programming-examples/java/Data_Structures/SegmentTree2.java

import java.util.*;

public class SegmentTree2 {

	// Modify the following 5 methods to implement your custom operations on the tree.
	// This example implements Add/Max operations. Operations like Add/Sum, Set/Max can also be implemented.
	int modifyOperation(int x, int y) {
		return x + y;
	}

	// query (or combine) operation
	int queryOperation(int leftValue, int rightValue) {
		return Math.max(leftValue, rightValue);
	}

	int deltaEffectOnSegment(int delta, int segmentLength) {
		if (delta == getNeutralDelta()) return getNeutralDelta();
		// Here you must write a fast equivalent of following slow code:
		// int result = delta;
		// for (int i = 1; i < segmentLength; i++) result = queryOperation(result, delta);
		// return result;
		return delta;
	}

	int getNeutralDelta() {
		return 0;
	}

	int getInitValue() {
		return 0;
	}

	// generic code
	int n;
	int[] value;
	int[] delta; // delta[i] affects value[2*i+1], value[2*i+2], delta[2*i+1] and delta[2*i+2]

	int joinValueWithDelta(int value, int delta) {
		if (delta == getNeutralDelta()) return value;
		return modifyOperation(value, delta);
	}

	int joinDeltas(int delta1, int delta2) {
		if (delta1 == getNeutralDelta()) return delta2;
		if (delta2 == getNeutralDelta()) return delta1;
		return modifyOperation(delta1, delta2);
	}

	void pushDelta(int root, int left, int right) {
		int mid = (left + right) >> 1;
		value[(2 * root + 1)] = joinValueWithDelta(value[(2 * root + 1)], deltaEffectOnSegment(delta[root], mid - left + 1));
		value[(2 * root + 2)] = joinValueWithDelta(value[(2 * root + 2)], deltaEffectOnSegment(delta[root], right - mid));
		delta[(2 * root + 1)] = joinDeltas(delta[(2 * root + 1)], delta[root]);
		delta[(2 * root + 2)] = joinDeltas(delta[(2 * root + 2)], delta[root]);
		delta[root] = getNeutralDelta();
	}

	public SegmentTree2(int n) {
		this.n = n;
		value = new int[4 * n];
		delta = new int[4 * n];
		init(0, 0, n - 1);
	}

	void init(int root, int left, int right) {
		if (left == right) {
			value[root] = getInitValue();
			delta[root] = getNeutralDelta();
		} else {
			init(2 * root + 1, left, (left + right) / 2);
			init(2 * root + 2, (left + right) / 2 + 1, right);
			value[root] = queryOperation(value[2 * root + 1], value[2 * root + 2]);
			delta[root] = getNeutralDelta();
		}
	}

	public int query(int from, int to) {
		return query(from, to, 0, 0, n - 1);
	}

	int query(int from, int to, int root, int left, int right) {
		if (from == left && to == right)
			return value[root];
		pushDelta(root, left, right);
		int mid = (left + right) >> 1;
		if (from <= mid && to > mid)
			return queryOperation(
					query(from, Math.min(to, mid), root * 2 + 1, left, mid),
					query(Math.max(from, mid + 1), to, root * 2 + 2, mid + 1, right));
		else if (from <= mid)
			return query(from, Math.min(to, mid), root * 2 + 1, left, mid);
		else if (to > mid)
			return query(Math.max(from, mid + 1), to, root * 2 + 2, mid + 1, right);
		else
			throw new RuntimeException("Incorrect query from " + from + " to " + to);
	}

	public void modify(int from, int to, int delta) {
		modify(from, to, delta, 0, 0, n - 1);
	}

	void modify(int from, int to, int delta, int root, int left, int right) {
		if (from == left && to == right) {
			value[root] = joinValueWithDelta(value[root], deltaEffectOnSegment(delta, right - left + 1));
			this.delta[root] = joinDeltas(this.delta[root], delta);
			return;
		}
		pushDelta(root, left, right);
		int mid = (left + right) >> 1;
		if (from <= mid)
			modify(from, Math.min(to, mid), delta, 2 * root + 1, left, mid);
		if (to > mid)
			modify(Math.max(from, mid + 1), to, delta, 2 * root + 2, mid + 1, right);
		value[root] = queryOperation(value[2 * root + 1], value[2 * root + 2]);
	}

	// Random test
	public static void main(String[] args) {
		Random rnd = new Random(1);
		for (int step = 0; step < 1000; step++) {
			int n = rnd.nextInt(50) + 1;
			int[] x = new int[n];
			SegmentTree2 t = new SegmentTree2(n);
			Arrays.fill(x, t.getInitValue());
			for (int i = 0; i < 1000; i++) {
				int b = rnd.nextInt(n);
				int a = rnd.nextInt(b + 1);
				int cmd = rnd.nextInt(3);
				if (cmd == 0) {
					int delta = rnd.nextInt(100) - 50;
					t.modify(a, b, delta);
					for (int j = a; j <= b; j++)
						x[j] = t.joinValueWithDelta(x[j], delta);
				} else if (cmd == 1) {
					int res1 = t.query(a, b);
					int res2 = x[a];
					for (int j = a + 1; j <= b; j++)
						res2 = t.queryOperation(res2, x[j]);
					if (res1 != res2)
						throw new RuntimeException();
				} else {
					for (int j = 0; j < n; j++) {
						if (t.query(j, j) != x[j])
							throw new RuntimeException();
					}
				}
			}
		}
		System.out.println("Test passed");
	}
}