Algorithm Design Course Project

Here are the projects of the Algorithm Design course, including:

• Arrangement of weighted colored cubes;
• Eight ministers (or queens) problem with obstacle
• Eight ministers (or queens) problem with scored obstacle

Arrangement of weighted colored cubes

Consider N number of cubes of the same size, each of which has a different weight. Each of the faces of the cubes has a color. We want to place the cubes on top of each other to design the tallest tower while observing the following:
a) When placing one cube on top of another, the lower face of the upper cube must be the same color as the upper face of the lower cube.
b) When placing one cube on top of another, the lower cube should be heavier than the upper cube.

Eight ministers (or queens) problem with obstacle

Regarding eight ministers, some places have walls and prevent threats. It is impossible to place the minister in places covered with walls. We want to find all the possible positions where eight ministers can be placed in such an environment. The following example is an example of a solution:

Eight ministers (or queens) problem with scored obstacle

In the previous problem, we distributed the numbers 1 to 64 as points between all the places. Now for each possible solution, we consider the total points of the location of the ministers as the points of that solution. We want to design and implement an optimal algorithm that, by taking a number like z, finds and displays only solutions whose score is greater than z.