feat: add epsilon tolerance for floating-point output comparison

Problem: output comparison used exact string equality after whitespace
normalisation, causing correct solutions to fail on problems where
floating-point answers are accepted within a tolerance (e.g. 1e-6).

Solution: add an optional ui.panel.epsilon config value. When set,
actual and expected output are compared token-by-token: numeric tokens
are compared with math.abs(a - b) <= epsilon, non-numeric tokens fall
back to exact string equality. Per-problem epsilon can also be stored
in the cache and takes precedence over the global default.

lua/cp/cache.lua

@@ -27,6 +27,7 @@
 ---@field multi_test? boolean
 ---@field memory_mb? number
 ---@field timeout_ms? number
+---@field epsilon? number
 ---@field combined_test? CombinedTest
 ---@field test_cases TestCase[]
 
@@ -273,6 +274,34 @@ function M.get_constraints(platform, contest_id, problem_id)
   return problem_data.timeout_ms, problem_data.memory_mb
 end
 
+---@param platform string
+---@param contest_id string
+---@param problem_id? string
+---@return number?
+function M.get_epsilon(platform, contest_id, problem_id)
+  vim.validate({
+    platform = { platform, 'string' },
+    contest_id = { contest_id, 'string' },
+    problem_id = { problem_id, { 'string', 'nil' }, true },
+  })
+
+  if
+    not cache_data[platform]
+    or not cache_data[platform][contest_id]
+    or not cache_data[platform][contest_id].index_map
+  then
+    return nil
+  end
+
+  local index = cache_data[platform][contest_id].index_map[problem_id]
+  if not index then
+    return nil
+  end
+
+  local problem_data = cache_data[platform][contest_id].problems[index]
+  return problem_data and problem_data.epsilon or nil
+end
+
 ---@param file_path string
 ---@return FileState|nil
 function M.get_file_state(file_path)

lua/cp/config.lua

@@ -20,6 +20,7 @@
 ---@class PanelConfig
 ---@field diff_modes string[]
 ---@field max_output_lines integer
+---@field epsilon number?
 
 ---@class DiffGitConfig
 ---@field args string[]
@@ -173,7 +174,7 @@ M.defaults = {
       add_test_key = 'ga',
       save_and_exit_key = 'q',
     },
-    panel = { diff_modes = { 'side-by-side', 'git', 'vim' }, max_output_lines = 50 },
+    panel = { diff_modes = { 'side-by-side', 'git', 'vim' }, max_output_lines = 50, epsilon = nil },
     diff = {
       git = {
         args = { 'diff', '--no-index', '--word-diff=plain', '--word-diff-regex=.', '--no-prefix' },
@@ -363,6 +364,13 @@ function M.setup(user_config)
       end,
       'positive integer',
     },
+    epsilon = {
+      cfg.ui.panel.epsilon,
+      function(v)
+        return v == nil or (type(v) == 'number' and v >= 0)
+      end,
+      'nil or non-negative number',
+    },
     git = { cfg.ui.diff.git, { 'table' } },
     git_args = { cfg.ui.diff.git.args, is_string_list, 'string[]' },
     width = {

lua/cp/runner/run.lua

@@ -19,6 +19,7 @@
 ---@class ProblemConstraints
 ---@field timeout_ms number
 ---@field memory_mb number
+---@field epsilon number?
 
 ---@class PanelState
 ---@field test_cases RanTestCase[]
@@ -56,7 +57,8 @@ local function load_constraints_from_cache(platform, contest_id, problem_id)
   cache.load()
   local timeout_ms, memory_mb = cache.get_constraints(platform, contest_id, problem_id)
   if timeout_ms and memory_mb then
-    return { timeout_ms = timeout_ms, memory_mb = memory_mb }
+    local epsilon = cache.get_epsilon(platform, contest_id, problem_id)
+    return { timeout_ms = timeout_ms, memory_mb = memory_mb, epsilon = epsilon }
   end
   return nil
 end
@@ -99,6 +101,49 @@ local function build_command(cmd, substitutions)
   return execute.build_command(cmd, substitutions)
 end
 
+local function compare_outputs(actual, expected, epsilon)
+  local norm_actual = normalize_lines(actual)
+  local norm_expected = normalize_lines(expected)
+
+  if epsilon == nil or epsilon == 0 then
+    return norm_actual == norm_expected
+  end
+
+  local actual_lines = vim.split(norm_actual, '\n', { plain = true })
+  local expected_lines = vim.split(norm_expected, '\n', { plain = true })
+
+  if #actual_lines ~= #expected_lines then
+    return false
+  end
+
+  for i = 1, #actual_lines do
+    local a_tokens = vim.split(actual_lines[i], '%s+', { plain = false, trimempty = true })
+    local e_tokens = vim.split(expected_lines[i], '%s+', { plain = false, trimempty = true })
+
+    if #a_tokens ~= #e_tokens then
+      return false
+    end
+
+    for j = 1, #a_tokens do
+      local a_tok, e_tok = a_tokens[j], e_tokens[j]
+      local a_num = tonumber(a_tok)
+      local e_num = tonumber(e_tok)
+
+      if a_num ~= nil and e_num ~= nil then
+        if math.abs(a_num - e_num) > epsilon then
+          return false
+        end
+      else
+        if a_tok ~= e_tok then
+          return false
+        end
+      end
+    end
+  end
+
+  return true
+end
+
 ---@param test_case RanTestCase
 ---@param debug boolean?
 ---@param on_complete fun(result: { status: "pass"|"fail"|"tle"|"mle", actual: string, actual_highlights: Highlight[], error: string, stderr: string, time_ms: number, code: integer, ok: boolean, signal: string?, tled: boolean, mled: boolean, rss_mb: number })
@@ -143,7 +188,9 @@ local function run_single_test_case(test_case, debug, on_complete)
     end
 
     local expected = test_case.expected or ''
-    local ok = normalize_lines(out) == normalize_lines(expected)
+    local epsilon = (panel_state.constraints and panel_state.constraints.epsilon)
+      or config.ui.panel.epsilon
+    local ok = compare_outputs(out, expected, epsilon)
 
     local signal = r.signal
     if not signal and r.code and r.code >= 128 then