Difference between revisions of "TADM2E 8.21"

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(Created page with "==== 1 ==== Sum every range and keep track of the maximum. Given a set of numbers N = { x0, x1 ... xn } M = 0 for i in (0 .. n) S[i, i] = xi for j in (i + 1 .....")
 
(Undo revision 960 by Erecua (talk))
 
(8 intermediate revisions by 5 users not shown)
Line 16: Line 16:
 
==== 2 ====
 
==== 2 ====
  
−
Sum from each end, resetting the prefix or suffix (i.e., discarding the summed numbers) if it goes negative.
+
    def max_range(items):
 +
        max_diff = max(items[0], 0)
 +
        temp_diff = 0
 +
        for number in items:
 +
            temp_diff = max(0, temp_diff + number)
 +
            max_diff = max(max_diff, temp_diff)
 +
        return max_diff
  
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#!/usr/bin/perl
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    assert max_range([1, 2, 3, 4, 5]) == 15
−
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    assert max_range([-1, -2, -3, -4, -5]) == 0
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sub max_range
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    assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84]) == 187
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  {
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    assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84, -200, 3]) == 187
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  my @numbers = @_;
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    assert max_range([11, -1, 11, -1, 11, -1, 11, -1, 11, -1, -100, 40, 5]) == 51
−
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    assert max_range([-100, 40, 5, -100, 11, -1, 11, -1, 11, -1, 11, -1, 11, -1]) == 51
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  my $prefix = 0;
 
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  my $suffix = 0;
 
−
 
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  for (my ($l, $r) = (0, @numbers - 1); $l <= $r; $l ++, $r --)
 
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    {
 
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    $prefix += $numbers[$l];
 
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    $prefix = 0 if $prefix < 0;
 
−
 
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    $suffix += $numbers[$r] if $l < $r;
 
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    $suffix = 0 if $suffix < 0;
 
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    }
 
−
 
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  return $prefix + $suffix;
 
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  }
 
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my $max = max_range 31, -41, 59, 26, -53, 58, 97, -93, -23, 84;
 
−
 
 
−
print $max, "\n";
 

Latest revision as of 13:13, 24 July 2020

1

Sum every range and keep track of the maximum. 

Given a set of numbers N = { x0, x1 ... xn }

M = 0

for i in (0 .. n)
  S[i, i] = xi
  for j in (i + 1 .. n)
    S[i, j] = S[i, j - 1] + xj
    if M < S[i, j]
      M = S[i, j]

2

   def max_range(items):
       max_diff = max(items[0], 0)
       temp_diff = 0
       for number in items:
           temp_diff = max(0, temp_diff + number)
           max_diff = max(max_diff, temp_diff)
       return max_diff

   assert max_range([1, 2, 3, 4, 5]) == 15
   assert max_range([-1, -2, -3, -4, -5]) == 0
   assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84]) == 187
   assert max_range([31, -41, 59, 26, -53, 58, 97, -93, -23, 84, -200, 3]) == 187
   assert max_range([11, -1, 11, -1, 11, -1, 11, -1, 11, -1, -100, 40, 5]) == 51
   assert max_range([-100, 40, 5, -100, 11, -1, 11, -1, 11, -1, 11, -1, 11, -1]) == 51
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