DSA Crash Course [Part 73] - Minimum Change Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function *min_change* that takes in an amount and a list of coins. The function should return the minimum number of coins required to create the amount. You may use each coin as many times as necessary.
>
> If it is not possible to create the amount, then return -1.

```
min_change(8, [1, 5, 4, 12]) # -> 2, because 4+4 is the minimum coins possible
```

```
min_change(13, [1, 9, 5, 14, 30]) # -> 5
```

```
min_change(23, [2, 5, 7]) # -> 4
```

```
min_change(102, [1, 5, 10, 25]) # -> 6
```

```
min_change(200, [1, 5, 10, 25]) # -> 8
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 72] - Sum Possible Walkthrough

In this lesson, Alvin walks through the python implementation for the *sum_possible* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/sum-possible?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

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DSA Crash Course [Part 71] - Sum Possible Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function *sum_possible* that takes in an amount and a list of positive numbers. The function should return a boolean indicating whether or not it is possible to create the amount by summing numbers of the list. You may reuse numbers of the list as many times as necessary.
>
> You may assume that the target amount is non-negative.

```
sum_possible(8, [5, 12, 4]) # -> True, 4 + 4
```

```
sum_possible(15, [6, 2, 10, 19]) # -> False
```

```
sum_possible(13, [6, 2, 1]) # -> True
```

```
sum_possible(103, [6, 20, 1]) # -> True
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 70] - Tribonacci Walkthrough

In this lesson, Alvin walks through the python implementation for the *tribonacci* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/tribonacci?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 69] - Tribonacci Approach

In this lesson, Alvin explores the strategy to solving the following problem using dynamic programming:

> Write a function *tribonacci* that takes in a number argument, *n*, and returns the *n*\-th number of the Tribonacci sequence.
>
> The 0-th and 1-st numbers of the sequence are both 0.
>
> The 2-nd number of the sequence is 1.
>
> To generate further numbers of the sequence, calculate the sum of previous three numbers.
>
> Solve this recursively.

```
tribonacci(0) # -> 0
```

```
tribonacci(1) # -> 0
```

```
tribonacci(2) # -> 1
```

```
tribonacci(5) # -> 4
```

```
tribonacci(7) # -> 13
```

```
tribonacci(14) # -> 927
```

```
tribonacci(20) # -> 35890
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

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DSA Crash Course [Part 68] - Fibonacci Walkthrough

In this lesson, Alvin walks through the python implementation for the *fib* problem. The goal here is to solve it recursively and then apply dynamic programming to speed it up.

Code along and test your work in the following editor workspace: <https://structy.net/problems/fib?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 67] - Fibonacci Approach

In this lesson, Alvin explains the fundamentals of dynamic programming by applying dynamic programming to fibonacci:

> Write a function *fib* that takes in a number argument, *n*, and returns the *n*\-th number of the Fibonacci sequence.
>
> The 0-th number of the sequence is 0.
>
> The 1-st number of the sequence is 1.
>
> To generate further numbers of the sequence, calculate the sum of previous two numbers.
>
> Solve this recursively.

```
fib(0); # -> 0
```

```
fib(1); # -> 1
```

```
fib(2); # -> 1
```

```
fib(3); # -> 2
```

```
fib(4); # -> 3
```

```
fib(5); # -> 5
```

```
fib(35); # -> 9227465
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

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DSA Crash Course [Part 66] - Minimum Island Walkthrough

In this lesson, Alvin walks through the python implementation for the *minimum_island* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/minimum-island?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 65] - Minimum Island Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *minimum_island*, that takes in a grid containing Ws and Ls. W represents water and L represents land. The function should return the size of the smallest island. An island is a vertically or horizontally connected region of land.
>
> You may assume that the grid contains at least one island.

```
grid = [
['W', 'L', 'W', 'W', 'W'],
['W', 'L', 'W', 'W', 'W'],
['W', 'W', 'W', 'L', 'W'],
['W', 'W', 'L', 'L', 'W'],
['L', 'W', 'W', 'L', 'L'],
['L', 'L', 'W', 'W', 'W'],
]

minimum_island(grid) # -> 2
```

```
grid = [
['L', 'W', 'W', 'L', 'W'],
['L', 'W', 'W', 'L', 'L'],
['W', 'L', 'W', 'L', 'W'],
['W', 'W', 'W', 'W', 'W'],
['W', 'W', 'L', 'L', 'L'],
]

minimum_island(grid) # -> 1
```

```
grid = [
['L', 'L', 'L'],
['L', 'L', 'L'],
['L', 'L', 'L'],
]

minimum_island(grid) # -> 9
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

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DSA Crash Course [Part 64] - Island Count Walkthrough

In this lesson, Alvin walks through the python implementation for the *island_count* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/island-count?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 63] - Island Count Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *island_count*, that takes in a grid containing Ws and Ls. W represents water and L represents land. The function should return the number of islands on the grid. An island is a vertically or horizontally connected region of land.

```
grid = [
['W', 'L', 'W', 'W', 'W'],
['W', 'L', 'W', 'W', 'W'],
['W', 'W', 'W', 'L', 'W'],
['W', 'W', 'L', 'L', 'W'],
['L', 'W', 'W', 'L', 'L'],
['L', 'L', 'W', 'W', 'W'],
]

island_count(grid) # -> 3
```

```
grid = [
['L', 'W', 'W', 'L', 'W'],
['L', 'W', 'W', 'L', 'L'],
['W', 'L', 'W', 'L', 'W'],
['W', 'W', 'W', 'W', 'W'],
['W', 'W', 'L', 'L', 'L'],
]

island_count(grid) # -> 4
```

```
grid = [
['L', 'L', 'L'],
['L', 'L', 'L'],
['L', 'L', 'L'],
]

island_count(grid) # -> 1
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 62] - Shortest Path Walkthrough

In this lesson, Alvin walks through the python implementation for the *shortest_path* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/shortest-path?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 61] - Shortest Path Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *shortest_path*, that takes in a list of edges for an undirected graph and two nodes (\*node_A\*, *node_B*). The function should return the length of the shortest path between *A* and *B*. Consider the length as the number of edges in the path, not the number of nodes. If there is no path between *A* and *B*, then return -1. You can assume that *A* and *B* exist as nodes in the graph.

```
edges = [
['w', 'x'],
['x', 'y'],
['z', 'y'],
['z', 'v'],
['w', 'v']
]

shortest_path(edges, 'w', 'z') # -> 2
```

```
edges = [
['w', 'x'],
['x', 'y'],
['z', 'y'],
['z', 'v'],
['w', 'v']
]

shortest_path(edges, 'y', 'x') # -> 1
```

```
edges = [
['a', 'c'],
['a', 'b'],
['c', 'b'],
['c', 'd'],
['b', 'd'],
['e', 'd'],
['g', 'f']
]

shortest_path(edges, 'a', 'e') # -> 3
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 60] - Largest Component Walkthrough

In this lesson, Alvin walks through the python implementation for the *largest_component* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/largest-component?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 59] - Largest Component Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *largest_component*, that takes in the adjacency list of an undirected graph. The function should return the size of the largest connected component in the graph.

```
largest_component({
  0: [8, 1, 5],
  1: [0],
  5: [0, 8],
  8: [0, 5],
  2: [3, 4],
  3: [2, 4],
  4: [3, 2]
}) # -> 4
```

```
largest_component({
  1: [2],
  2: [1,8],
  6: [7],
  9: [8],
  7: [6, 8],
  8: [9, 7, 2]
}) # -> 6
```

```
largest_component({
  3: [],
  4: [6],
  6: [4, 5, 7, 8],
  8: [6],
  7: [6],
  5: [6],
  1: [2],
  2: [1]
}) # -> 5
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 58] - Connected Components Count Walkthrough

In this lesson, Alvin walks through the python implementation for the *connected_components_count* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/connected-components-count?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 57] - Connected Components Count Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *connected_components_count*, that takes in the adjacency list of an undirected graph. The function should return the number of connected components within the graph.

```
connected_components_count({
  0: [8, 1, 5],
  1: [0],
  5: [0, 8],
  8: [0, 5],
  2: [3, 4],
  3: [2, 4],
  4: [3, 2]
}) # -> 2
```

```
connected_components_count({
  1: [2],
  2: [1,8],
  6: [7],
  9: [8],
  7: [6, 8],
  8: [9, 7, 2]
}) # -> 1
```

```
connected_components_count({
  3: [],
  4: [6],
  6: [4, 5, 7, 8],
  8: [6],
  7: [6],
  5: [6],
  1: [2],
  2: [1]
}) # -> 3
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 56] - Undirected Path Walkthrough

In this lesson, Alvin walks through the python implementation for the *undirected_path* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/undirected-path?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 55] - Undirected Path Approach

In this lesson, Alvin explores the strategy to solving the following interview problem:

> Write a function, *undirected_path*, that takes in a list of edges for an undirected graph and two nodes (\*node_A\*, *node_B*). The function should return a boolean indicating whether or not there exists a path between *node_A* and *node_B*.

```
edges = [
('i', 'j'),
('k', 'i'),
('m', 'k'),
('k', 'l'),
('o', 'n')
]

undirected_path(edges, 'j', 'm') # -> True
```

```
edges = [
('i', 'j'),
('k', 'i'),
('m', 'k'),
('k', 'l'),
('o', 'n')
]

undirected_path(edges, 'm', 'j') # -> True
```

```
edges = [
('i', 'j'),
('k', 'i'),
('m', 'k'),
('k', 'l'),
('o', 'n')
]

undirected_path(edges, 'l', 'j') # -> True
```

```
edges = [
('i', 'j'),
('k', 'i'),
('m', 'k'),
('k', 'l'),
('o', 'n')
]

undirected_path(edges, 'k', 'o') # -> False
```

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: [**https://www.linkedin.com/in/alvin-zablan-b73a92117/**](https://www.linkedin.com/in/alvin-zablan-b73a92117/)

DSA Crash Course [Part 54] - Has Path Walkthrough

In this lesson, Alvin walks through the python implementation for the *has_path* problem.

Code along and test your work in the following editor workspace: <https://structy.net/problems/has-path?language=py>

If you need additional support taking these DSA skills and actually applying them, take [**Alvin's**](https://www.linkedin.com/in/alvin-zablan-b73a92117/) *complete* data structures and algorithms course on [**Structy**](https://structy.net/?utm_source=taro). You can try out the concepts yourself in their interactive code editor and learn advanced DSA patterns like stack exhaustive recursion.

Use [**this link to get 20% off**](https://structy.net/purchase?promo_code=taro20) the entire Structy DSA learning experience.

Follow Alvin on LinkedIn: <https://www.linkedin.com/in/alvin-zablan-b73a92117/>

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