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Add pythagorean-triplet exercise #263

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Jun 5, 2024
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Add pythagorean-triplet exercise #263

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11 changes: 11 additions & 0 deletions config.json
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"prerequisites": [],
"difficulty": 4
},
{
"slug": "pythagorean-triplet",
"name": "Pythagorean Triplet",
"uuid": "548fa68b-98ff-4c3f-87ae-ef3a0cc605c1",
"practices": [],
"prerequisites": [],
"difficulty": 6,
"topics": [
"math"
]
},
{
"slug": "all-your-base",
"name": "All Your Base",
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6 changes: 6 additions & 0 deletions exercises/practice/pythagorean-triplet/.docs/hints.md
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# Hints

## General

- The `$t0-9` registers can be used to temporarily store values
- The instructions specify which registers are used as input and output
12 changes: 12 additions & 0 deletions exercises/practice/pythagorean-triplet/.docs/instructions.append.md
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# Instructions append

## Registers

| Register | Usage | Type | Description |
| -------- | ------------ | ------- | ---------------------------- |
| `$a0` | input | integer | N, sum of sides of triangle |
| `$a1` | input/output | address | a values |
| `$a2` | input/output | address | b values |
| `$a3` | input/output | address | c values |
| `$v0` | output | integer | number of triplets |
| `$t0-9` | temporary | any | for temporary storage |
23 changes: 23 additions & 0 deletions exercises/practice/pythagorean-triplet/.docs/instructions.md
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# Instructions

A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,

```text
a² + b² = c²
```

and such that,

```text
a < b < c
```

For example,

```text
3² + 4² = 5².
```

Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`.

For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`: `{200, 375, 425}`.
19 changes: 19 additions & 0 deletions exercises/practice/pythagorean-triplet/.meta/config.json
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{
"authors": [
"keiravillekode"
],
"files": {
"solution": [
"impl.mips"
],
"test": [
"runner.mips"
],
"example": [
".meta/example.mips"
]
},
"blurb": "There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the triplet.",
"source": "Problem 9 at Project Euler",
"source_url": "https://projecteuler.net/problem=9"
}
59 changes: 59 additions & 0 deletions exercises/practice/pythagorean-triplet/.meta/example.mips
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# | Register | Usage | Type | Description |
# | -------- | ------------ | ------- | -------------------------------------------- |
# | `$a0` | input | integer | N, sum of sides of triangle |
# | `$a1` | input/output | address | a values |
# | `$a2` | input/output | address | b values |
# | `$a3` | input/output | address | c values |
# | `$v0` | output | integer | number of triplets |
# | `$t0` | temporary | address | start of a values |
# | `$t1` | temporary | integer | a |
# | `$t2` | temporary | integer | b |
# | `$t3` | temporary | integer | c |
# | `$t5` | temporary | integer | remainder |
# | `$t6` | temporary | integer | numerator |
# | `$t7` | temporary | integer | denominator |

# For every Pythagorean triplet with total a + b + c = N,
# a² + b² = c²
# <=> a² + b² = (N - a - b)², substituting c
# <=> 0 = N² - 2*N*a - 2*N*b + 2*a*b
# <=> (2*N - 2*a) b = (N² - 2*N*a)
# <=> b = (N² - 2*N*a) / (2*N - 2*a)
#
# The denominator is never 0, as N exceeds a side length.

.globl triplets_with_sum

triplets_with_sum:
move $t0, $a1 # start of a values
blt $a0, 2, return # Stop immediately if N < 2
move $t1, $zero # Initialize a
j increment_a

check_remainder:
mfhi $t5 # remainder
bnez $t5, increment_a
sub $t3, $a0, $t1
sub $t3, $t3, $t2 # c = N - a - b

sw $t1, 0($a1)
sw $t2, 0($a2)
sw $t3, 0($a3)
addi $a1, $a1, 4 # Increment pointer for a
addi $a2, $a2, 4 # Increment pointer for b
addi $a3, $a3, 4 # Increment pointer for c

increment_a:
addi $t1, $t1, 1
sub $t7, $a0, $t1 # N - a
sub $t6, $t7, $t1 # N - 2*a
sll $t7, $t7, 1 # denominator = 2*N - 2*a
mulu $t6, $a0, $t6 # numerator = N² - 2*N*a
div $t6, $t7
mflo $t2 # b
bgt $t2, $t1, check_remainder # loop while b > a

return:
sub $v0, $a1, $t0 # compute number of triplets
srl $v0, $v0, 2
jr $ra
31 changes: 31 additions & 0 deletions exercises/practice/pythagorean-triplet/.meta/tests.toml
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# This is an auto-generated file.
#
# Regenerating this file via `configlet sync` will:
# - Recreate every `description` key/value pair
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
# - Preserve any other key/value pair
#
# As user-added comments (using the # character) will be removed when this file
# is regenerated, comments can be added via a `comment` key.

[a19de65d-35b8-4480-b1af-371d9541e706]
description = "triplets whose sum is 12"

[48b21332-0a3d-43b2-9a52-90b2a6e5c9f5]
description = "triplets whose sum is 108"

[dffc1266-418e-4daa-81af-54c3e95c3bb5]
description = "triplets whose sum is 1000"

[5f86a2d4-6383-4cce-93a5-e4489e79b186]
description = "no matching triplets for 1001"

[bf17ba80-1596-409a-bb13-343bdb3b2904]
description = "returns all matching triplets"

[9d8fb5d5-6c6f-42df-9f95-d3165963ac57]
description = "several matching triplets"

[f5be5734-8aa0-4bd1-99a2-02adcc4402b4]
description = "triplets for large number"
13 changes: 13 additions & 0 deletions exercises/practice/pythagorean-triplet/impl.mips
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# | Register | Usage | Type | Description |
# | -------- | ------------ | ------- | -------------------------------------------- |
# | `$a0` | input | integer | N, sum of sides of triangle |
# | `$a1` | input/output | address | a values |
# | `$a2` | input/output | address | b values |
# | `$a3` | input/output | address | c values |
# | `$v0` | output | integer | number of triplets |
# | `$t0-9` | temporary | any | for temporary storage |

.globl triplets_with_sum

triplets_with_sum:
jr $ra
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