the problem is UVa 11157 — lazy frog
i understand that the subproblem is to find the minimax jump between two closest big stones. but how to prove that alternating jumps on the small stones is the best strategy ?
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the problem is UVa 11157 — lazy frog
i understand that the subproblem is to find the minimax jump between two closest big stones. but how to prove that alternating jumps on the small stones is the best strategy ?
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Let us prove this by contradiction. Let this not be the optimal strategy and the maximum jump is Mi - 1 → Mi + 1. Using optimal solution frog will jump:
Mi - 1 → Mi frog must jump Mi - 2 → Mi + 1 — greater distance than Mi - 1 → Mi + 1;
Mi → Mi + 1 frog must jump Mi - 1 → Mi + 2 — greater distance than Mi - 1 → Mi + 1.
We got a contradiction, so your greedy is correct.