""" 遅延セグメント木(区間演算、区間更新) data[] の要素に モノイド X をもつ lazy[] の要素に Aut(X) をもつ(ただし作用素は「左」から作用とする) アクセスは0-indexed, 内部のツリーは 1-indexed(つまりすべての和は tree[1]) 関数は半開区間 引数: op_X: モノイド演算 (max, min, __add__,ラムダ式,関数定義など) e_X: 単位元 compose: 作用素を合成させる関数[注:普通の関数合成と同じく、左作用](max, min, __add__,ラムダ式,関数定義など) mapping(f,x) = f(x) 関数適用 id_M: 恒等作用素 N: 処理する区間の長さ array: この配列で初期化 """ """ 作用素の例: f \mapsto min(f,-) compose = min funcval = min ID_M = INF = 10**18 f \mapsto max(f,-) compose = max funcval = max ID_M = 0 f \mapsto f (定数関数)(区間代入、最後の操作のみが影響する) compose = lambda f,g: (g if f is ID_M else f) funcval = lambda f,x: (x if f is ID_M else f) ID_M = None #Noneではなく、範囲外の数にすると速くなる """ class LazySegmentTree: #seg = LazySegmentTree(op_X, e_X, mapping, composision_of_Aut_X, id_of_Aut_X, N, array=None): def __init__(self, op_X, e_X, mapping, composision_of_Aut_X, id_of_Aut_X, N, array=None): # それぞれ Xの演算, 単位元, f(x), f\circ g, Xの恒等変換 # M が X に作用する #__slots__ = ["op_X", "e_X", "mapping","compose","id_M","N","log","N0","data","lazy"] self.e_X = e_X; self.op_X = op_X; self.mapping = mapping; self.compose = composision_of_Aut_X; self.id_M = id_of_Aut_X self.N = N self.log = (N-1).bit_length() self.N0 = 1<>i if self.lazy[k] is self.id_M: continue self.data[2*k ] = self.mapping(self.lazy[k], self.data[2*k]) self.data[2*k+1] = self.mapping(self.lazy[k], self.data[2*k+1]) if 2*k < self.N0: self.lazy[2*k] = self.compose(self.lazy[k], self.lazy[2*k]) self.lazy[2*k+1] = self.compose(self.lazy[k], self.lazy[2*k+1]) self.lazy[k] = self.id_M def _update_above(self,k): while k >= 2: k >>= 1 self.data[k] = self.op_X(self.data[2*k], self.data[2*k+1]) def all_apply(self, k, f): self.data[k] = self.mapping(f, self.data[k]) if k < self.N0: self.lazy[k] = self.compose(f, self.lazy[k]) def push(self, k): #propagate と同じ if self.lazy[k] is self.id_M: return self.data[2*k ] = self.mapping(self.lazy[k], self.data[2*k]) self.data[2*k+1] = self.mapping(self.lazy[k], self.data[2*k+1]) if 2*k < self.N0: self.lazy[2*k] = self.compose(self.lazy[k], self.lazy[2*k]) self.lazy[2*k+1] = self.compose(self.lazy[k], self.lazy[2*k+1]) self.lazy[k] = self.id_M def _make_binarytree_string(self,lst): def str_modify(x): return "INF" if type(x)==int and x >= 10**19+1 else str(x) A = list(map(str_modify,lst)) N = len(lst); assert N&(N-1)==0 # pow of 2 spacestring = [" "*len(A[(N//(i&-i)+i)//2]) for i in range(1,N)] res = [] for i in range(N.bit_length()-1): base = 1<>= 1 r >>= 1 return self.op_X(sml, smr) # 全体をopでまとめる def all_prod(self): return self.data[1] # 1点作用 def apply_point(self, p, f): p += self.N0 self._propagate_above(p) self.data[p] = self.mapping(f, self.data[p]) self._update_above(p) # 区間作用 def apply(self, l, r, f): if l == r: return l += self.N0 r += self.N0 L, R = l//(l&-l), r//(r&-r)-1 self._propagate_above(L) self._propagate_above(R) while l < r: if l & 1: self.data[l] = self.mapping(f, self.data[l]) if l < self.N0: self.lazy[l] = self.compose(f, self.lazy[l]) l += 1 if r & 1: r -= 1 self.data[r] = self.mapping(f, self.data[r]) if r < self.N0: self.lazy[r] = self.compose(f, self.lazy[r]) l >>= 1 r >>= 1 self._update_above(L) self._update_above(R) """ 始点 l を固定 f(x_l*...*x_{r-1}) が True になる最大の r つまり TTTTFFFF となるとき、F となる最小の添え字 存在しない場合 n が返る f(e_M) = True でないと壊れる """ def max_right(self, l, g): if l == self.N: return self.N l += self.N0 l //= (l&-l) self._propagate_above(l) sm = self.e_X while True: if not g(self.op_X(sm, self.data[l])): while l < self.N0: self.push(l) l *= 2 if g(self.op_X(sm, self.data[l])): sm = self.op_X(sm, self.data[l]) l += 1 return l - self.N0 sm = self.op_X(sm, self.data[l]) l += 1 if l&-l == l: break return self.N """ 終点 r を固定 f(x_l*...*x_{r-1}) が True になる最小の l つまり FFFFTTTT となるとき、T となる最小の添え字 存在しない場合 r が返る f(e_M) = True でないと壊れる """ def min_left(self, r, g): if r == 0: return 0 r += self.N0 for i in range(self.log, 0, -1): self.push((r-1)>>i) sm = self.e_X while True: r -= 1 while r>1 and r&1: r >>= 1 if not g(self.op_X(self.data[r], sm)): while r < self.N0: self.push(r) r = 2*r + 1 if g(self.op_X(self.data[r], sm)): sm = self.op_X(self.data[r], sm) r -= 1 return r + 1 - self.N0 sm = self.op_X(self.data[r], sm) if r&-r == r: break return 0 ################################################################### # ################################################################### from operator import add class RangeAddRangeMin(LazySegmentTree): def __init__(self,N,MAX,array=None): super().__init__(min, MAX, add, add, 0, N, array) import sys readline = sys.stdin.readline n, = map(int, readline().split()) *a, = map(int, readline().split()) q, = map(int, readline().split()) seg = RangeAddRangeMin(n,1<<60,a) for _ in range(q): k,l,r,c = map(int, readline().split()) if k==1: seg.apply(l-1,r,c) else: print(seg.prod(l-1,r)) #print(seg) #print()