⚡️ Speed up function binomial_coefficient_recursive by 561,283%

[codeflash-ai]

📄 561,283% (5,612.83x) speedup for binomial_coefficient_recursive in src/numpy_pandas/numerical_methods.py

⏱️ Runtime : 558 milliseconds → 99.5 microseconds (best of 5 runs)

📝 Explanation and details

Here is a faster version of your recursive binomial coefficient program using memoization. This avoids the massive recomputation by caching previous results. The function signature and output are unchanged.

How this optimizes your code:

• The original recursion recalculates the same values many times. Memoization ensures each unique (n, k) is only computed once, reducing exponential time to polynomial.
• All earlier comments have been preserved except for an explanatory comment about the cache, which is critical to understanding the updated code.

Performance improvement:
For large n and k, this optimizes from O(2^n) to approximately O(n*k) runtime.

Let me know if you want an even more memory-optimal or further vectorized solution!

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 224 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 1 Passed
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import pytest  # used for our unit tests
from src.numpy_pandas.numerical_methods import binomial_coefficient_recursive

# unit tests

# =========================
# Basic Test Cases
# =========================

def test_binomial_basic_small_values():
    # C(0, 0) = 1
    codeflash_output = binomial_coefficient_recursive(0, 0) # 166ns -> 333ns (50.2% slower)
    # C(1, 0) = 1
    codeflash_output = binomial_coefficient_recursive(1, 0) # 166ns -> 333ns (50.2% slower)
    # C(1, 1) = 1
    codeflash_output = binomial_coefficient_recursive(1, 1) # 166ns -> 333ns (50.2% slower)
    # C(2, 1) = 2
    codeflash_output = binomial_coefficient_recursive(2, 1) # 166ns -> 333ns (50.2% slower)
    # C(3, 2) = 3
    codeflash_output = binomial_coefficient_recursive(3, 2) # 166ns -> 333ns (50.2% slower)
    # C(4, 2) = 6
    codeflash_output = binomial_coefficient_recursive(4, 2) # 166ns -> 333ns (50.2% slower)

def test_binomial_basic_symmetry():
    # C(n, k) == C(n, n-k)
    for n in range(6):
        for k in range(n + 1):
            codeflash_output = binomial_coefficient_recursive(n, k) # 125ns -> 291ns (57.0% slower)

def test_binomial_basic_pascal_identity():
    # C(n, k) = C(n-1, k-1) + C(n-1, k)
    for n in range(2, 8):
        for k in range(1, n):
            codeflash_output = binomial_coefficient_recursive(n, k); val = codeflash_output # 125ns -> 250ns (50.0% slower)
            codeflash_output = binomial_coefficient_recursive(n-1, k-1); left = codeflash_output # 125ns -> 250ns (50.0% slower)
            codeflash_output = binomial_coefficient_recursive(n-1, k); right = codeflash_output # 125ns -> 250ns (50.0% slower)

# =========================
# Edge Test Cases
# =========================

def test_binomial_edge_k_zero_or_k_equals_n():
    # k == 0 or k == n should always return 1
    for n in range(0, 15):
        codeflash_output = binomial_coefficient_recursive(n, 0) # 83ns -> 291ns (71.5% slower)
        codeflash_output = binomial_coefficient_recursive(n, n) # 83ns -> 291ns (71.5% slower)




def test_binomial_edge_large_k_zero_and_k_equals_n():
    # Very large n, k=0 and k=n should always return 1
    codeflash_output = binomial_coefficient_recursive(100, 0) # 250ns -> 708ns (64.7% slower)
    codeflash_output = binomial_coefficient_recursive(100, 100) # 250ns -> 708ns (64.7% slower)

# =========================
# Large Scale Test Cases
# =========================

def test_binomial_large_scale_middle_value():
    # Test a moderately large value, e.g., C(20, 10) = 184756
    codeflash_output = binomial_coefficient_recursive(20, 10) # 18.3ms -> 1.38μs (1328797% faster)

def test_binomial_large_scale_small_k():
    # C(30, 1) = 30
    codeflash_output = binomial_coefficient_recursive(30, 1) # 3.08μs -> 1.12μs (174% faster)
    # C(30, 2) = 435
    codeflash_output = binomial_coefficient_recursive(30, 2) # 3.08μs -> 1.12μs (174% faster)

def test_binomial_large_scale_symmetry():
    # C(25, 5) == C(25, 20)
    codeflash_output = binomial_coefficient_recursive(25, 5) # 4.77ms -> 1.54μs (309203% faster)

def test_binomial_large_scale_near_edges():
    # C(50, 2) = 1225
    codeflash_output = binomial_coefficient_recursive(50, 2) # 102μs -> 708ns (14342% faster)
    # C(50, 48) = 1225
    codeflash_output = binomial_coefficient_recursive(50, 48) # 102μs -> 708ns (14342% faster)

# =========================
# Miscellaneous/Mutation Tests
# =========================

def test_binomial_mutation_no_off_by_one():
    # C(5, 3) = 10, not 9 or 11
    codeflash_output = binomial_coefficient_recursive(5, 3) # 1.50μs -> 542ns (177% faster)
    # C(6, 3) = 20
    codeflash_output = binomial_coefficient_recursive(6, 3) # 1.50μs -> 542ns (177% faster)

def test_binomial_mutation_no_wrong_base_case():
    # If base case is wrong, these will fail
    codeflash_output = binomial_coefficient_recursive(7, 0) # 166ns -> 417ns (60.2% slower)
    codeflash_output = binomial_coefficient_recursive(7, 7) # 166ns -> 417ns (60.2% slower)



import pytest  # used for our unit tests
from src.numpy_pandas.numerical_methods import binomial_coefficient_recursive

# unit tests

# 1. Basic Test Cases

def test_binomial_coefficient_basic_small_values():
    # C(0, 0) = 1
    codeflash_output = binomial_coefficient_recursive(0, 0) # 125ns -> 292ns (57.2% slower)
    # C(1, 0) = 1
    codeflash_output = binomial_coefficient_recursive(1, 0) # 125ns -> 292ns (57.2% slower)
    # C(1, 1) = 1
    codeflash_output = binomial_coefficient_recursive(1, 1) # 125ns -> 292ns (57.2% slower)
    # C(2, 1) = 2
    codeflash_output = binomial_coefficient_recursive(2, 1) # 125ns -> 292ns (57.2% slower)
    # C(3, 2) = 3
    codeflash_output = binomial_coefficient_recursive(3, 2) # 125ns -> 292ns (57.2% slower)
    # C(4, 2) = 6
    codeflash_output = binomial_coefficient_recursive(4, 2) # 125ns -> 292ns (57.2% slower)
    # C(5, 3) = 10
    codeflash_output = binomial_coefficient_recursive(5, 3) # 125ns -> 292ns (57.2% slower)

def test_binomial_coefficient_basic_symmetry():
    # C(n, k) == C(n, n-k)
    for n in range(6):
        for k in range(n + 1):
            codeflash_output = binomial_coefficient_recursive(n, k) # 125ns -> 292ns (57.2% slower)

def test_binomial_coefficient_basic_pascal_identity():
    # C(n, k) = C(n-1, k-1) + C(n-1, k)
    for n in range(2, 7):
        for k in range(1, n):
            codeflash_output = binomial_coefficient_recursive(n, k) # 375ns -> 292ns (28.4% faster)

# 2. Edge Test Cases

def test_binomial_coefficient_k_zero_or_n():
    # C(n, 0) = 1, C(n, n) = 1 for n >= 0
    for n in range(10):
        codeflash_output = binomial_coefficient_recursive(n, 0) # 125ns -> 250ns (50.0% slower)
        codeflash_output = binomial_coefficient_recursive(n, n) # 125ns -> 250ns (50.0% slower)




def test_binomial_coefficient_edge_cases():
    # C(0, 0) is a special edge case
    codeflash_output = binomial_coefficient_recursive(0, 0) # 166ns -> 375ns (55.7% slower)
    # C(1, 0) and C(1, 1)
    codeflash_output = binomial_coefficient_recursive(1, 0) # 166ns -> 375ns (55.7% slower)
    codeflash_output = binomial_coefficient_recursive(1, 1) # 166ns -> 375ns (55.7% slower)

def test_binomial_coefficient_one_off_from_edges():
    # C(n, 1) = n
    for n in range(1, 10):
        codeflash_output = binomial_coefficient_recursive(n, 1) # 125ns -> 292ns (57.2% slower)
    # C(n, n-1) = n
    for n in range(1, 10):
        codeflash_output = binomial_coefficient_recursive(n, n-1) # 125ns -> 292ns (57.2% slower)

# 3. Large Scale Test Cases

def test_binomial_coefficient_large_n_k():
    # Test with moderately large n and k, but not too large to avoid recursion depth issues
    # C(20, 10) = 184756
    codeflash_output = binomial_coefficient_recursive(20, 10) # 642μs -> 417ns (153907% faster)
    # C(15, 7) = 6435
    codeflash_output = binomial_coefficient_recursive(15, 7) # 642μs -> 417ns (153907% faster)
    # C(25, 12) = 5200300
    codeflash_output = binomial_coefficient_recursive(25, 12) # 642μs -> 417ns (153907% faster)

@pytest.mark.timeout(5)
def test_binomial_coefficient_performance_reasonable():
    # Test with n=18, k=9, should complete quickly and correctly
    codeflash_output = binomial_coefficient_recursive(18, 9) # 4.83ms -> 708ns (682545% faster)

def test_binomial_coefficient_large_k_zero_or_n():
    # Large n, k=0 or k=n should still be 1
    codeflash_output = binomial_coefficient_recursive(100, 0) # 209ns -> 458ns (54.4% slower)
    codeflash_output = binomial_coefficient_recursive(100, 100) # 209ns -> 458ns (54.4% slower)

# 4. Miscellaneous/Mutation-resistance

def test_binomial_coefficient_mutation_resistance():
    # Changing the + to - or * in the recursion should fail this test
    # C(6, 3) = 20
    codeflash_output = binomial_coefficient_recursive(6, 3) # 2.62μs -> 459ns (472% faster)
    # C(7, 4) = 35
    codeflash_output = binomial_coefficient_recursive(7, 4) # 2.62μs -> 459ns (472% faster)



from src.numpy_pandas.numerical_methods import binomial_coefficient_recursive

def test_binomial_coefficient_recursive():
    binomial_coefficient_recursive(7, 3)

To edit these changes git checkout codeflash/optimize-binomial_coefficient_recursive-mc5g3d2v and push.