⚡️ Speed up function compute_and_sort by 719%

[codeflash-ai]

📄 719% (7.19x) speedup for compute_and_sort in code_to_optimize/process_and_bubble_sort_codeflash_trace.py

⏱️ Runtime : 2.23 seconds → 272 milliseconds (best of 32 runs)

📝 Explanation and details

The optimized code achieves a 718% speedup through two key algorithmic improvements:

1. Mathematical Optimization of calculate_pairwise_products:

• Original: O(n²) nested loops explicitly computing all pairs arr[i] * arr[j] where i ≠ j
• Optimized: O(n) mathematical formula using the identity: sum of all pairwise products = total² - total_sq where total = sum(arr) and total_sq = sum(x² for x in arr)
• Impact: Reduces ~28.2 seconds to ~7ms for large arrays (99.97% reduction in this function's runtime)

2. Bubble Sort Early Termination:

• Original: Always performs full passes through the entire array
• Optimized:
  • Reduces inner loop range by i each iteration since last i elements are already sorted
  • Adds already_sorted flag to exit early when no swaps occur
• Impact: Reduces sorting time from ~16.2 seconds to ~6.6 seconds (59% improvement)

Performance by Test Case Type:

• Large uniform arrays (1000 elements, same values): ~77,000% faster due to mathematical optimization
• Large sequential/random arrays: ~300-800% faster from combined optimizations
• Small arrays (<10 elements): Minimal improvement (0-20%) as overhead dominates
• Edge cases (zeros, negatives): Consistent improvements across all sizes

The mathematical optimization dominates performance gains for large arrays since it eliminates the quadratic bottleneck in pairwise product calculation.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 41 Passed
⏪ Replay Tests	✅ 1 Passed
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import pytest  # used for our unit tests
from code_to_optimize.process_and_bubble_sort_codeflash_trace import \
    compute_and_sort

# --------------------------
# Unit Tests for compute_and_sort
# --------------------------

# 1. Basic Test Cases

def test_empty_list():
    # Edge: empty input
    codeflash_output = compute_and_sort([]) # 18.0μs -> 16.9μs (6.11% faster)

def test_single_element():
    # Edge: single element input
    codeflash_output = compute_and_sort([5]) # 18.0μs -> 17.3μs (4.35% faster)

def test_two_elements():
    # Basic: two elements
    # Pairwise products: 2*3 and 3*2 -> [6,6], average = 6
    codeflash_output = compute_and_sort([2,3]) # 19.0μs -> 19.8μs (3.69% slower)

def test_three_elements():
    # Basic: three elements
    # Pairs: (0,1):2*3=6, (0,2):2*5=10, (1,0):3*2=6, (1,2):3*5=15, (2,0):5*2=10, (2,1):5*3=15
    # sum=6+10+6+15+10+15=62, count=6, average=62/6=10.333...
    codeflash_output = compute_and_sort([2,3,5]); result = codeflash_output # 19.9μs -> 19.8μs (0.591% faster)

def test_negative_numbers():
    # Basic: negative numbers
    # [1, -2] => 1*-2=-2, -2*1=-2, avg=-2
    codeflash_output = compute_and_sort([1, -2]) # 19.3μs -> 20.2μs (4.75% slower)

def test_mixed_sign_numbers():
    # Basic: mix of positive, negative, zero
    # [0, 2, -3]
    # (0,1):0*2=0, (0,2):0*-3=0, (1,0):2*0=0, (1,2):2*-3=-6, (2,0):-3*0=0, (2,1):-3*2=-6
    # sum=0+0+0+(-6)+0+(-6) = -12, count=6, avg=-2
    codeflash_output = compute_and_sort([0, 2, -3]) # 21.0μs -> 21.1μs (0.607% slower)

def test_all_zeros():
    # Basic: all zeros
    codeflash_output = compute_and_sort([0,0,0]) # 19.8μs -> 19.4μs (2.17% faster)

def test_duplicates():
    # Basic: duplicate elements
    # [2,2,2] -> all pairs 2*2=4, 6 pairs, avg=4
    codeflash_output = compute_and_sort([2,2,2]) # 20.5μs -> 19.8μs (3.48% faster)

# 2. Edge Test Cases

def test_large_positive_and_negative():
    # Edge: very large and very small numbers
    arr = [10**9, -10**9, 0]
    # (0,1):1e9*-1e9=-1e18, (0,2):1e9*0=0, (1,0):-1e9*1e9=-1e18, (1,2):-1e9*0=0, (2,0):0*1e9=0, (2,1):0*-1e9=0
    # sum = -1e18 + 0 + -1e18 + 0 + 0 + 0 = -2e18, count=6, avg = -2e18/6 = -3.333...e17
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 23.6μs -> 22.1μs (6.90% faster)

def test_floats():
    # Edge: floating point values
    arr = [1.5, 2.5]

def test_repeated_large_negative():
    # Edge: repeated large negative values
    arr = [-1000, -1000, -1000]
    # all pairs: -1000*-1000=1,000,000, avg=1,000,000
    codeflash_output = compute_and_sort(arr) # 21.3μs -> 20.5μs (3.51% faster)

def test_non_integer_values():
    # Edge: floats and integers
    arr = [1, 2.5, -3]
    # (0,1):1*2.5=2.5, (0,2):1*-3=-3, (1,0):2.5*1=2.5, (1,2):2.5*-3=-7.5, (2,0):-3*1=-3, (2,1):-3*2.5=-7.5
    # sum=2.5-3+2.5-7.5-3-7.5 = -16, count=6, avg=-16/6=-2.666...
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 25.1μs -> 24.1μs (3.80% faster)

def test_extreme_float_precision():
    # Edge: float precision
    arr = [1e-10, 1e10]

def test_input_not_mutated():
    # Edge: input array should not be mutated by compute_and_sort
    arr = [5, 2, 1]
    arr_copy = arr[:]
    compute_and_sort(arr) # 20.5μs -> 21.1μs (2.66% slower)

# 3. Large Scale Test Cases

def test_large_uniform_array():
    # Large: all elements the same
    arr = [7] * 1000
    # All pairs: 7*7=49, 1000*999=999000 pairs, avg=49
    codeflash_output = compute_and_sort(arr) # 145ms -> 187μs (77730% faster)

def test_large_sequential_array():
    # Large: sequential numbers
    arr = list(range(1000))  # 0..999
    # Compute expected average:
    # sum of all elements: S = n(n-1)/2 = 999*1000/2 = 499500
    # sum of squares: Q = sum(i^2 for i in 0..999)
    n = 1000
    S = n*(n-1)//2
    Q = sum(i*i for i in range(n))
    # sum of all i!=j: sum_i sum_j!=i (i*j) = (sum_i sum_j (i*j)) - sum_i (i*i) = (S^2) - Q
    total_pairs = n * (n-1)
    expected = ((S*S) - Q) / total_pairs
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 164ms -> 208μs (78719% faster)

def test_large_random_array():
    # Large: random numbers, check only that it runs and returns a float
    import random
    arr = [random.randint(-1000, 1000) for _ in range(1000)]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 181ms -> 44.7ms (307% faster)

def test_large_negative_and_positive():
    # Large: mix of negative and positive
    arr = [-i if i % 2 == 0 else i for i in range(1, 1001)]
    # Just check that it runs and returns a float
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 174ms -> 40.7ms (328% faster)

def test_large_sparse_array():
    # Large: mostly zeros, with a few non-zeros
    arr = [0]*995 + [5, -5, 10, -10, 100]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 133ms -> 25.1ms (433% faster)

# Extra: Test that function does not mutate input for large inputs
def test_large_input_not_mutated():
    arr = list(range(1000))
    arr_copy = arr[:]
    compute_and_sort(arr) # 167ms -> 213μs (77957% faster)

# Extra: Test for input with repeated zeros and negatives
def test_many_zeros_and_negatives():
    arr = [0]*500 + [-1]*500
    # All pairs: 0*-1=0, -1*0=0, -1*-1=1, 0*0=0
    # Total pairs: 1000*999=999000
    # Number of -1*-1 pairs: 500*499=249500
    # Total sum: 249500*1 = 249500, rest are zeros
    expected = 249500 / 999000
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 155ms -> 36.9ms (322% faster)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.
#------------------------------------------------
import pytest  # used for our unit tests
from code_to_optimize.process_and_bubble_sort_codeflash_trace import \
    compute_and_sort

# unit tests

# ------------------ BASIC TEST CASES ------------------

def test_empty_list():
    # Edge: empty input
    arr = []
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 20.4μs -> 17.0μs (20.2% faster)

def test_single_element():
    # Edge: single element input
    arr = [7]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 18.2μs -> 17.5μs (4.30% faster)

def test_two_elements():
    # Basic: two elements
    arr = [2, 3]
    # Pairwise products: 2*3 and 3*2 = 6, 6 (count=2, sum=12, avg=6)
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 20.1μs -> 19.9μs (0.916% faster)

def test_three_distinct_elements():
    # Basic: three distinct elements
    arr = [1, 2, 3]
    # Pairs: 1*2, 1*3, 2*1, 2*3, 3*1, 3*2 = 2,3,2,6,3,6 sum=22, count=6, avg=22/6=3.666...
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 20.4μs -> 20.7μs (1.28% slower)

def test_negative_and_positive():
    # Basic: mix of negative and positive
    arr = [-1, 0, 1]
    # Pairs: -1*0=0, -1*1=-1, 0*-1=0, 0*1=0, 1*-1=-1, 1*0=0; sum=-2, count=6, avg=-1/3
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 19.8μs -> 20.3μs (2.16% slower)

def test_all_zeros():
    # Basic: all elements zero
    arr = [0, 0, 0, 0]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 22.0μs -> 20.2μs (8.79% faster)

def test_duplicates():
    # Basic: duplicates in array
    arr = [2, 2, 2]
    # Pairs: all 2*2=4, 6 pairs, sum=24, avg=4
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 20.2μs -> 20.1μs (0.278% faster)

# ------------------ EDGE TEST CASES ------------------

def test_large_positive_and_negative():
    # Edge: large positive and negative numbers
    arr = [1000000, -1000000]
    # Pairs: 1000000*-1000000, -1000000*1000000 = -10**12, -10**12, sum=-2*10**12, count=2, avg=-10**12
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 21.1μs -> 21.4μs (1.43% slower)

def test_float_elements():
    # Edge: floats in array
    arr = [0.5, 1.5, -2.0]
    # Pairs: 0.5*1.5=0.75, 0.5*-2=-1, 1.5*0.5=0.75, 1.5*-2=-3, -2*0.5=-1, -2*1.5=-3
    # sum=0.75-1+0.75-3-1-3 = -6.5, count=6, avg=-6.5/6 = -1.083333...
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 24.5μs -> 24.9μs (1.45% slower)

def test_large_list_same_element():
    # Edge: large list of same element
    arr = [5] * 1000
    # Each pair: 5*5=25, total pairs=1000*999, sum=25*999000, avg=25
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 145ms -> 187μs (77532% faster)

def test_list_with_min_and_max_int():
    # Edge: Python's min/max int (simulate 32-bit)
    min_int = -2**31
    max_int = 2**31 - 1
    arr = [min_int, max_int]
    # Pairs: min*max, max*min = both min_int*max_int
    expected = min_int * max_int
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 24.9μs -> 21.2μs (17.6% faster)

def test_list_with_zeros_and_large_numbers():
    # Edge: zeros and large numbers
    arr = [0, 0, 1000000, -1000000]
    # Pairs: 0*0=0, 0*1e6=0, 0*-1e6=0, 1e6*0=0, 1e6*-1e6=-1e12, -1e6*0=0, -1e6*1e6=-1e12
    # All zero pairs: 0, 1e6*-1e6=-1e12 (twice)
    # Let's enumerate:
    # (0,0): 0
    # (0,1e6): 0
    # (0,-1e6): 0
    # (0,0): 0
    # (0,1e6): 0
    # (0,-1e6): 0
    # (1e6,0): 0
    # (1e6,0): 0
    # (1e6,-1e6): -1e12
    # (1e6,0): 0
    # (1e6,0): 0
    # (1e6,-1e6): -1e12
    # (-1e6,0): 0
    # (-1e6,0): 0
    # (-1e6,1e6): -1e12
    # (-1e6,0): 0
    # (-1e6,0): 0
    # (-1e6,1e6): -1e12
    # Actually, the function computes for all i!=j, so for each pair, both (i,j) and (j,i) are counted.
    # Let's just compute sum:
    # For each 0, the products with others: 0*0=0, 0*1e6=0, 0*-1e6=0 (3*3=9 pairs for zeros, but all zero)
    # 1e6*0=0, 1e6*0=0, 1e6*-1e6=-1e12 (3 pairs)
    # -1e6*0=0, -1e6*0=0, -1e6*1e6=-1e12 (3 pairs)
    # All pairs: n=4, count=12
    # Let's enumerate:
    # (0,0): 0
    # (0,1e6): 0
    # (0,-1e6): 0
    # (1e6,0): 0
    # (1e6,0): 0
    # (1e6,-1e6): -1e12
    # (-1e6,0): 0
    # (-1e6,0): 0
    # (-1e6,1e6): -1e12
    # (0,1e6): 0
    # (0,-1e6): 0
    # (1e6,-1e6): -1e12
    # (-1e6,1e6): -1e12
    # So total -1e12 appears 4 times, rest zero, count=12
    # sum=-4e12, avg=-4e12/12 = -3.333...e11
    expected = -1e12 * 4 / 12
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 24.0μs -> 23.2μs (3.87% faster)

def test_list_with_one_large_rest_small():
    # Edge: one large, rest small
    arr = [1]*999 + [10**6]
    # For each 1, pairs: 1*1=1 (998 times), 1*1e6=1e6 (once)
    # For 1e6: 1e6*1=1e6 (999 times)
    # Total pairs: 1000*999=999000
    # sum = (998*1*1) + (1*1*1e6) + (999*1e6*1) = 998 + 1e6 + 999e6 = 998 + 1e6 + 999e6
    # Actually, need to sum all i!=j: for each i, sum over j!=i
    # For 1: (999 times) each, sum of products with all others:
    # Each 1 has 998 other 1s (product 1), and 1 with 1e6 (product 1e6)
    # So for each 1, sum = 998*1 + 1*1e6 = 998 + 1e6
    # For 999 such 1s: total = 999*(998 + 1e6) = 997002 + 999e6
    # For 1e6: sum with 999 ones: 999*1e6 = 999e6
    # Total sum = 997002 + 999e6 + 999e6 = 997002 + 1998e6
    # But each pair is counted twice (i,j) and (j,i), so let's just use the code to check
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 145ms -> 185μs (78356% faster)

# ------------------ LARGE SCALE TEST CASES ------------------

def test_large_random_list():
    # Large scale: random values, test for performance and basic correctness
    import random
    random.seed(42)
    arr = [random.randint(-1000, 1000) for _ in range(1000)]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 181ms -> 44.9ms (305% faster)

def test_large_list_alternating_signs():
    # Large scale: alternating positive and negative
    arr = [(-1)**i * i for i in range(1000)]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 174ms -> 40.7ms (328% faster)

def test_large_list_all_ones():
    # Large scale: all ones
    arr = [1] * 1000
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 145ms -> 188μs (77145% faster)

def test_large_list_all_zeros():
    # Large scale: all zeros
    arr = [0] * 1000
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 133ms -> 179μs (74360% faster)

def test_large_list_mixed_extremes():
    # Large scale: mix of min/max int and zeros
    arr = [0] * 996 + [2**31-1, -2**31, 2**31-1, -2**31]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 133ms -> 25.1ms (433% faster)

# ------------------ ADDITIONAL EDGE CASES ------------------

def test_input_not_mutated():
    # Ensure input array is not mutated by compute_and_sort
    arr = [3, 2, 1]
    arr_copy = arr.copy()
    compute_and_sort(arr) # 25.8μs -> 21.4μs (20.4% faster)


def test_return_type():
    # Test that function always returns a float
    arr = [7, 8, 9]
    codeflash_output = compute_and_sort(arr); result = codeflash_output # 22.3μs -> 20.5μs (8.85% faster)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

⏪ Replay Tests and Runtime

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
test_pytest_code_to_optimizetestspytest__replay_test_0.py::test_code_to_optimize_process_and_bubble_sort_codeflash_trace_compute_and_sort	44.5ms	12.2ms	266%✅

To edit these changes git checkout codeflash/optimize-compute_and_sort-mf3l39px and push.