feat(algorithms, hash-maps): powerful integers#196
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BrianLusina
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📝 WalkthroughWalkthroughThis change introduces a new "Powerful Integers" algorithm to the hash table section, featuring two implementation approaches and comprehensive documentation. Additionally, documentation was added to the max subarray problem, and a minor formatting adjustment was made to an existing file. Changes
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Actionable comments posted: 1
🧹 Nitpick comments (3)
algorithms/hash_table/powerful_integers/README.md (1)
56-62: Math notation could be clearer.
m^n <= boundimpliesn <= log_m(bound), but the rendered textn<=log(m) boundreads ambiguously (it looks likelog(m) * bound). Consider rewriting asn <= log_m(bound)or using LaTeX:$n \le \log_m(\text{bound})$for clarity. Similarly in the Algorithm section (Lines 66-67),a=log(x)bound/b=log(y)boundwould be clearer asa = log_x(bound)/b = log_y(bound).🤖 Prompt for AI Agents
Verify each finding against the current code and only fix it if needed. In `@algorithms/hash_table/powerful_integers/README.md` around lines 56 - 62, Rewrite ambiguous logarithm notation in the README: replace "m^n <= bound" implication text "n<=log(m) bound" with a clear form such as "n <= log_m(bound)" (or LaTeX "$n \\le \\log_m(\\text{bound})$"), and likewise change "a=log(x)bound" / "b=log(y)bound" in the Algorithm section to "a = log_x(bound)" and "b = log_y(bound)" (or use LaTeX "$a = \\log_x(\\text{bound})$, $b = \\log_y(\\text{bound})$") so the base of the log is explicit for symbols m, n, x, y, a, b.algorithms/hash_table/powerful_integers/test_powerful_integers.py (1)
9-17: Good test coverage.Nice inclusion of edge cases:
bound=0returning[],x=y=1returning[2], and a large-bound case(100, 100, 1000000)that exercises the log-based path. Consider also adding a case wherex**k == boundexactly (e.g.(2, 3, 1024)or similar) to guard against any futureint(log(...))rounding regressions noted in__init__.py.🤖 Prompt for AI Agents
Verify each finding against the current code and only fix it if needed. In `@algorithms/hash_table/powerful_integers/test_powerful_integers.py` around lines 9 - 17, Add a test case to POWERFUL_INTEGERS_TEST_CASE that covers the exact-equality boundary where x**k (or y**k) equals bound (for example use a tuple like (2, 3, 1024, [...expected results...]) or another appropriate exact power) so the test guards against off-by-one/rounding issues in the log-based path; update the expected output list accordingly and ensure the new case is appended to the existing POWERFUL_INTEGERS_TEST_CASE in test_powerful_integers.py (this addresses the potential rounding regression noted in __init__.py).algorithms/hash_table/powerful_integers/__init__.py (1)
33-55: Minor efficiency and style nits inpowerful_integers_logarithmic_bounds.A few small refinements:
x**iis recomputed on every inner-loop iteration; hoist it out of thejloop.- When
x == 1,a = boundallocates a potentially hugerange(bound+1)even though the outerbreakat Line 52-53 ensures only a single iteration runs. Since the break already guards this,a = 0(and likewiseb = 0) makes the intent clearer and avoids the oversized range.- Once
value > boundfor a giveni, all furtherjyield larger sums (wheny > 1), so the inner loop can break early.set([])can be simplified toset().♻️ Proposed refactor
- a = bound if x == 1 else int(log(bound, x)) - b = bound if y == 1 else int(log(bound, y)) - - result_set = set([]) - - for i in range(a + 1): - for j in range(b + 1): - value = x**i + y**j - - if value <= bound: - result_set.add(value) - - if y == 1: - break - - if x == 1: - break + a = 0 if x == 1 else int(log(bound, x)) + b = 0 if y == 1 else int(log(bound, y)) + + result_set: Set[int] = set() + + for i in range(a + 1): + pow_x = x**i + for j in range(b + 1): + value = pow_x + y**j + if value > bound: + break + result_set.add(value) + if y == 1: + break + if x == 1: + break🤖 Prompt for AI Agents
Verify each finding against the current code and only fix it if needed. In `@algorithms/hash_table/powerful_integers/__init__.py` around lines 33 - 55, In powerful_integers_logarithmic_bounds, avoid recomputing x**i and oversized ranges: set a = 0 when x == 1 (and b = 0 when y == 1) instead of bound, replace set([]) with set(), hoist x_pow = x**i (or compute x_pow incrementally per outer loop) before the inner j loop, and inside the inner loop break early when value > bound for y > 1 (since further j will only increase the sum); update uses of a, b, result_set, x_pow, and the inner break accordingly in the function.
🤖 Prompt for all review comments with AI agents
Verify each finding against the current code and only fix it if needed.
Inline comments:
In `@algorithms/dynamic_programming/max_subarray/README.md`:
- Line 50: Remove the comma before "because" in the sentence that reads "The
time complexity of this solution is O(n), because we are iterating the array
once, where n is the total number of" in README.md; edit that sentence to read
"The time complexity of this solution is O(n) because we are iterating the array
once, where n is the total number of" so the essential clause is not set off by
a comma.
---
Nitpick comments:
In `@algorithms/hash_table/powerful_integers/__init__.py`:
- Around line 33-55: In powerful_integers_logarithmic_bounds, avoid recomputing
x**i and oversized ranges: set a = 0 when x == 1 (and b = 0 when y == 1) instead
of bound, replace set([]) with set(), hoist x_pow = x**i (or compute x_pow
incrementally per outer loop) before the inner j loop, and inside the inner loop
break early when value > bound for y > 1 (since further j will only increase the
sum); update uses of a, b, result_set, x_pow, and the inner break accordingly in
the function.
In `@algorithms/hash_table/powerful_integers/README.md`:
- Around line 56-62: Rewrite ambiguous logarithm notation in the README: replace
"m^n <= bound" implication text "n<=log(m) bound" with a clear form such as "n
<= log_m(bound)" (or LaTeX "$n \\le \\log_m(\\text{bound})$"), and likewise
change "a=log(x)bound" / "b=log(y)bound" in the Algorithm section to "a =
log_x(bound)" and "b = log_y(bound)" (or use LaTeX "$a =
\\log_x(\\text{bound})$, $b = \\log_y(\\text{bound})$") so the base of the log
is explicit for symbols m, n, x, y, a, b.
In `@algorithms/hash_table/powerful_integers/test_powerful_integers.py`:
- Around line 9-17: Add a test case to POWERFUL_INTEGERS_TEST_CASE that covers
the exact-equality boundary where x**k (or y**k) equals bound (for example use a
tuple like (2, 3, 1024, [...expected results...]) or another appropriate exact
power) so the test guards against off-by-one/rounding issues in the log-based
path; update the expected output list accordingly and ensure the new case is
appended to the existing POWERFUL_INTEGERS_TEST_CASE in
test_powerful_integers.py (this addresses the potential rounding regression
noted in __init__.py).
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DIRECTORY.mdalgorithms/dynamic_programming/max_subarray/README.mdalgorithms/hash_table/powerful_integers/README.mdalgorithms/hash_table/powerful_integers/__init__.pyalgorithms/hash_table/powerful_integers/test_powerful_integers.pyalgorithms/trie/index_pairs_of_a_string/__init__.py
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Describe your change:
Algorithm to find the powerful integers given x and y and an upper bound
Checklist:
Fixes: #{$ISSUE_NO}.Summary by CodeRabbit
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New Features
Documentation
Tests