algorithm-class/算法周更班/class_2022_05_2_week/Code03_SortedSubsequenceMaxSum.java

package class_2022_05_2_week;

import java.util.Arrays;

// 来自字节
// 一共有n个人，从左到右排列，依次编号0~n-1
// h[i]是第i个人的身高
// v[i]是第i个人的分数
// 要求从左到右选出一个子序列，在这个子序列中的人，从左到右身高是不下降的
// 返回所有符合要求的子序列中，分数最大累加和是多大
// n <= 10的5次方, 1 <= h[i] <= 10的9次方, 1 <= v[i] <= 10的9次方
public class Code03_SortedSubsequenceMaxSum {

	// 为了测试
	// 绝对正确的暴力方法
	public static int right(int[] h, int[] v) {
		return process(h, v, 0, 0);
	}

	public static int process(int[] h, int[] v, int index, int preValue) {
		if (index == h.length) {
			return 0;
		}
		int p1 = process(h, v, index + 1, preValue);
		int p2 = h[index] >= preValue ? (v[index] + process(h, v, index + 1, h[index])) : 0;
		return Math.max(p1, p2);
	}

	// 正式方法
	// 时间复杂度O(N * logN)
	public static int maxSum(int[] h, int[] v) {
		int n = h.length;
		int[] rank = new int[n];
		for (int i = 0; i < n; i++) {
			rank[i] = h[i];
		}
		Arrays.sort(rank);
		SegmentTree st = new SegmentTree(n);
		for (int i = 0; i < n; i++) {
			int height = rank(rank, h[i]);
			// 1~height max
			st.update(height, st.max(height) + v[i]);
		}
		return st.max(n);
	}

	// [150, 152, 160, 175]  160
	//   1    2    3    4
	// 3
	public static int rank(int[] rank, int num) {
		int l = 0;
		int r = rank.length - 1;
		int m = 0;
		int ans = 0;
		while (l <= r) {
			m = (l + r) / 2;
			if (rank[m] >= num) {
				ans = m;
				r = m - 1;
			} else {
				l = m + 1;
			}
		}
		return ans + 1;
	}

	public static class SegmentTree {
		private int n;
		private int[] max;
		private int[] update;

		public SegmentTree(int maxSize) {
			n = maxSize + 1;
			max = new int[n << 2];
			update = new int[n << 2];
			Arrays.fill(update, -1);
		}

		public void update(int index, int c) {
			update(index, index, c, 1, n, 1);
		}

		public int max(int right) {
			return max(1, right, 1, n, 1);
		}

		private void pushUp(int rt) {
			max[rt] = Math.max(max[rt << 1], max[rt << 1 | 1]);
		}

		private void pushDown(int rt, int ln, int rn) {
			if (update[rt] != -1) {
				update[rt << 1] = update[rt];
				max[rt << 1] = update[rt];
				update[rt << 1 | 1] = update[rt];
				max[rt << 1 | 1] = update[rt];
				update[rt] = -1;
			}
		}

		private void update(int L, int R, int C, int l, int r, int rt) {
			if (L <= l && r <= R) {
				max[rt] = C;
				update[rt] = C;
				return;
			}
			int mid = (l + r) >> 1;
			pushDown(rt, mid - l + 1, r - mid);
			if (L <= mid) {
				update(L, R, C, l, mid, rt << 1);
			}
			if (R > mid) {
				update(L, R, C, mid + 1, r, rt << 1 | 1);
			}
			pushUp(rt);
		}

		private int max(int L, int R, int l, int r, int rt) {
			if (L <= l && r <= R) {
				return max[rt];
			}
			int mid = (l + r) >> 1;
			pushDown(rt, mid - l + 1, r - mid);
			int ans = 0;
			if (L <= mid) {
				ans = Math.max(ans, max(L, R, l, mid, rt << 1));
			}
			if (R > mid) {
				ans = Math.max(ans, max(L, R, mid + 1, r, rt << 1 | 1));
			}
			return ans;
		}

	}

	// 为了测试
	public static int[] randomArray(int n, int v) {
		int[] ans = new int[n];
		for (int i = 0; i < n; i++) {
			ans[i] = (int) (Math.random() * v) + 1;
		}
		return ans;
	}

	// 为了测试
	public static void main(String[] args) {
		int N = 30;
		int V = 100;
		int testTime = 20000;
		System.out.println("测试开始");
		for (int i = 0; i < testTime; i++) {
			int n = (int) (Math.random() * N) + 1;
			int[] h = randomArray(n, V);
			int[] v = randomArray(n, V);
			if (right(h, v) != maxSum(h, v)) {
				System.out.println("出错了!");
			}
		}
		System.out.println("测试结束");
	}

}