HDU - 4417 Super Mario （划分树+二分）

最新推荐文章于 2019-10-02 17:37:55 发布

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本文探讨了一种用于马里奥游戏中的路径优化算法，该算法通过构建一种特殊的树结构来快速查找指定区间内高度小于马里奥跳跃高度的砖块数量。通过对道路上的每个砖块高度进行预处理，并使用递归方式构建树结构，实现对查询区间的高效搜索。此算法适用于处理大量查询，为游戏中的路径规划和资源收集提供了有效的解决方案。

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Mario is world-famous plumber. His “burly” figure and amazing jumping ability reminded in our memory. Now the poor princess is in trouble again and Mario needs to save his lover. We regard the road to the boss’s castle as a line (the length is n), on every integer point i there is a brick on height hi. Now the question is how many bricks in [L, R] Mario can hit if the maximal height he can jump is H.

Input

The first line follows an integer T, the number of test data.
For each test data:
The first line contains two integers n, m (1 <= n <=10^5, 1 <= m <= 10^5), n is the length of the road, m is the number of queries.
Next line contains n integers, the height of each brick, the range is [0, 1000000000].
Next m lines, each line contains three integers L, R,H.( 0 <= L <= R < n 0 <= H <= 1000000000.)

Output

For each case, output "Case X: " (X is the case number starting from 1) followed by m lines, each line contains an integer. The ith integer is the number of bricks Mario can hit for the ith query.

Sample Input

1
10 10
0 5 2 7 5 4 3 8 7 7 
2 8 6
3 5 0
1 3 1
1 9 4
0 1 0
3 5 5
5 5 1
4 6 3
1 5 7
5 7 3

Sample Output

静态查找某个区间内所指示的数k比几个数大。。。建划分树直接暴力二分查找看看是第几大。

#include<bits/stdc++.h>
using namespace std;
const int maxn = 200010;
int tree[20][maxn];
int sorted[maxn];
int toleft[20][maxn];
void build(int l, int r, int dep) {
	if (l == r)return;
	int mid = (l + r) >> 1;
	int same = mid - l + 1;
	for (int i = l; i <= r; i++) {
		if (tree[dep][i] < sorted[mid])
			same--;
	}
	int lpos = l;
	int rpos = mid + 1;
	for (int i = l; i <= r; i++) {
		if (tree[dep][i] < sorted[mid])
			tree[dep + 1][lpos++] = tree[dep][i];
		else if (tree[dep][i] == sorted[mid] && same > 0) {
			tree[dep + 1][lpos++] = tree[dep][i];
			same--;
		}
		else
			tree[dep + 1][rpos++] = tree[dep][i];
		toleft[dep][i] = toleft[dep][l - 1] + lpos - l;
	}
	build(l, mid, dep + 1);
	build(mid + 1, r, dep + 1);
}
int query(int L, int R, int l, int r, int dep, int k) {
	if (l == r)return tree[dep][l];
	int mid = (L + R) >> 1;
	int cnt = toleft[dep][r] - toleft[dep][l - 1];
	if (cnt >= k) {
		int newl = L + toleft[dep][l - 1] - toleft[dep][L - 1];
		int newr = newl + cnt - 1;
		return query(L, mid, newl, newr, dep + 1, k);
	}
	else {
		int newr = r + toleft[dep][R] - toleft[dep][r];
		int newl = newr - (r - l - cnt);
		return query(mid + 1, R, newl, newr, dep + 1, k - cnt);
	}
}
int main() {
	int n, m;
	int te, cas = 1;
	scanf("%d", &te);
	while (te--) {
		scanf("%d%d", &n, &m);
		printf("Case %d:\n", cas++);
		for (int i = 1; i <= n; i++) {
			scanf("%d", &tree[0][i]);
			sorted[i] = tree[0][i];
		}
		sort(sorted + 1, sorted + n + 1);
		build(1, n, 0);
		int s, t, k;
		while (m--) {
			scanf("%d%d%d", &s, &t, &k);
			s++; t++;
			int l = 1, r = (t - s + 1), ans = 0;
			while (l <= r) {
				int mid = (l + r) >> 1;
				int tmp = query(1, n, s, t, 0, mid);
			//	cout << l << " " << r << " tmp: " << tmp << " k:" << k << endl;
				if (tmp<= k) {
					ans = mid;
					l = mid + 1;
				}
				else {
					r = mid - 1;
				}
			}
			printf("%d\n", ans);
		}
	}
	return 0;
}