## Editorial for A Coin Problem

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**Author:

This is a very classical dynamic programming problem.

Let \(dp[x]\) denote whether it is possible to make a sum of \(x\) using the given coins.

\(dp[x]\) would be true if any of \(dp[x-c_i]\) is true.

Thus, after computing the DP table, we can check \(dp[S]\) to determine whether we can make a sum of \(S\) or not.

**Time Complexity:** \(\mathcal{O}(SN)\)

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