⚡️ Speed up function coin_change by 1,249%

[codeflash-ai]

📄 1,249% (12.49x) speedup for coin_change in src/dsa/caching_memoization.py

⏱️ Runtime : 3.12 milliseconds → 231 microseconds (best of 5 runs)

📝 Explanation and details

The optimized code implements memoization to eliminate redundant recursive calculations in the coin change problem.

Key optimization: Instead of recalculating the same (amount, index) combinations repeatedly, the optimized version stores results in a memo dictionary and reuses them when encountered again.

Why this creates massive speedup:

• The original recursive approach has exponential time complexity due to overlapping subproblems
• Line profiler shows the original made 66,970 recursive calls vs the optimized version making far fewer
• The memo dictionary transforms this from O(2^n) to O(amount × coins) time complexity

Performance characteristics from tests:

• Small inputs: Optimized version is actually slower (35-60% overhead) due to memoization setup costs
• Medium inputs (amount=20, few coins): ~87% faster as memoization starts paying off
• Large inputs (amount=20, many coins): 2667% faster - the exponential blow-up is completely avoided

The optimization is most effective for problems with:

1. Large amounts relative to coin denominations
2. Many possible coin combinations
3. Deep recursion trees with significant overlap

For trivial cases, the memoization overhead outweighs benefits, but for any non-trivial coin change computation, the speedup is dramatic.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 29 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
🔮 Hypothesis Tests	✅ 4 Passed
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import pytest  # used for our unit tests
from src.dsa.caching_memoization import coin_change

# unit tests

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

def test_single_coin_exact_amount():
    # One coin type, amount is exactly the coin value
    codeflash_output = coin_change([5], 5, 0) # 1.46μs -> 2.25μs (35.2% slower)

def test_single_coin_not_divisible():
    # One coin type, amount is not divisible by coin value
    codeflash_output = coin_change([2], 3, 0) # 1.58μs -> 2.42μs (34.5% slower)

def test_two_coins_simple():
    # Two coin types, amount can be made in two ways
    # Ways to make 4 with [1,2]: 1+1+1+1, 1+1+2, 2+2
    codeflash_output = coin_change([1,2], 4, 0) # 2.38μs -> 4.58μs (48.2% slower)

def test_three_coins():
    # Three coin types, amount can be made in multiple ways
    # Ways to make 5 with [1,2,5]: 1+1+1+1+1, 1+1+1+2, 1+2+2, 5
    codeflash_output = coin_change([1,2,5], 5, 0) # 3.67μs -> 6.00μs (38.9% slower)

def test_zero_amount():
    # Any coin set, amount zero should always return 1 (the empty set)
    codeflash_output = coin_change([1,2,3], 0, 0) # 333ns -> 791ns (57.9% slower)

def test_empty_coins_nonzero_amount():
    # No coins, nonzero amount: can't make any change
    codeflash_output = coin_change([], 7, 0) # 458ns -> 958ns (52.2% slower)

def test_empty_coins_zero_amount():
    # No coins, zero amount: one way (use no coins)
    codeflash_output = coin_change([], 0, 0) # 292ns -> 708ns (58.8% slower)

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

def test_negative_amount():
    # Negative amount should always return 0
    codeflash_output = coin_change([1,2,3], -5, 0) # 375ns -> 833ns (55.0% slower)

def test_index_beyond_length():
    # Index is already past the end of coins, should return 0 for nonzero amount
    codeflash_output = coin_change([1,2], 4, 2) # 417ns -> 833ns (49.9% slower)

def test_index_beyond_length_zero_amount():
    # Index past coins, but amount is zero, should return 1
    codeflash_output = coin_change([1,2], 0, 2) # 292ns -> 709ns (58.8% slower)

def test_coin_larger_than_amount():
    # All coins larger than amount, should return 0
    codeflash_output = coin_change([10, 20], 5, 0) # 1.21μs -> 2.04μs (40.8% slower)

def test_duplicate_coins():
    # Duplicates in coins should not affect the count (since order matters in recursion)
    # Ways to make 4 with [1,2,2]: 1+1+1+1, 1+1+2, 2+2 (should be 3 ways)
    codeflash_output = coin_change([1,2,2], 4, 0) # 3.21μs -> 5.42μs (40.8% slower)

def test_large_coin_and_small_amount():
    # Coin much larger than amount, should skip it
    codeflash_output = coin_change([1, 100], 2, 0) # 1.33μs -> 2.46μs (45.7% slower)



def test_large_amount_small_coins():
    # Large amount, small coins
    # Ways to make 10 with [1,2]: Should be 6
    # (10x1), (8x1+1x2), (6x1+2x2), (4x1+3x2), (2x1+4x2), (5x2)
    codeflash_output = coin_change([1,2], 10, 0) # 6.38μs -> 9.25μs (31.1% slower)

def test_large_amount_three_coins():
    # Ways to make 20 with [1,2,5]
    # This is a classic DP problem; answer is 41
    codeflash_output = coin_change([1,2,5], 20, 0) # 39.5μs -> 21.0μs (87.5% faster)

def test_many_coins_small_amount():
    # Many coin types, small amount
    coins = list(range(1, 11))  # [1,2,...,10]
    # Ways to make 5: There are 30 ways (verified by combinatorics)
    codeflash_output = coin_change(coins, 5, 0) # 13.2μs -> 14.4μs (8.38% slower)

def test_many_coins_large_amount():
    # Many coin types, larger amount but still tractable
    coins = list(range(1, 11))  # [1,2,...,10]
    # Ways to make 10: There are 42 ways (verified by DP)
    codeflash_output = coin_change(coins, 10, 0) # 75.7μs -> 28.5μs (166% faster)

def test_large_input_stress():
    # Stress test: 20 coins, amount 20
    coins = list(range(1, 21))  # [1,2,...,20]
    # The answer is 627 (verified by DP)
    codeflash_output = coin_change(coins, 20, 0) # 2.95ms -> 106μs (2667% faster)




def test_order_of_coins_does_not_matter():
    # The order of coins in the list should not affect the result
    coins1 = [1,2,5]
    coins2 = [5,2,1]
    amount = 5
    codeflash_output = coin_change(coins1, amount, 0) # 4.17μs -> 7.79μs (46.5% slower)

def test_index_argument_behavior():
    # Changing the starting index should change the result
    # For coins [1,2,5], amount 5:
    # - Starting at index 0: 4 ways (all coins)
    # - Starting at index 1: 2 ways (using only 2,5)
    codeflash_output = coin_change([1,2,5], 5, 0) # 3.54μs -> 6.04μs (41.4% slower)
    codeflash_output = coin_change([1,2,5], 5, 1) # 917ns -> 2.12μs (56.8% slower)
    codeflash_output = coin_change([1,2,5], 5, 2) # 333ns -> 708ns (53.0% slower)
    codeflash_output = coin_change([1,2,5], 5, 3) # 208ns -> 458ns (54.6% slower)

# ----------------------------- #
#        INVALID INPUTS         #
# ----------------------------- #

def test_invalid_coin_types():
    # Non-integer coins: should raise TypeError
    with pytest.raises(TypeError):
        coin_change(['a', 2, 3], 4, 0)
    with pytest.raises(TypeError):
        coin_change([1.5, 2, 3], 4, 0)

def test_invalid_amount_type():
    # Non-integer amount: should raise TypeError
    with pytest.raises(TypeError):
        coin_change([1,2,3], '4', 0)
    with pytest.raises(TypeError):
        coin_change([1,2,3], 4.5, 0)

def test_invalid_index_type():
    # Non-integer index: should raise TypeError
    with pytest.raises(TypeError):
        coin_change([1,2,3], 4, '0') # 1.62μs -> 1.92μs (15.2% slower)
    with pytest.raises(TypeError):
        coin_change([1,2,3], 4, 0.5) # 1.46μs -> 2.04μs (28.6% slower)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.
#------------------------------------------------
from src.dsa.caching_memoization import coin_change

To edit these changes git checkout codeflash/optimize-coin_change-mha3cm4w and push.