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package leetcode.hard;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
public class P_84 {
public int largestRectangleArea(int[] heights) {
final Deque<Integer> stack = new ArrayDeque<>(Collections.singleton(-1));
int res = 0;
for (int i = 0; i <= heights.length; i++) {
while (stack.size() > 1 && (i == heights.length || heights[stack.getFirst()] > heights[i])) {
final int top = stack.removeFirst();
final int area = heights[top] * (i - stack.getFirst() - 1);
res = Math.max(res, area);
}
stack.addFirst(i);
}
return res;
}
public int largestRectangleAreaNew(int[] heights) {
final int n = heights.length;
final int[] ls = new int[n];
final int[] rs = new int[n];
final Deque<int[]> dq = new ArrayDeque<>();
dq.addFirst(new int[] { -1, -1 });
for (int i = 0; i < n; i++) {
while (dq.getFirst()[0] >= heights[i]) {
dq.removeFirst();
}
ls[i] = dq.getFirst()[1];
dq.addFirst(new int[] { heights[i], i });
}
dq.clear();
dq.addFirst(new int[] { -1, n });
for (int i = n - 1; i >= 0; i--) {
while (dq.getFirst()[0] >= heights[i]) {
dq.removeFirst();
}
rs[i] = dq.getFirst()[1];
dq.addFirst(new int[] { heights[i], i });
}
int res = 0;
for (int i = 0; i < n; i++) {
res = Math.max(res, heights[i] * (rs[i] - ls[i] - 1));
}
return res;
}
private static class SegTree {
int leftMost, rightMost;
SegTree left, right;
int minIdx;
int val;
SegTree(int leftMost, int rightMost, int[] arr) {
this.leftMost = leftMost;
this.rightMost = rightMost;
if (leftMost == rightMost) {
minIdx = leftMost;
val = arr[leftMost];
} else {
final int mid = leftMost + rightMost >>> 1;
left = new SegTree(leftMost, mid, arr);
right = new SegTree(mid + 1, rightMost, arr);
minIdx = arr[left.minIdx] < arr[right.minIdx] ? left.minIdx : right.minIdx;
}
}
private int query(int l, int r, int[] arr) {
if (l > rightMost || r < leftMost) {
return -1;
}
if (l <= leftMost && rightMost <= r) {
return minIdx;
}
final int ll = left.query(l, r, arr);
final int rr = right.query(l, r, arr);
if (ll == -1) {
return rr;
}
if (rr == -1) {
return ll;
}
return arr[ll] < arr[rr] ? ll : rr;
}
}
public int largestRectangleAreaST(int[] heights) {
final SegTree segTree = new SegTree(0, heights.length - 1, heights);
return dfs(segTree, heights, 0, heights.length - 1);
}
private static int dfs(SegTree root, int[] heights, int start, int end) {
if (start > end) {
return -1;
}
if (start == end) {
return heights[start];
}
final int minIndex = root.query(start, end, heights);
final int leftMax = dfs(root, heights, start, minIndex - 1);
final int rightMax = dfs(root, heights, minIndex + 1, end);
final int minMax = heights[minIndex] * (end - start + 1);
return Math.max(Math.max(leftMax, rightMax), minMax);
}
private static final class UnionFind {
private final int[] parent;
private final int[] size;
private int count;
private UnionFind(int n) {
parent = new int[n];
size = new int[n];
count = n;
for (int i = 0; i < n; i++) {
parent[i] = i;
size[i] = 1;
}
}
public int find(int p) {
// path compression
while (p != parent[p]) {
parent[p] = parent[parent[p]];
p = parent[p];
}
return p;
}
public void union(int p, int q) {
final int rootP = find(p);
final int rootQ = find(q);
if (rootP == rootQ) {
return;
}
// union by size
if (size[rootP] > size[rootQ]) {
parent[rootQ] = rootP;
size[rootP] += size[rootQ];
} else {
parent[rootP] = rootQ;
size[rootQ] += size[rootP];
}
count--;
}
public int count() { return count; }
public int[] size() { return size; }
}
public int largestRectangleAreaUF(int[] heights) {
final int n = heights.length;
final UnionFind uf = new UnionFind(n);
final int[][] pairs = new int[n][2];
for (int i = 0; i < n; i++) {
pairs[i] = new int[] { heights[i], i };
}
Arrays.sort(pairs, (a, b) -> Integer.compare(b[0], a[0]));
int res = 0;
for (int i = 0; i < n; i++) {
final int h = pairs[i][0];
final int idx = pairs[i][1];
if (idx > 0 && heights[idx - 1] >= h) {
uf.union(idx, idx - 1);
}
if (idx < (n - 1) && heights[idx + 1] >= h) {
uf.union(idx, idx + 1);
}
res = Math.max(res, uf.size()[uf.find(idx)] * h);
}
return res;
}
}