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POCoin flipping game: Optimization problem
 

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    <p>There is a rectangular grid of coins, with heads being represented by the value 1 and tails being represented by the value 0. You represent this using a 2D integer array table (between 1 to 10 rows/columns, inclusive).</p> <p>In each move, you choose any single cell (R, C) in the grid (R-th row, C-th column) and flip the coins in all cells (r, c), where r is between 0 and R, inclusive, and c is between 0 and C, inclusive. Flipping a coin means inverting the value of a cell from zero to one or one to zero.</p> <p>Return the minimum number of moves required to change all the cells in the grid to tails. This will always be possible.</p> <p>Examples: </p> <pre><code>1111 1111 returns: 1 01 01 returns: 2 010101011010000101010101 returns: 20 000 000 001 011 returns: 6 </code></pre> <p>This is what i tried: Since the order of flipping doesn't matter, and making a move on a coin twice is like not making a move at all, we can just find all distinct combinations of flipping coins, and minimizing the size of good combinations(good meaning those that give all tails).</p> <p>This can be done by making a set consisting of all coins, each represented by an index.(i.e. if there were 20 coins in all, this set would contain 20 elements, giving them an index 1 to 20). Then make all possible subsets and see which of them give the answer(i.e. if making a move on the coins in the subset gives us all tails). Finally, minimize size of the good combinations.</p> <p>I don't know if I've been able to express myself too clearly... I'll post a code if you want. Anyway, this method is too time consuming and wasteful, and not possible for no.of coins>20(in my code). How to go about this?</p>
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