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Unformatted text preview: PI is optimal solution to P. (where PI is PI' union {p_hat}) Proof by contradiction: Assume PI is not optimal solution to P. Recall, from the greedy choice property (which we already proved), there is some OPTIMAL solution PI* that uses {p_hat}. PI* > PI, because PI is not optimal. PI*  {p_hat} > PI  {p_hat} PI*  {p_hat} > PI' but since PI* uses p_hat, PI*  {p_hat} is a solution to P'. So PI*  {p_hat} is a better solution to P' than PI' which is a contradiction, because PI' is assume to be optimal solution to P'...
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 Spring '08
 cse441

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