High Dynamic Range Photography

Overview & Rules

Following the footsteps other Number Logic puzzles such as Kakuro, Loopy is another member of the family of logic puzzles invented in Japan. This game is a loop-forming puzzle with a rectangular lattice of dots as platform which contains clues in a number of different spots. The ultimate goal of the game is to link adjacent dots by placing lines between them in a way to form a continuous closed loop with no crossings and or branches. Additionally the number of lines around each clue, if specified, should exactly equal to the value of that clue. To summarize the rules:    The clue inside each clue should be equal to the number of lines surrounding it Empty squares are fair game and could have as many lines surrounding them as desired Once finished, the solution must be a single continuous close loop with no crossing and or branches.

Figure 1: The left image shows the clues and the dots. The right image contains the solution. Note that there are exactly n number of lines surrounding each clue where n is the value of that clue.

Algorithms & Simplification Techniques:

To start solving such puzzles we will start by several simple techniques to gain some knowledge about the whereabouts of containing lines. Once these techniques are applied we can algorithmically begin to solve for the solution Starting Techniques:

1) This is the most obvious one of all. If there are zeros in any clues all the lines surrounding it should be marked.

2) The next trivial case is where we have a 0 and a 3 adjacent to one another. In this case there are clearly exactly 3 lines that need to marked as part of the solution.

3) Having a 0 and a 3 diagonal to one another leaves us with two options presented in the image on the left and marked in gray. There are two lines in common between the two possibilities and thus they will always be part of the solution in this case.

4) The case of having two adjacent 3’s also produces the following two possibilities which suggest...