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Count

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Count[list, pattern] gives the number of elements in list that match pattern.
Count[expr, pattern, levelspec] gives the total number of subexpressions matching pattern that appear at the levels in expr specified by levelspec.
Count[pattern] represents an operator form of Count that can be applied to an expression.

Examples

No verified examples yet for this function.

Implementation notes

Algorithm. builtin_count (src/patterns.c) tallies the subexpressions matching a pattern. Level-spec (default {1,1} — immediate elements only), the Heads -> True|False option, and the argument shapes mirror Cases. The worker do_count_at_level recurses depth-first into the head (when heads) and every argument, and at each in-range node calls match(e, pattern, env) from src/match.c, incrementing a size_t counter on success; level membership for negative specs is resolved via get_expr_depth_patterns. Unlike Cases/Position it stores nothing and has no result limit — it just returns the final count as an EXPR_INTEGER. Count[pat] with one argument returns the operator form Function[Count[#1, pat]].

Data structures. A single size_t accumulator; one MatchEnv per node tested. No results buffer.

  • Uses standard level specifications, defaulting to level {1}.
  • Option Heads -> True evaluates heads of expressions.
  • Effectively returns the length of the list generated by Cases for the same arguments.
  • p:def: Optional[p, def], matches p, but if omitted defaults to def.
  • x_.: Optional[Pattern[x, _]], matches x_, but if omitted defaults to globally specified Default values.
  • p..: Repeated[p], matches a sequence of one or more expressions, each matching p.
  • p...: RepeatedNull[p], matches a sequence of zero or more expressions, each matching p.
  • Repeated[p, max], Repeated[p, {min, max}], Repeated[p, {n}]: match sequences of length bounded by max or {min, max}. Equivalent properties exist for RepeatedNull.

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Count[{1,2,1,3,1},1]
Out[1]= 3

In[1]:= Count[{1,2,3,4,5,6},_?EvenQ]
Out[1]= 3

In[1]:= Count[Range[100], _?PrimeQ]
Out[1]= 25

In[1]:= Count[{a, b, {c, a}, a, {a, {a}}}, a, Infinity]
Out[1]= 5

In[1]:= Count[IntegerDigits[2^100], _?(# > 5 &)]
Out[1]= 11

Notes

The second argument is a pattern, so Count[list, _?EvenQ] counts elements satisfying a predicate, not just literal matches. A level specification such as Infinity makes Count recurse into subexpressions, so it counts every matching leaf at any depth — here Count[Range[100], _?PrimeQ] recovers the prime-counting value 25, and the last example tallies how many decimal digits of 2^100 exceed 5.