算法习题之IndexTree

IndexTree

特点：
1）支持区间查询
2）没有线段树那么强，但是非常容易改成一维、二维、三维的结构
3）只支持单点更新

习题一 手写IndexTree

	// 下标从1开始！
	public static class IndexTree {

		private int[] tree;
		private int N;

		// 0位置弃而不用！
		public IndexTree(int size) {
			N = size;
			tree = new int[N + 1];
		}

		// 1~index 累加和是多少？
		public int sum(int index) {
			int ret = 0;
			while (index > 0) {
				ret += tree[index];
				index -= index & -index;
			}
			return ret;
		}

		// index & -index : 提取出index最右侧的1出来
		// index :           0011001000
		// index & -index :  0000001000
		public void add(int index, int d) {
			while (index <= N) {
				tree[index] += d;
				index += index & -index;
			}
		}
	}

	public static class Right {
		private int[] nums;
		private int N;

		public Right(int size) {
			N = size + 1;
			nums = new int[N + 1];
		}

		public int sum(int index) {
			int ret = 0;
			for (int i = 1; i <= index; i++) {
				ret += nums[i];
			}
			return ret;
		}

		public void add(int index, int d) {
			nums[index] += d;
		}

	}

	public static void main(String[] args) {
		int N = 100;
		int V = 100;
		int testTime = 2000000;
		IndexTree tree = new IndexTree(N);
		Right test = new Right(N);
		System.out.println("test begin");
		for (int i = 0; i < testTime; i++) {
			int index = (int) (Math.random() * N) + 1;
			if (Math.random() <= 0.5) {
				int add = (int) (Math.random() * V);
				tree.add(index, add);
				test.add(index, add);
			} else {
				if (tree.sum(index) != test.sum(index)) {
					System.out.println("Oops!");
				}
			}
		}
		System.out.println("test finish");
	}

习题2 手写二维的indexTree

private int[][] tree;
	private int[][] nums;
	private int N;
	private int M;

	public Code02_IndexTree2D(int[][] matrix) {
		if (matrix.length == 0 || matrix[0].length == 0) {
			return;
		}
		N = matrix.length;
		M = matrix[0].length;
		tree = new int[N + 1][M + 1];
		nums = new int[N][M];
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < M; j++) {
				update(i, j, matrix[i][j]);
			}
		}
	}

	private int sum(int row, int col) {
		int sum = 0;
		for (int i = row + 1; i > 0; i -= i & (-i)) {
			for (int j = col + 1; j > 0; j -= j & (-j)) {
				sum += tree[i][j];
			}
		}
		return sum;
	}

	public void update(int row, int col, int val) {
		if (N == 0 || M == 0) {
			return;
		}
		int add = val - nums[row][col];
		nums[row][col] = val;
		for (int i = row + 1; i <= N; i += i & (-i)) {
			for (int j = col + 1; j <= M; j += j & (-j)) {
				tree[i][j] += add;
			}
		}
	}

	public int sumRegion(int row1, int col1, int row2, int col2) {
		if (N == 0 || M == 0) {
			return 0;
		}
		return sum(row2, col2) + sum(row1 - 1, col1 - 1) - sum(row1 - 1, col2) - sum(row2, col1 - 1);
	}