USACO 2013 March Contest, Gold

Problem 1. The Cow Run

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Problem 1: The Cow Run [Chris Tzamos, 2006] Farmer John has forgotten to repair a hole in the fence on his farm, and his N cows (1 <= N <= 1,000) have escaped and gone on a rampage! Each minute a cow is outside the fence, she causes one dollar worth of damage. FJ must visit each cow to install a halter that will calm the cow and stop the damage. Fortunately, the cows are positioned at distinct locations along a straight line on a road outside the farm. FJ knows the location P_i of each cow i (-500,000 <= P_i <= 500,000, P_i != 0) relative to the gate (position 0) where FJ starts. FJ moves at one unit of distance per minute and can install a halter instantly. Please determine the order that FJ should visit the cows so he can minimize the total cost of the damage; you should compute the minimum total damage cost in this case. PROBLEM NAME: cowrun INPUT FORMAT: * Line 1: The number of cows, N. * Lines 2..N+1: Line i+1 contains the integer P_i. SAMPLE INPUT (file 4 -2 -12 3 7 INPUT DETAILS: Four cows placed in positions: -2, -12, 3, and 7. OUTPUT FORMAT: * Line 1: The minimum total cost of the damage. SAMPLE OUTPUT (file cowrun.out): 50 OUTPUT DETAILS: The optimal visit order is -2, 3, 7, -12. FJ arrives at position -2 in 2 minutes for a total of 2 dollars in damage for that cow. He then travels to position 3 (distance: 5) where the cumulative damage is 2 + 5 = 7 dollars for that cow. He spends 4 more minutes to get to 7 at a cost of 7 + 4 = 11 dollars for that cow. Finally, he spends 19 minutes to go to -12 with a cost of 11 + 19 = 30 dollars. The total damage is 2 + 7 + 11 + 30 = 50 dollars.
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