【Python CheckiO 题解】Largest Rectangle in a Histogram

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Title Description

Largest Rectangle in a Histogram [] : seeking a histogram of the maximum area of the matrix, given a list, the list element represents a histogram of all the height of the rectangle, calculating the maximum rectangular area constructed in the histogram.

[Link] : https://py.checkio.org/mission/largest-histogram/

[Enter] : the height of the histogram list of all the rectangles

[Output] : the largest rectangle

[Premise] : 0 <len (data) <

[Example] :

largest_histogram([5]) == 5
largest_histogram([5, 3]) == 6
largest_histogram([1, 1, 4, 1]) == 4
largest_histogram([1, 1, 3, 1]) == 4
largest_histogram([2, 1, 4, 5, 1, 3, 3]) == 8

Code

def largest_histogram(histogram):
    i = 0
    max_value = 0
    stack = []
    histogram.append(0)
    while i < len(histogram):
        if len(stack) == 0 or histogram[stack[-1]] <= histogram[i]:
            stack.append(i)
            i += 1
        else:
            now_idx = stack.pop()
            if len(stack) == 0:
                max_value = max(max_value,i * histogram[now_idx])
            else:                    
                max_value = max(max_value,(i- stack[-1] -1) * histogram[now_idx])
    return max_value


if __name__ == "__main__":
    #These "asserts" using only for self-checking and not necessary for auto-testing
    assert largest_histogram([5]) == 5, "one is always the biggest"
    assert largest_histogram([5, 3]) == 6, "two are smallest X 2"
    assert largest_histogram([1, 1, 4, 1]) == 4, "vertical"
    assert largest_histogram([1, 1, 3, 1]) == 4, "horizontal"
    assert largest_histogram([2, 1, 4, 5, 1, 3, 3]) == 8, "complex"
    print("Done! Go check it!")

Okami answer

Okami answer NO.1

def largest_histogram(h):
    result = min(h) * len(h)
    for w in range(1, len(h)):
        for i in range(len(h) - w + 1):
            result = max(result, min(h[i:i + w]) * w)
    return result

Okami answer NO.2

def largest_histogram(h):
    n = len(h)
    return max((j - i) * min(h[i:j]) for i in range(n) for j in range(i+1, n+1))

Okami answer NO.3

def largest_histogram(histogram):
    return max(height * max(len(strip) for strip in ''.join('x' if x >= height else ' ' for x in histogram).split()) for height in set(histogram))

Okami answer NO.4

def mesure(hist):
    return min(hist) * len(hist)
    
def sub_histograms(hist):
    for start in range(len(hist)):
        for stop in range(start+1, len(hist)+1):
            yield hist[start:stop]

def largest_histogram(histogram):
    return max(map(mesure, sub_histograms(histogram)))