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You're unlikely to find exactly what you want as existing code example. Break it into parts and solve it in parts.
You can't "Run a sketch" based on reading a value of an LDR. You can write a new sketch that reads an LDR, and calls a function if it's dark, or a different function if it is light. You will need to refactor your code from your other ...
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I assume, that your problem is how to connect everything to the power supply.
You have some different options, depending on your requirements. The linked adaptor (barrel plug to alligator clips) doesn't seem to fit the barrel plug of the power supply. So you cannot use that. Especially it seems, that both are the male part of the connection. For every plug ...
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