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# Instructions | ||
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Correctly determine the fewest number of coins to be given to a customer such that the sum of the coins' value would equal the correct amount of change. | ||
Determine the fewest number of coins to give a customer so that the sum of their values equals the correct amount of change. | ||
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## For example | ||
## Examples | ||
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- An input of 15 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) or [5, 10] | ||
- An input of 40 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) and one quarter (25) or [5, 10, 25] | ||
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## Edge cases | ||
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- Does your algorithm work for any given set of coins? | ||
- Can you ask for negative change? | ||
- Can you ask for a change value smaller than the smallest coin value? | ||
- An amount of 15 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5 and one coin of value 10, or [5, 10]. | ||
- An amount of 40 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5, one coin of value 10, and one coin of value 25, or [5, 10, 25]. |
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exercises/practice/collatz-conjecture/.docs/instructions.md
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# Instructions | ||
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The Collatz Conjecture or 3x+1 problem can be summarized as follows: | ||
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Take any positive integer n. | ||
If n is even, divide n by 2 to get n / 2. | ||
If n is odd, multiply n by 3 and add 1 to get 3n + 1. | ||
Repeat the process indefinitely. | ||
The conjecture states that no matter which number you start with, you will always reach 1 eventually. | ||
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Given a number n, return the number of steps required to reach 1. | ||
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## Examples | ||
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Starting with n = 12, the steps would be as follows: | ||
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0. 12 | ||
1. 6 | ||
2. 3 | ||
3. 10 | ||
4. 5 | ||
5. 16 | ||
6. 8 | ||
7. 4 | ||
8. 2 | ||
9. 1 | ||
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Resulting in 9 steps. | ||
So for input n = 12, the return value would be 9. | ||
Given a positive integer, return the number of steps it takes to reach 1 according to the rules of the Collatz Conjecture. |
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# Introduction | ||
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Bob is a thief. | ||
After months of careful planning, he finally manages to crack the security systems of a fancy store. | ||
Lhakpa is a [Sherpa][sherpa] mountain guide and porter. | ||
After months of careful planning, the expedition Lhakpa works for is about to leave. | ||
She will be paid the value she carried to the base camp. | ||
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In front of him are many items, each with a value and weight. | ||
Bob would gladly take all of the items, but his knapsack can only hold so much weight. | ||
Bob has to carefully consider which items to take so that the total value of his selection is maximized. | ||
In front of her are many items, each with a value and weight. | ||
Lhakpa would gladly take all of the items, but her knapsack can only hold so much weight. | ||
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[sherpa]: https://en.wikipedia.org/wiki/Sherpa_people#Mountaineering |
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# Instructions | ||
# Description | ||
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A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which, | ||
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# Instructions | ||
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Given a natural radicand, return its square root. | ||
Your task is to calculate the square root of a given number. | ||
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Note that the term "radicand" refers to the number for which the root is to be determined. | ||
That is, it is the number under the root symbol. | ||
- Try to avoid using the pre-existing math libraries of your language. | ||
- As input you'll be given a positive whole number, i.e. 1, 2, 3, 4… | ||
- You are only required to handle cases where the result is a positive whole number. | ||
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Check out the Wikipedia pages on [square root][square-root] and [methods of computing square roots][computing-square-roots]. | ||
Some potential approaches: | ||
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Recall also that natural numbers are positive real whole numbers (i.e. 1, 2, 3 and up). | ||
- Linear or binary search for a number that gives the input number when squared. | ||
- Successive approximation using Newton's or Heron's method. | ||
- Calculating one digit at a time or one bit at a time. | ||
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[square-root]: https://en.wikipedia.org/wiki/Square_root | ||
You can check out the Wikipedia pages on [integer square root][integer-square-root] and [methods of computing square roots][computing-square-roots] to help with choosing a method of calculation. | ||
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[integer-square-root]: https://en.wikipedia.org/wiki/Integer_square_root | ||
[computing-square-roots]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots |
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