As per update, fixed the bug in solution_1, with little modification to performance improvement. Regarding the contention that baseline and solution_1 are doing fewer prints, of course they are. If IO is a bottle neck, then a method that can reduce calls to IO is a better method. But, if you want to eliminate those benefits of the algorithms, benchmarking with subroutines including lines like

print OUT "$_\n" foreach @list;

result in the following comparisons, where _pr specifies a version with more print statements: 

Benchmark: timing 100000 iterations of Baseline, Baseline_pr, Queue, Q
+ueue_pr...
  Baseline: 1.62739 wallclock secs ( 1.62 usr +  0.01 sys =  1.63 CPU)
+ @ 61349.69/s (n=100000)
Baseline_pr: 2.13879 wallclock secs ( 2.14 usr +  0.00 sys =  2.14 CPU
+) @ 46728.97/s (n=100000)
     Queue: 3.61375 wallclock secs ( 3.61 usr +  0.00 sys =  3.61 CPU)
+ @ 27700.83/s (n=100000)
  Queue_pr: 3.70646 wallclock secs ( 3.71 usr +  0.00 sys =  3.71 CPU)
+ @ 26954.18/s (n=100000)
               Rate    Queue_pr       Queue Baseline_pr    Baseline
Queue_pr    26954/s          --         -3%        -42%        -56%
Queue       27701/s          3%          --        -41%        -55%
Baseline_pr 46729/s         73%         69%          --        -24%
Baseline    61350/s        128%        121%         31%          --
Benchmark: timing 1000 iterations of Baseline, Baseline_pr, Queue, Que
+ue_pr...
  Baseline: 5.63275 wallclock secs ( 5.60 usr +  0.03 sys =  5.63 CPU)
+ @ 177.62/s (n=1000)
Baseline_pr: 8.3455 wallclock secs ( 8.32 usr +  0.02 sys =  8.34 CPU)
+ @ 119.90/s (n=1000)
     Queue: 25.3093 wallclock secs (25.29 usr +  0.01 sys = 25.30 CPU)
+ @ 39.53/s (n=1000)
  Queue_pr: 25.1902 wallclock secs (25.17 usr +  0.02 sys = 25.19 CPU)
+ @ 39.70/s (n=1000)
              Rate       Queue    Queue_pr Baseline_pr    Baseline
Queue       39.5/s          --         -0%        -67%        -78%
Queue_pr    39.7/s          0%          --        -67%        -78%
Baseline_pr  120/s        203%        202%          --        -32%
Baseline     178/s        349%        347%         48%          --

[download]

In reply to Re^3: Challenge: Sorting Sums Of Sorted Series by kennethk
in thread Challenge: Sorting Sums Of Sorted Series by Limbic~Region

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