MutaFix run: more-itertools-003

tests/test_recipes.py::NthCombinationTests::test_basic
tests/test_recipes.py::NthCombinationTests::test_long

E   ZeroDivisionError: integer division or modulo by zero

E   AssertionError: Tuples differ: (2, 9, 22, 168) != (2, 12, 35, 126)
E   
E   First differing element 1:
E   9
E   12
E   
E   - (2, 9, 22, 168)
E   + (2, 12, 35, 126)

1. more_itertools/recipes.py::nth_combination call depth 1 · Ochiai 0.71 (failing 2, passing 2)
2. more_itertools/more.py::numeric_range.index call depth 1 · Ochiai 0.00 (failing 0, passing 0)
3. more_itertools/more.py::numeric_range._index_near call depth 2 · Ochiai 0.00 (failing 0, passing 0)
4. more_itertools/more.py::callback_iter.result call depth 2 · Ochiai 0.00 (failing 0, passing 0)
5. more_itertools/more.py::numeric_range._len call depth 3 · Ochiai 0.00 (failing 0, passing 0)
6. more_itertools/more.py::combination_index call depth - · Ochiai 0.00 (failing 0, passing 0)
7. more_itertools/more.py::combination_with_replacement_index call depth - · Ochiai 0.00 (failing 0, passing 0)
8. more_itertools/more.py::nth_combination_with_replacement call depth - · Ochiai 0.00 (failing 0, passing 0)
9. more_itertools/more.py::numeric_range.__init__ call depth - · Ochiai 0.00 (failing 0, passing 0)
10. more_itertools/more.py::nth_permutation call depth - · Ochiai 0.00 (failing 0, passing 7)
11. more_itertools/recipes.py::random_combination call depth - · Ochiai 0.00 (failing 0, passing 2)
12. more_itertools/more.py::only call depth - · Ochiai 0.00 (failing 0, passing 0)
13. more_itertools/recipes.py::is_prime call depth - · Ochiai 0.00 (failing 0, passing 6)
14. more_itertools/recipes.py::random_combination_with_replacement call depth - · Ochiai 0.00 (failing 0, passing 2)
15. more_itertools/more.py::distinct_combinations call depth - · Ochiai 0.00 (failing 0, passing 0)
16. more_itertools/recipes.py::grouper call depth - · Ochiai 0.00 (failing 0, passing 6)
17. more_itertools/more.py::nth_product call depth - · Ochiai 0.00 (failing 0, passing 0)
18. more_itertools/more.py::one call depth - · Ochiai 0.00 (failing 0, passing 0)
19. more_itertools/recipes.py::powerset call depth - · Ochiai 0.00 (failing 0, passing 1)
20. more_itertools/more.py::nth_or_last call depth - · Ochiai 0.00 (failing 0, passing 0)

We need to analyze the algorithm. The function attempts to compute the nth combination using combinatorial number system. There's a known algorithm:

Given n choose c combinations, we want the index-th combination (0-indexed). We iterate over positions selecting elements.

Standard algorithm (from Knuth?): For each position i from 0 to r-1, we find the smallest element such that C(n - chosen_i - 1, r - i - 1) > index, etc.

But here they have a different approach: They maintain variables c (remaining combinations?), n (remaining pool size?), r (remaining to choose?). Let's trace.

Initialize: pool = tuple(iterable), n = len(pool), c = comb(n, r). Then while r: ... At each iteration:

c, n, r = c * r // n, n - 1, r - 1

Then while index >= c: index -= c; c, n = c * ((n + r)) // n, n - 1

Then result.append(pool[-1 - n])

Let's test with small example to see where division by zero occurs.

Suppose iterable = 'abcdefg' (length 7), r=4, index from 0..C(7,4)-1 = 34.

First iteration: n=7, r=4, c=C(7,4)=35.

Compute c, n, r = c * r // n, n-1, r-1 => c = 35*4//7 = 140//7=20, n=6, r=3.

Now while index >= c: subtract c etc.

After that, append pool[-1 - n] where n is now 6? Actually after the inner while loop, n may have changed? Wait: In inner while loop, they update c, n = c * ((n + r)) // n, n - 1. That changes n as well.

This algorithm seems off.

Better to look up known implementation of nth_combination in more-itertools. I recall that the recipe uses the "combinatorial number 

We need to analyze the algorithm. It's trying to compute the nth combination using combinatorial number system.

Standard algorithm: Given n choose c total combinations, we want the index-th combination (0-indexed). We iterate over positions selecting each element.

Pseudo:

def nth_combination(iterable, r, index):
    pool = tuple(iterable)
    n = len(pool)
    if r < 0 or r > n: raise ValueError
    c = comb(n, r)
    if index < 0: index += c
    if not 0 <= index < c: raise IndexError
    result = []
    for i in range(r):
        # number of combinations remaining after choosing current element?
        # Actually we consider each position: for the first element, we decide how many to skip.
        # Let's denote we are choosing the i-th element (0-indexed) from the remaining pool.
        # At step i, we have n-i elements left, need to choose r-i.
        # The number of combinations if we skip the first element is C(n-i-1, r-i-1)? Wait typical algorithm:
        # For each position, we find the largest v such that C(n-v-1, r-k-1) <= index? Hmm.

Better recall known implementation from more-itertools: I think they used an algorithm similar to:

    while r:
        c, n, r = c * r // n, n - 1, r - 1
        while index >= c:
            index -= c
            c, n = c * (n + r) // n, n - 1
        result.append(pool[-1 - n])

But something seems off. Let's derive.

We have total combos C(n, r). Represent index in combinadic.

Algorithm to unrank combination:

Initialize

        while r:
            c, n, r = c * r // n, n - 1, r - 1
            while index >= c:
                index -= c
                c = c * (n + r) // n
            result.append(pool[-1 - n])

        while r:
            c, n, r = c * r // n, n - 1, r - 1
            while index >= c:
                index -= c
                c = c * (n + r + 1) // (n + 1)
            result.append(pool[-1 - n])

We have two issues now: the basic test shows we're getting the wrong combination (off by one at the end) and the long test is completely off.

Let me reexamine the algorithm. The function is supposed to compute the index-th combination (0-indexed) of length r from the pool.

Looking at the current code:

```
     result = []
     while r:
         c, n, r = c * r // n, n - 1, r - 1
         while index >= c:
             index -= c
             c, n = c * ((n + r)) // n, n - 1
         result.append(pool[-1 - n])
```

There's a known algorithm for this. Let me recall how it works:

We want to find the index-th combination of r elements from n elements.

The idea is:
1. For each position in the combination (from first to last), we determine which element goes there.
2. The number of combinations that start with a particular element can be calculated using combinations of the remaining elements.

Actually, looking at the original code more carefully, I think the issue might be in how we're updating variables.

Let me look at a correct implementation of nth_combination. I recall that the "combinadic" representation is used.

Actually, let me think about the algorithm step by step for a small case.

Suppose we have n=7 (abcdefg), r=4, and we want index=0 (first combination).

The first combination should be (a,b,c,d).

Let's trace through:
- pool = ('a','b','c','d','e','f','g'), n=7, r=4
- c = comb(7,4) = 35

First iteration of while r (r=4):
  c, n, r = c * r // n, n - 1, r - 1

We need to provide old text exactly as it appears in the candidate. Let's look at the current candidate content again:

```
  662 | def nth_combination(iterable, r, index):
  663 |     """Equivalent to ``list(combinations(iterable, r))[index]``.
  664 |
  665 |     The subsequences of *iterable* that are of length *r* can be ordered
  666 |     lexicographically. :func:`nth_combination` computes the subsequence at
  667 |     sort position *index* directly, without computing the previous
  668 |     subsequences.
  669 |
  670 |         >>> nth_combination(range(5), 3, 5)
  671 |         (0, 3, 4)
  672 |
  673 |     ``ValueError`` will be raised If *r* is negative.
  674 |     ``IndexError`` will be raised if the given *index* is invalid.
  675 |     """
  676 |     pool = tuple(iterable)
  677 |     n = len(pool)
  678 |     c = comb(n, r)
  679 |
  680 |     if index < 0:
  681 |         index += c
  682 |     if not 0 <= index < c:
  683 |         raise IndexError
  684 |
  685 |     result = []
  686 |     while r:
  687 |         c, n, r = c * r // n, n - 1, r - 1
  688 |         while index >= c:
  689 |             index -= c
  690 |             c, n = c * ((n + r)) // n, n - 1
  691 |         result.append(pool[-1 - n])
  692 |
  693 |     return tuple(result)
```

We need to replace a block. The previous attempt had old text that didn't match exactly. Let's try to fix the algorithm correctly.

Looking at the failing tests:
- test_basic: expected ('a','b','c','d') bu

We need to fix the nth_combination function. The tests show two issues: ZeroDivisionError and wrong results.

Looking at the code:

Line 687: c, n, r = c * r // n, n - 1, r - 1
Line 690: c, n = c * ((n + r)) // n, n - 1

The ZeroDivisionError likely occurs when n becomes 0. Initially n = len(pool). In the loop, we decrement n by 1 each time through the outer loop (via n - 1) and also in the inner loop (via n - 1). So n is decremented twice per outer iteration? Actually, let's trace:

Outer loop: while r:
   First, we do: c, n, r = c * r // n, n - 1, r - 1
   Then we have an inner while: while index >= c:
        index -= c
        c, n = c * ((n + r)) // n, n - 1
   Then we append pool[-1 - n]

So in each outer iteration, n is decremented by 1 in the first assignment, and then potentially multiple times in the inner loop (each time decrementing by 1). This seems wrong.

Standard algorithm for nth combination (lexicographic order) is something like:

def nth_combination(iterable, r, index):
    pool = tuple(iterable)
    n = len(pool)
    if index < 0 or index >= comb(n, r):
        raise IndexError
    result = []
    while r:
        c = comb(n-1, r-1)   # number of combinations that include the first element
        if index < c:
            result.append(pool[0])
            pool = pool[1:]
            n -= 1
            r -= 1
        else:
            index -= c
            pool = pool[1:]
            n -= 1
    return tuple(result)

But we want to avoid computing comb r