# 1.1 Algorithms

## 1.1-1¶

Give a real-world example that requires sorting or a real-world example that requires computing a convex hull.

• Sorting: browse the price of the restaurants with ascending prices on NTU street.
• Convex hull: computing the diameter of set of points.

## 1.1-2¶

Other than speed, what other measures of efficiency might one use in a real-world setting?

Memory efficiency and coding efficiency.

## 1.1-3¶

Select a data structure that you have seen previously, and discuss its strengths and limitations.

• Strengths: insertion and deletion.
• Limitations: random access.

## 1.1-4¶

How are the shortest-path and traveling-salesman problems given above similar? How are they different?

• Similar: finding path with shortest distance.
• Different: traveling-salesman has more constraints.

## 1.1-5¶

Come up with a real-world problem in which only the best solution will do. Then come up with one in which a solution that is "approximately" the best is good enough.

• Best: find the GCD of two positive integer numbers.
• Approximately: find the solution of differential equations.