sicp-all-tasks/sicp/3_002e70

Exercise 3.70: It would be nice to be able to
generate streams in which the pairs appear in some useful order, rather than in
the order that results from an ad hoc interleaving process.  We can use
a technique similar to the merge procedure of Exercise 3.56, if we
define a way to say that one pair of integers is “less than” another.  One
way to do this is to define a “weighting function” 
  
    W
    (
    i
    ,
    j
    )
  
 and
stipulate that 
  
    (
    
      i
      1
    
    ,
    
      j
      1
    
    )
  
 is less than 
  
    (
    
      i
      2
    
    ,
    
      j
      2
    
    )
  
 if

  
    W
    (
    
      i
      1
    
    ,
    
      j
      1
    
    )
    <
  
  
    W
    (
    
      i
      2
    
    ,
    
      j
      2
    
    )
  
.  Write a procedure
merge-weighted that is like merge, except that
merge-weighted takes an additional argument weight, which is a
procedure that computes the weight of a pair, and is used to determine the
order in which elements should appear in the resulting merged
stream.197  Using this, generalize pairs to a procedure
weighted-pairs that takes two streams, together with a procedure that
computes a weighting function, and generates the stream of pairs, ordered
according to weight.  Use your procedure to generate


 the stream of all pairs of positive integers 
  
    (
    i
    ,
    j
    )
  
 with 
  
    i
    ≤
    j
  

ordered according to the sum 
  
    i
    +
    j
  
,

 the stream of all pairs of positive integers 
  
    (
    i
    ,
    j
    )
  
 with 
  
    i
    ≤
    j
  
,
where neither 
  i
 nor 
  j
 is divisible by 2, 3, or 5, and the pairs are
ordered according to the sum 
  
    2
    i
    +
    3
    j
    +
    5
    i
    j
  
.