-- Hopcroft-Karp ABmatch = {} ABmatch.create = function(self, an, bn) self.dst = {} self.edge = {} for i = 1, an do self.dst[i] = false self.edge[i] = {} end self.src = {} self.invcnt = {} self.invs = {} self.invpos = {} self.padded = {} for i = 1, bn do self.src[i] = false self.invs[i] = {} end self.p = {} self.tasks = {} self.level = {} end ABmatch.addEdge = function(self, a, b) table.insert(self.edge[a], b) if not self.dst[a] and not self.src[b] then self.dst[a] = b self.src[b] = a end end ABmatch.makeAugPath = function(self) local tasknum = 0 local tasks = self.tasks local level = self.level local edge = self.edge local src = self.src local an = #self.dst local bn = #src local invcnt, invs = self.invcnt, self.invs local p, psize = self.p, 0 local padded = self.padded local lvinf = an + 1 for i = 1, an do if self.dst[i] then level[i] = lvinf else tasknum = tasknum + 1 tasks[tasknum] = i level[i] = 1 end end for i = 1, bn do invcnt[i] = 0 padded[i] = false end local done = 0 local lvmax = lvinf while done < tasknum do done = done + 1 local a = tasks[done] if lvmax < level[a] then break end for i = 1, #edge[a] do local b = edge[a][i] local sb = src[b] if sb then if level[sb] == lvinf then tasknum = tasknum + 1 tasks[tasknum] = sb level[sb] = level[a] + 1 invcnt[b] = invcnt[b] + 1 invs[b][invcnt[b]] = a elseif level[sb] == level[a] + 1 then invcnt[b] = invcnt[b] + 1 invs[b][invcnt[b]] = a end else if lvmax == lvinf then lvmax = level[a] end if padded[b] then else padded[b] = true psize = psize + 1 p[psize] = b end invcnt[b] = invcnt[b] + 1 invs[b][invcnt[b]] = a end end end self.psize = psize return lvmax end -- ABmatch.dfs = function(self, b, lv) -- for i = 1, self.invcnt[b] do -- local a = self.invs[b][i] -- if self.level[a] == 1 or (self.level[a] == lv and self:dfs(self.dst[a], lv - 1)) then -- self.dst[a], self.src[b] = b, a -- self.level[a] = -1 -- return true -- end -- end -- end ABmatch.restore = function(self, bend, lvend) local invs, invcnt, invpos = self.invs, self.invcnt, self.invpos local dst, src, level = self.dst, self.src, self.level local bn = #src for i = 1, bn do invpos[i] = 0 end local accept = false local tasks = self.tasks local taskpos = 1 tasks[1] = bend while 0 < taskpos do local b = tasks[taskpos] if accept then local a = invs[b][invpos[b]] dst[a], src[b] = b, a level[a] = -1 taskpos = taskpos - 1 else if invpos[b] == invcnt[b] then taskpos = taskpos - 1 else local ip = invpos[b] + 1 invpos[b] = ip local a = invs[b][ip] if level[a] == 1 then accept = true dst[a], src[b] = b, a level[a] = -1 taskpos = taskpos - 1 elseif level[a] + taskpos == lvend + 1 then taskpos = taskpos + 1 tasks[taskpos] = dst[a] end end end end end ABmatch.matching = function(self) local an = #self.dst local lv = self:makeAugPath() while lv <= an do for i = 1, self.psize do self:restore(self.p[i], lv) -- self:dfs(self.p[i], lv) end lv = self:makeAugPath() end self.executed = true end ABmatch.getMatchCount = function(self) if not self.executed then self:matching() end local cnt = 0 for i = 1, #self.dst do if self.dst[i] then cnt = cnt + 1 end end return cnt end ABmatch.new = function(an, bn) local obj = {} setmetatable(obj, {__index = ABmatch}) obj:create(an, bn) return obj end local n = io.read("*n") local abm = ABmatch.new(n, n) for i = 1, n do local a, b = io.read("*n", "*n") abm:addEdge(i, a) abm:addEdge(i, b) end if abm:getMatchCount() == n then print("Yes") for i = 1, n do print(abm.dst[i]) end else print("No") end