The document discusses the coin change problem and the application of dynamic programming (DP) as a method to solve it efficiently. It contrasts the greedy approach, which can lead to suboptimal solutions, with DP, which finds the optimal number of coins needed. The document also includes mentions of algorithm code in C/C++ for implementing the solution.

1. COIN CHANGE USING DP

2. INTRODUCTION
WHAT IS DP, THE COIN CHANGE PROBLEM, GREEDY APPROACH BOUNDARIES.

3. LETS START WITH A QUOTE!

4. WHAT IS DP?
 DYNAMIC PROGRAMMING: Dynamic programming is a method for solving a complex problem by
1. Breaking it down into a collection of simpler sub problems,
2. Solving each of those sub problems just once and
3. Storing their solutions.
 sub problem
 memoization

5. COIN CHANGE PROBLEM.
 Given a value whole N, if we want to make change for N with coins, and we have infinite supply of each
of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change?
 Find the Fewest Coins: Greedy approach:
Given 30 cents, and coins {1, 5, 10, 25}
Here is what a casher will do: always go with coins of highest value first.
Step: 1. Choose the coin with highest value 25 • 1 quarter 25 valued coin given.
Step: 2. Now we have 5 cents left • one 5 valued coin given.

6. PROBLEM WITH GREEDY APPROACH.
Another example:
 Coins Set = {1, 3, 4, 5}
 7 cents
 Greedy solution: – 3 coins: one 5 + two 1
 Optimal solution: – 2 coins: one 3 + one 4
So we need different solution.

7. DYNAMIC PROGRAMMING APPROACH TO SOLVE
COIN CHANGE.
THE ALGORITHM

8. CODE.
C/C++

9. CODE.
C/C++