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top down:

You formulate the problem and solve it inroducing simple operations, for instance, you need to add 2 numbers. This is your problem which you have to solve.

You devide it in simpler problems. Remember in computer memoty first additive, then second. And then add it to each other and show result or save in another variable and show the result.Top down approach is the most popular method in programming.

bottom up:

This method is more complicated because it's not easy to formulate simple problems and end up with a global problem. In most cases bottom up is reversed to top down approach.

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