Accuracy

Why do later passes not mess up earlier sorts?

Prove that after pass p, sorted for digit p+1 to last digit
Prove by induction over p

• True for p=1. Apply Stable sort to digit 1, sorted after pass
• Assume true for p=i, prove true for p=i+1
• After pass i, compare two numbers x and y
• If x appears before y then one of following conditions must be true

  1.

  x < y for digit i, then x belongs before y in sorted order

  2.

  x = y for digit i, then x < y for rest of number, placed in that order in earlier pass, not swapped because use stable sort