Answer:
(a) 4i iterations
(b) "i × n" iterations
Step-by-step explanation:
(a) The provided algorithm segment shows:
for i:= 1 to 4, (Outer loop)
for j:= 1 to i (Inner loop)
next j,
next i
The inner loop executes i times while the outer loop completes 4 cycles.
The inner loop’s total execution when the full algorithm runs is:
= i × 4
= 4i iterations
(b) In the given algorithm segment;
for i:= 1 to n, (Outer loop)
for j:= 1 to i (Inner loop)
next j,
next i
where n denotes a set of positive integers.
<pthe inner="" loop="" also="" runs="" for="" times="" and="" the="" outer="" times.=""><pthus the="" total="" iterations="" of="" inner="" loop="" for="" entire="" algorithm="" is:="">
= i × n
= "i × n" iterations
</pthus></pthe>
Let L represent the yards in a roll of lace ribbon and S represent the yards in a roll of satin ribbon. We can formulate two equations: 3L + 2S = 120 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). If we multiply Equation 1 by 2 and subtract Equation 2, we have: 6L + 4S = 240 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). Thus, 4L equals 80 yards, leading to L equating to 20 yards. For Equation 1, substituting gives 3(20 yards) + 2S = 120 yards, leading to 2S equal to 60 yards, so S equals 30 yards. Therefore, a roll of lace ribbon contains 20 yards, while a roll of satin ribbon has 30 yards.
