Modularize lazy segment tree

content/data-structures/LazySegmentTree.h

@@ -16,51 +16,54 @@
 
 const int inf = 1e9;
 struct Node {
+	typedef int T; // data type
+	struct L { int mset, madd; }; // lazy type
+	const T tneut = -inf;     // neutral elements
+	const L lneut = {inf, 0};
+	T f (T a, T b) { return max(a, b); } // (any associative fn)
+	T apply (T a, L b) {
+		return b.mset != inf ? b.mset + b.madd : a + b.madd;
+	} // Apply lazy
+	L comb(L a, L b) {
+		if (b.mset != inf) return b;
+		return {a.mset, a.madd + b.madd};
+	} // Combine lazy
+
 	Node *l = 0, *r = 0;
-	int lo, hi, mset = inf, madd = 0, val = -inf;
-	Node(int lo,int hi):lo(lo),hi(hi){} // Large interval of -inf
-	Node(vi& v, int lo, int hi) : lo(lo), hi(hi) {
+	int lo, hi; T val = tneut; L lazy = lneut;
+	Node(int lo,int hi):lo(lo),hi(hi){}//Large interval of tneut
+	Node(vector<T>& v, int lo, int hi) : lo(lo), hi(hi) {
 		if (lo + 1 < hi) {
 			int mid = lo + (hi - lo)/2;
 			l = new Node(v, lo, mid); r = new Node(v, mid, hi);
-			val = max(l->val, r->val);
+			val = f(l->val, r->val);
 		}
 		else val = v[lo];
 	}
-	int query(int L, int R) {
-		if (R <= lo || hi <= L) return -inf;
-		if (L <= lo && hi <= R) return val;
+	T query(int L, int R) {
+		if (R <= lo || hi <= L) return tneut;
+		if (L <= lo && hi <= R) return apply(val, lazy);
 		push();
-		return max(l->query(L, R), r->query(L, R));
+		return f(l->query(L, R), r->query(L, R));
 	}
-	void set(int L, int R, int x) {
-		if (R <= lo || hi <= L) return;
-		if (L <= lo && hi <= R) mset = val = x, madd = 0;
-		else {
-			push(), l->set(L, R, x), r->set(L, R, x);
-			val = max(l->val, r->val);
-		}
-	}
-	void add(int L, int R, int x) {
-		if (R <= lo || hi <= L) return;
-		if (L <= lo && hi <= R) {
-			if (mset != inf) mset += x;
-			else madd += x;
-			val += x;
-		}
+	void upd(int Le, int Ri, L x) {
+		if (Ri <= lo || hi <= Le) return;
+		if (Le <= lo && hi <= Ri) lazy = comb(lazy, x);
 		else {
-			push(), l->add(L, R, x), r->add(L, R, x);
-			val = max(l->val, r->val);
+			push(), l->upd(Le, Ri, x), r->upd(Le, Ri, x);
+			val = f(l->query(lo, hi), r->query(lo, hi));
 		}
 	}
+	void set(int L, int R, int x) { upd(L, R, {x, 0}); }
+	void add(int L, int R, int x) { upd(L, R, {inf, x}); }
 	void push() {
 		if (!l) {
 			int mid = lo + (hi - lo)/2;
-			l = new Node(lo, mid); r = new Node(mid, hi);
+			l = new Node(lo, mid), r = new Node(mid, hi);
 		}
-		if (mset != inf)
-			l->set(lo,hi,mset), r->set(lo,hi,mset), mset = inf;
-		else if (madd)
-			l->add(lo,hi,madd), r->add(lo,hi,madd), madd = 0;
+		l->lazy = comb(l->lazy, lazy);
+		r->lazy = comb(r->lazy, lazy);
+		lazy = lneut;
+		val = f(l->query(lo, hi), r->query(lo, hi));
 	}
 };