weeks, as the followig example:

Week 1:

pivot => 1

m m m m m m m m 
| | | | | | | |
1 2 3 4 5 6 7 8
8 7 6 5 4 3 2 1

Week 2:

pivot => 1

permute => 1 3 4 5 6 7 8 2

m m m m m m m m 
| | | | | | | |
1 3 4 5 6 7 8 2
2 8 7 6 5 4 3 1

Eficience

Doing this way the algorithm eficient in the worst case (asintotic notation) is O(n^2), else we should permute all cases until n!

Divide and Conquer (Round Robin)

Using the divide and conquer algorithm, we could solve the problem by dividing the problem, from 2^K, by two recursively, from 1 to 2^(k-1) and from 2^(k-1) + 1 to 2^n.

Before the merge of both subsolutions, we need to use other strategy to fulfill the solution matrix by pairing between them. We could maybe, permute one each week (and apply Round Robin again).

Eficience

aT (n/b) + dn^j

int medio;

if (rowMax - rowMin == 1) {
	t[rowMin][0] = rowMax;
	t[rowMax][0] = rowMin;
} else {
	medio = ((rowMax + rowMin) / 2);
	divide(t, medio + 1, rowMax); // Call 1 ( T = 1)
    divide(t, rowMin, medio); // Call 2 ( T = 2)
    
	conquer(t, rowMin, medio, (medio - rowMin), (medio - rowMin) * 2, medio + 1); // O(n^2)
	conquer(t, (medio + 1), rowMax, (rowMax - (medio + 1)), (rowMax - (medio + 1)) * 2, rowMin); // O(n^2)
}

for (int sum = 0, j = colMin; j <= colMax; sum++, j++) { // O(n/2)
	t[rowMin][j] = (eqInic + sum);
}

for (int i = rowMin + 1; i <= rowMax; i++) { // O(n) 
	t[i][colMin] = t[i - 1][colMax];
	for (int j = colMin + 1; j <= colMax; j++) { // O(n/2)
		t[i][j] = t[i - 1][j - 1];
	}
}

Recursive calls: 2 Problem division: 2 Worst recursive time: O (n^2) Worst base case: 2

t(n) = | 2, si n = 2 | 2T (n/2) + n^2, si n > 2

2T (n/2) + n^2 € O(n^2 + 2^log2n ...) € O(n^2)

Then the worst case (asintotic notation) is O(n^2).

Doing this way the algorithm eficient in the worst case (asintotic notation) is O(n^2)