g0001_0100.s0085_maximal_rectangle.Solution.kt Maven / Gradle / Ivy
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package g0001_0100.s0085_maximal_rectangle
// #Hard #Array #Dynamic_Programming #Matrix #Stack #Monotonic_Stack
// #2022_09_25_Time_463_ms_(55.17%)_Space_58.5_MB_(62.07%)
class Solution {
fun maximalRectangle(matrix: Array): Int {
/*
* idea: using [LC84 Largest Rectangle in Histogram]. For each row of the matrix, construct
* the histogram based on the current row and the previous histogram (up to the previous
* row), then compute the largest rectangle area using LC84.
*/
val m = matrix.size
var n = 0
if (m == 0 || matrix[0].size.also { n = it } == 0) {
return 0
}
var i: Int
var j: Int
var res = 0
val heights = IntArray(n)
i = 0
while (i < m) {
j = 0
while (j < n) {
if (matrix[i][j] == '0') {
heights[j] = 0
} else {
heights[j] += 1
}
j++
}
res = Math.max(res, largestRectangleArea(heights))
i++
}
return res
}
private fun largestRectangleArea(heights: IntArray): Int {
/*
* idea: scan and store if a[i-1]<=a[i] (increasing), then as long as a[i]a[i], which
* is a[j]*(i-j). And meanwhile, all these bars (a[j]'s) are already done, and thus are
* throwable (using pop() with a stack).
*
* We can use an array nLeftGeq[] of size n to simulate a stack. nLeftGeq[i] = the number
* of elements to the left of [i] having value greater than or equal to a[i] (including a[i]
* itself). It is also the index difference between [i] and the next index on the top of the
* stack.
*/
val n = heights.size
if (n == 0) {
return 0
}
val nLeftGeq = IntArray(n)
// the number of elements to the left
// of [i] with value >= heights[i]
nLeftGeq[0] = 1
// preIdx=the index of stack.peek(), res=max area so far
var preIdx = 0
var res = 0
for (i in 1 until n) {
nLeftGeq[i] = 1
// notice that preIdx = i - 1 = peek()
while (preIdx >= 0 && heights[i] < heights[preIdx]) {
res = Math.max(res, heights[preIdx] * (nLeftGeq[preIdx] + i - preIdx - 1))
// pop()
nLeftGeq[i] += nLeftGeq[preIdx]
// peek() current top
preIdx = preIdx - nLeftGeq[preIdx]
}
if (preIdx >= 0 && heights[i] == heights[preIdx]) {
// pop()
nLeftGeq[i] += nLeftGeq[preIdx]
}
// otherwise nothing to do
preIdx = i
}
// compute the rest largest rectangle areas with (indices of) bases
// on stack
while (preIdx >= 0 && 0 < heights[preIdx]) {
res = Math.max(res, heights[preIdx] * (nLeftGeq[preIdx] + n - preIdx - 1))
// peek() current top
preIdx = preIdx - nLeftGeq[preIdx]
}
return res
}
}