General - Implementation

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function arrange_soldiers(n, heights)
 max_val := maximum value in heights
 min_val := minimum value in heights
 pos_max := leftmost position of max_val
 pos_min := rightmost position of min_val
 swaps := pos_max + (n - 1 - pos_min)
 // If max is to the right of min, they cross
 if pos_max > pos_min then
 swaps := swaps - 1
 return swaps

You scan the array once to find positions of the maximum and minimum values. For the maximum, you want the leftmost occurrence. For the minimum, you want the rightmost. Time: $O(n)$. Space: $O(1)$.