package main import ( . "fmt" "math" "math/rand" . "sort" "time" ) func main() { var input string Scan(&input) if input == "LOCAL" { runLocal() return } var n int Sscan(input, &n) a := make([]int64, n, n) b := make([]int64, n, n) for i := range a { Scan(&a[i], &b[i]) } s := NewSolver(n, a, b) s.Solve() u, v := s.Answer() if err := check(n, u, v); err != nil { if err == errZeroIndexed { fixIndex(u, v) } else { Println(err) panic(err) } } output(u, v) } func output(u, v []int) { Println(len(u)) for i, ui := range u { Println(ui, v[i]) } } func fixIndex(u, v []int) { isZeroIndexed := false for i, ui := range u { if ui == 0 || v[i] == 0 { isZeroIndexed = true break } } if isZeroIndexed { for i := range u { u[i]++ v[i]++ } } } const ( N = 45 ABmax = int64(1e18) ABmin = int64(1e17) X = 50 Base = int64(5e17) Seed = 12121212 ) func generate(n int, seed int64) (a, b []int64) { a = make([]int64, n, n) b = make([]int64, n, n) r := rand.New(rand.NewSource(seed)) for i := range a { a[i] = r.Int63n(ABmax-ABmin) + ABmin } for i := range b { b[i] = r.Int63n(ABmax-ABmin) + ABmin } return } var errZeroIndexed = Errorf("ErrZeroIndexed") func check(n int, u, v []int) error { if len(u) != len(v) { return Errorf("<<>> len(u)=%d != len(v)=%d ", len(u), len(v)) } if len(u) > X { return Errorf("<<>> len(u) > %d", len(u), X) } if len(u) == 0 { return nil } min, max := n, 0 for i, ui := range u { if ui == v[i] { return Errorf("<<>> u[%d]=%d == v[%d]=%d", i, ui, i, v[i]) } if ui < min { min = ui } if v[i] < min { min = v[i] } if ui > max { max = ui } if v[i] > max { max = v[i] } } if !((min == 0 && max < n) || (min == 1 && max <= n)) { return Errorf("<<>> min(u,v)=%d, max(u,v)=%d", min, max) } if min == 0 { return errZeroIndexed } return nil } func show(n int, a, b []int64) { Println("N =", n) for i, ai := range a { Printf("A[%2d] = %19d, B[%2d] = %19d\n", i, ai, i, b[i]) } } func abs(a int64) int64 { if a < 0 { return -a } return a } func max(a, b int64) int64 { if a < b { return b } return a } func min(a, b int64) int64 { if a < b { return a } return b } func process(n int, a, b []int64, u, v []int) { ta := make([]int64, n, n) tb := make([]int64, n, n) copy(ta, a) copy(tb, b) a, b = nil, nil Println("Len = ", len(u)) for i, ui := range u { vi := v[i] Printf("u[%2d] = %2d, v[%2d] = %2d\n", i, ui, i, vi) Printf(" A[%2d] = %19d, B[%2d] = %19d\n", ui, ta[ui], ui, tb[ui]) Printf(" A[%2d] = %19d, B[%2d] = %19d\n", vi, ta[vi], vi, tb[vi]) aa, bb := (ta[ui]+ta[vi])/2, (tb[ui]+tb[vi])/2 Printf(" A[**] = %19d, B[**] = %19d\n", aa, bb) da, db := abs(aa-Base), abs(bb-Base) Printf(" diff = %19d, diff = %19d\n", da, db) Printf(" max = %19d, len = %2d\n", max(da, db), len(Sprint(max(da, db)))) ta[ui], tb[ui] = aa, bb ta[vi], tb[vi] = aa, bb } va, vb := abs(ta[0]-Base), abs(tb[0]-Base) Printf("V(A) = %19d, V(B) = %19d\n", va, vb) Printf(" max = %19d, len = %2d\n", max(va, vb), len(Sprint(max(va, vb)))) score := int64(2e6) - int64(1e5*math.Log10(float64(max(va, vb)+1))) if max(va, vb) == 0 { score += X - int64(len(u)) } Printf("SCORE = %7d, SCORE*50 = %9d\n", score, score*50) } func runLocal() { var n int = N var seed int64 = Seed Scan(&n, &seed) a, b := generate(n, seed) show(n, a, b) t := time.Now() s := NewSolver(n, a, b) s.Solve() u, v := s.Answer() Println(time.Since(t)) Println(s.info) if err := check(n, u, v); err != nil { if err != errZeroIndexed { Println(err) panic(err) } } process(n, a, b, u, v) } type Solver struct { n int a, b []int64 u, v []int info string } func NewSolver(n int, a, b []int64) *Solver { ta := make([]int64, n, n) tb := make([]int64, n, n) copy(ta, a) copy(tb, b) return &Solver{n, ta, tb, []int{}, []int{}, ""} } func (s *Solver) Clone() *Solver { ta := make([]int64, s.n, s.n) tb := make([]int64, s.n, s.n) copy(ta, s.a) copy(tb, s.b) return &Solver{s.n, ta, tb, []int{}, []int{}, ""} } func (s *Solver) Answer() (u, v []int) { return s.u, s.v } func (s *Solver) score() int64 { return max(abs(s.a[0]-Base), abs(s.b[0]-Base)) } func (s *Solver) Solve() { if s.n != N { s.greedy() return } t := s.Clone() t.dp() if t.score() < s.score() { s.u, s.v = t.u, t.v } } func (s *Solver) goodluck() *Solver { var best *Solver { g := s.Clone() g.info = "greedy" g.greedy() best = g } for p := 4; p <= 32; p *= 2 { t := s.Clone() t.info = Sprint("greedy&average(", p, ")") if !t.greedy() || len(s.u)+p+1 >= X { continue } if err := t.average(p); err != nil { continue } if t.greedy() { t.info += "&greedy" } if t.score() < best.score() { best = t } } for p := 4; p <= 32; p *= 2 { for i := 0; i < 100; i++ { t := s.Clone() t.info = Sprint("avarage(", p, ")") t.average(p) if t.greedy() { t.info += "&greedy" } if t.score() < best.score() { best = t } } } for p := 4; p <= 32; p *= 2 { for sz := 10; sz+p < X-2; sz++ { for i := 0; i < 100; i++ { t := s.Clone() t.info = Sprint("random(", sz, ")&avarage(", p, ")") t.random(sz) if err := t.average(p); err != nil { continue } if t.greedy() { t.info += "&greedy" } if t.score() < best.score() { best = t } } } } for sz := 15; sz < X; sz++ { for i := 0; i < 2000; i++ { t := s.Clone() t.info = Sprint("random(", sz, ")") t.random(sz) if t.greedy() { t.info += "&greedy" } if t.score() < best.score() { best = t } } } return best } func (s *Solver) greedy() bool { before := len(s.u) for i := len(s.u); i < X; i++ { best := s.score() zk := -1 for k := 1; k < s.n; k++ { aa := (s.a[0] + s.a[k]) / 2 bb := (s.b[0] + s.b[k]) / 2 s := max(abs(aa-Base), abs(bb-Base)) if s < best { best, zk = s, k } } if zk < 0 { break } s.u = append(s.u, 0) s.v = append(s.v, zk) aa := (s.a[0] + s.a[zk]) / 2 bb := (s.b[0] + s.b[zk]) / 2 s.a[0], s.b[0] = aa, bb s.a[zk], s.b[zk] = aa, bb } return before != len(s.u) } // size .. 2,4,8,16,32 func (s *Solver) average(size int) error { switch size { default: return Errorf("wrong size %d", size) case 2, 4, 8, 16, 32: if len(s.u)+size+1 >= X { return Errorf("over") } } const Div = 100 target := (Base / Div) * int64(size) idx := rand.Perm(N) for i, x := range idx { if x == 0 { idx[0], idx[i] = idx[i], idx[0] break } } var sumA, sumB int64 for _, i := range idx[:size] { sumA += s.a[i] / Div sumB += s.b[i] / Div } best := max(abs(sumA-target), abs(sumB-target)) for { update := 0 for i := 1; i < size; i++ { ii := idx[i] sumA -= s.a[ii] / Div sumB -= s.b[ii] / Div xk := -1 for k := size; k < N; k++ { ik := idx[k] sumA += s.a[ik] / Div sumB += s.b[ik] / Div v := max(abs(sumA-target), abs(sumB-target)) if v < best { best, xk = v, k } sumA -= s.a[ik] / Div sumB -= s.b[ik] / Div } if xk < 0 { sumA += s.a[ii] / Div sumB += s.b[ii] / Div } else { ik := idx[xk] sumA += s.a[ik] / Div sumB += s.b[ik] / Div idx[i], idx[xk] = ik, ii update++ } } if update == 0 { break } } for p := 1; p < size; p *= 2 { for i := 0; i < size; i += p * 2 { ii, ip := idx[i], idx[i+p] s.u = append(s.u, ii) s.v = append(s.v, ip) aa := (s.a[ii] + s.a[ip]) / 2 bb := (s.b[ii] + s.b[ip]) / 2 s.a[ii], s.b[ii] = aa, bb s.a[ip], s.b[ip] = aa, bb } } return nil } func (s *Solver) random(size int) { for ; size > 0; size-- { x := rand.Intn(s.n) y := (x + rand.Intn(s.n-1) + 1) % s.n s.u = append(s.u, x) s.v = append(s.v, y) aa := (s.a[x] + s.a[y]) / 2 bb := (s.b[x] + s.b[y]) / 2 s.a[x], s.b[x] = aa, bb s.a[y], s.b[y] = aa, bb } } func (s *Solver) dp() { const ( Div = 100 Vmax = 1e4 ) type State struct { c int flag, sumA, sumB int64 } score := func(st *State) int64 { a := abs(st.sumA - Base/Div*int64(st.c)) b := abs(st.sumB - Base/Div*int64(st.c)) return max(a, b) } index := func(st *State) int { return int(score(st) / (Base / Div * int64(st.c) / Vmax)) } add := func(st *State, x int) *State { if st == nil { return &State{ c: 1, flag: 1 << uint(x), sumA: s.a[x] / Div, sumB: s.b[x] / Div, } } else { return &State{ c: st.c + 1, flag: st.flag | (1 << uint(x)), sumA: st.sumA + s.a[x]/Div, sumB: st.sumB + s.b[x]/Div, } } } better := func(st1, st2 *State) *State { if st1 == nil { return st2 } else if st2 == nil { return st1 } else if score(st1)/int64(st1.c) < score(st2)/int64(st2.c) { return st1 } else { return st2 } } dp := make([][]*State, 33) for i := range dp { dp[i] = make([]*State, Vmax+1) } first := add(nil, 0) dp[1][index(first)] = first for x := 1; x < N; x++ { for i := 31; i > 0; i-- { for _, e := range dp[i] { if e == nil { continue } st := add(e, x) idx := index(st) dp[i+1][idx] = better(dp[i+1][idx], st) } } } xx := []*State{} for i := 2; i <= 32; i *= 2 { for _, e := range dp[i] { if e != nil { xx = append(xx, e) } } } Slice(xx, func(i, j int) bool { return score(xx[i])/int64(xx[i].c) < score(xx[j])/int64(xx[j].c) }) best := xx[0] pp := make([]int, 0, best.c) for i := 0; i < N; i++ { if best.flag&(1<