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Backtracking

Backtracking may be one of the most "brute-force" algorithm. When all the other algorithms, such as, breadth-first-search (bfs), depth-first-search(dfs), and others, do not work, we can consider backtracking. With backtracking, the problem will be solved incrementally.

One of key features of backtracking is that we will do a "try step" first. Then we continue the search. If eventually the result is not valid, we have to back-track the "try step". And then make a second "try step", and so on, until make all the possible try steps.

If there are N steps in total, and for each step, there are M possible trials, then the overall complexity is (M^N), which increases really fast as a function of M or N.

The trial structure is layer by layer: once you make a trial, then based on this trial, you may continue to make the next trial on the "next layer", since we do not know yet whether the trials is a valid one or not. So we may have a chain of trials in different layers. Once we reach the step (converging to the base case) to know the correctness, we can make a decision. If it is valid, it means we find a good (valid) solution; if not, we need to go back to the "most recent" trial (or the one in the most recent layer of trial), reset the trial, and try the second possible route, ..., until we finish all the trial in the last layer.

If all the trials in the last layer do not work, then we need to go back to the second last layer, and reset the trial that we had made there, and try the second possible route, ...

Until we iterate all the possible trials in "all the layers".

Maybe you still do not get the point of the backtracking, but no worries, there are many classic questions to help illustrate the concept of it, some of which will be included in the question posts below.

To sum up, backtracking is

1. pretty brute-force;

2. make a trial step first; if does not work eventually, need to step back and start the next possible trial;

3. solve problems incrementally


Question List


Upper Layer

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