rodrigogiraoserrao · August 6, 2020 16:02
diff --git a/P8Phase2_2020.dyalog b/P8Phase2_2020.dyalog
 ⍝ PROBLEM 8.1
 Balance ← {
    (⎕IO ⎕ML ⎕WX) ← 0 1 3
    ⍝ Given an integer vector ⍵, find a 2-partition with equal sums.
    ⍝ Monadic function expecting an integer vector.
    ⍝ This algorithm is O(2*≢⍵); we compute possible partitions of ⍵ and check
    ⍝  if their sums satisfy the requirement.
    ⍝ Return a 2-element vector of integer vectors.
    S ← 1⊥⍵     ⍝ Check simple necessary properties:
    2|S: ⍬      ⍝ odd sum can't be evenly split 
    (∧/0≤⍵)∧S<2×⌈/⍵: ⍬  ⍝ all integers are ≥0 and largest element is too big
    s ← S÷2
    ⍝ compute all relevant possible partitions of ⍵; we can arbitrarily fix the partition in which the 1st elem. of ⍵ appears
    mask ← 1 ⍪ 2∘⊥⍣¯1 ⍳2*¯1+≢⍵ 
    ss ← 1⊥ mask× (⍪⍵)/⍨ 1⊃⍴ mask
    ps ← ⍉mask /⍨ s = ss 
    0=⊃⍴ps: ⍬   ⍝ return ⍬ if there is no solution.
    p ← ⊃↓ps
    (⊂p/⍵),(⊂⍵/⍨~p)     
 }
	⍝ PROBLEM 8.1
	Balance ← {
	(⎕IO ⎕ML ⎕WX) ← 0 1 3
	⍝ Given an integer vector ⍵, find a 2-partition with equal sums.
	⍝ Monadic function expecting an integer vector.
	⍝ This algorithm is O(2*≢⍵); we compute possible partitions of ⍵ and check
	⍝ if their sums satisfy the requirement.
	⍝ Return a 2-element vector of integer vectors.
	S ← 1⊥⍵ ⍝ Check simple necessary properties:
	2\|S: ⍬ ⍝ odd sum can't be evenly split
	(∧/0≤⍵)∧S<2×⌈/⍵: ⍬ ⍝ all integers are ≥0 and largest element is too big
	s ← S÷2
	⍝ compute all relevant possible partitions of ⍵; we can arbitrarily fix the partition in which the 1st elem. of ⍵ appears
	mask ← 1 ⍪ 2∘⊥⍣¯1 ⍳2*¯1+≢⍵
	ss ← 1⊥ mask× (⍪⍵)/⍨ 1⊃⍴ mask
	ps ← ⍉mask /⍨ s = ss
	0=⊃⍴ps: ⍬ ⍝ return ⍬ if there is no solution.
	p ← ⊃↓ps
	(⊂p/⍵),(⊂⍵/⍨~p)
	}