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封印宝石(编程题) - 题解

思路



贪心:按照1~n的顺序依次选择一个宝石放入第$i$个盒子(宝石值最大且min(i) - j <= k,否则盒子为空)

step



b用于保存a[1~n]离散化后的值,然后将a中值相同的放在一起。
用线段树维护当前不同宝石值对应的最小下标,对于第$i$个盒子,宝石的下标满足$ j <= k + i $,查找到最右边的宝石(即满足条件最大值的宝石)下标即为答案
当某一值的宝石用完,可以将线段树中值置为INF(大于 k即可)

#include <bits/stdc++.h>
using namespace std;

#define lson u << 1
#define rson u << 1 | 1
const int N = 100010, INF = 0x3f3f3f3f;
int n, k;
int a[N], idx[N], b[N], tr[N << 2];
vector<int> g[N];

void pushup(int u)
{
	tr[u] = min(tr[lson], tr[rson]);
}

void build(int u, int l, int r)
{
	if (l == r) tr[u] = g[l].back();
	else{
		int mid = (l + r) >> 1;
		build(lson, l, mid), build(rson, mid + 1, r);
		pushup(u);
	}
}

void update(int u, int l, int r, int x, int v)
{
	if (l == r) tr[u] = v;
	else
	{
		int mid = (l + r) >> 1;
		if (x <= mid) update(lson, l, mid, x, v);
		else update(rson, mid + 1, r, x, v);
		pushup(u);
	}
}

int query(int u, int l, int r, int x)
{
	if (l == r) return tr[u];
	int mid = (l + r) >> 1;
	if (tr[rson] <= x) return query(rson, mid + 1, r, x);
	else if (tr[lson] <= x) return query(lson, l, mid, x);
	return -1;
}

int main()
{
	scanf("%d%d", &n, &k);
	for (int i = 1; i <= n; i++)
	{
		scanf("%d", &a[i]);
		b[i] = a[i];
	}
	sort(b + 1, b + 1 + n);
	int len = unique(b + 1, b + 1 + n) - b - 1;
	for (int i = n; i >= 1; i--)
	{
		int x = lower_bound(b + 1, b + 1 + len, a[i]) - b;
		idx[i] = x;
		g[x].emplace_back(i);
	}
	build(1, 1, len);
	for (int i = 1, last = 0; i <= n; i++)
	{
		int x = query(1, 1, len, i + k);
		if (x != -1 && a[x] == a[last])
		{
			update(1, 1, len, idx[x], INF);
			x = query(1, 1, len, i + k);
			update(1, 1, len, idx[last], g[idx[last]].back());
		}
		if (g[idx[i]].size() && g[idx[i]].back() == i)
		{
			g[idx[i]].pop_back();
			int v = g[idx[i]].size() ? g[idx[i]].back():INF;
			update(1, 1, len, idx[i], v);
		}
		if (x != -1 && g[idx[x]].size() && g[idx[x]].back() == x)
		{
			g[idx[x]].pop_back();
			int v = g[idx[x]].size() ? g[idx[x]].back():INF;
			update(1, 1, len, idx[x], v);
			k -= x - i;
			// cout<<"F"<<endl;
		}
		last = x == -1 ? 0:x;
		if (x == -1) printf("-1 ");
		else printf("%d ", a[x]);
	}
	return 0;
}
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