One example of a problem that can be solved using the greedy algorithm approach is the "Fractional Knapsack Problem".

  In this problem, we are given a set of items, each with a weight and a value, and a knapsack which can only hold a certain weight. The goal is to maximize the total value of the items placed in the knapsack.

  The greedy algorithm for the Fractional Knapsack Problem works by selecting items based on their value-to-weight ratio. The algorithm repeatedly selects the item with the highest value-to-weight ratio and adds it to the knapsack as long as there is still space available.

  Here is an example to illustrate the process:

  Suppose we have the following items:

  Item 1: weight = 2, value = 5

  Item 2: weight = 3, value = 8

  Item 3: weight = 4, value = 10

  Item 4: weight = 5, value = 12

  And the knapsack can hold a maximum weight of 10.

  First, we calculate the value-to-weight ratio for each item:

  Item 1: ratio = 5/2 = 2.5

  Item 2: ratio = 8/3 ≈ 2.67

  Item 3: ratio = 10/4 = 2.5

  Item 4: ratio = 12/5 = 2.4

  Next, we sort the items in descending order of their value-to-weight ratio:

  Item 2: weight = 3, value = 8, ratio = 2.67

  Item 1: weight = 2, value = 5, ratio = 2.5

  Item 3: weight = 4, value = 10, ratio = 2.5

  Item 4: weight = 5, value = 12, ratio = 2.4

  We start adding items to the knapsack in the order of their sorted ratio until we reach the maximum weight capacity of the knapsack. In this case, the greedy algorithm approach would select Item 2 (value = 8) and add it to the knapsack, leaving 7 units of weight capacity. Then it would select Item 1 (value = 5) and add it to the knapsack, leaving 5 units of weight capacity. Finally, it would stop because adding any other item would exceed the capacity.

  In this example, the greedy algorithm would select Item 2 and Item 1, resulting in a total value of 13. This is the optimal solution for this particular problem instance.