4 Queen's problem using backtracking| design and analysis of algorithms (DAA)
Backtracking is a systematic way to go through all possible
configuration of search space.
The basic idea of backtracking is build up a vector one component at a time and to test whether the
vector being formed has any chance of success.
Backtracking algorithm is that if it is realized that the partial vector generated does not lead to an
optimal solution then that vector may be ignored.
In this method input is provided in the form of different component present in one set
For example:
Input X = { x
1, x2, x3,………… xn}
X = Card deck then xn =52
The
solution is generated by the reorganize in the given i/p with respect to certain constraints.
For example:
Output Y = { y1, y2, y3,………… yn}.
There are two types of constraints
1. Explicit constraints.
2. Implicit constraints
1. Explicit constraints:
If any condition is specifically specified in a given problem then it is called as explicit constraints
(given constraints)
2. Implicit constraints:
If the condition is derived from the given problem it is called as implicit constraints.
Note that:
The most important aspect of backtracking is to define the constraints. There is no process involve
between input and output, we have organize all input to get the output
1. 4- Queen’s problem:
First define the constraints
Explicit constraints:
Chess board 4× 4 is given in the problem where ‘4’ is the number of Queen’s
Implicit constraints:
1. No two Queen’s should be in same row
2. No two Queen’s should be in same column
3. No two Queen’s should be in same diagonally
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