Editorial for UTS Open '15 #1 - Caesar Salad

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Map the $i^{th}$ ~i^{th}~ letter of the alphabet to the number $i - 1$ ~i - 1~: A is mapped to $0$ ~0~, B to $1$ ~1~, etc. Then the value of the $n^{th}$ ~n^{th}~ bowl after $B$ ~B~ button presses is $(c_n + B \cdot s_n) \% 26$ ~(c_n + B \cdot s_n) \% 26~. Simulate all values of $B$ ~B~ and take the minimum value which produces an acceptable result. Since $(c_n + B \cdot s_n) \equiv (c_n + (B + 26) \cdot s_n) \pmod{26}$ , it is never optimal to have $B \ge 26$ ~B \ge 26~.

Complexity: $\mathcal{O}(\sum N)$ ~\mathcal{O}(\sum N)~

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