Find the Minimum Area to Cover All Ones II
<p>You are given a 2D <strong>binary</strong> array <code>grid</code>. You need to find 3 <strong>non-overlapping</strong> rectangles having <strong>non-zero</strong> areas with horizontal and vertical sides such that all the 1&#39;s in <code>grid</code> lie inside these rectangles.</p>

<p>Return the <strong>minimum</strong> possible sum of the area of these rectangles.</p>

<p><strong>Note</strong> that the rectangles are allowed to touch.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,0,1],[1,1,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3197.Find%20the%20Minimum%20Area%20to%20Cover%20All%20Ones%20II/images/example0rect21.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 280px; height: 198px;" /></p>

<ul>
	<li>The 1&#39;s at <code>(0, 0)</code> and <code>(1, 0)</code> are covered by a rectangle of area 2.</li>
	<li>The 1&#39;s at <code>(0, 2)</code> and <code>(1, 2)</code> are covered by a rectangle of area 2.</li>
	<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>
</ul>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,0,1,0],[0,1,0,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3197.Find%20the%20Minimum%20Area%20to%20Cover%20All%20Ones%20II/images/example1rect2.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 356px; height: 198px;" /></p>

<ul>
	<li>The 1&#39;s at <code>(0, 0)</code> and <code>(0, 2)</code> are covered by a rectangle of area 3.</li>
	<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>
	<li>The 1 at <code>(1, 3)</code> is covered by a rectangle of area 1.</li>
</ul>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either 0 or 1.</li>
	<li>The input is generated such that there are at least three 1&#39;s in <code>grid</code>.</li>
</ul>
Array; Enumeration; Matrix
func minimumSum(grid [][]int) int {
	m := len(grid)
	n := len(grid[0])
	ans := m * n
	inf := math.MaxInt32

	f := func(i1, j1, i2, j2 int) int {
		x1, y1 := inf, inf
		x2, y2 := -inf, -inf
		for i := i1; i <= i2; i++ {
			for j := j1; j <= j2; j++ {
				if grid[i][j] == 1 {
					x1 = min(x1, i)
					y1 = min(y1, j)
					x2 = max(x2, i)
					y2 = max(y2, j)
				}
			}
		}
		if x1 == inf {
			return 0
		}
		return (x2 - x1 + 1) * (y2 - y1 + 1)
	}

	for i1 := 0; i1 < m-1; i1++ {
		for i2 := i1 + 1; i2 < m-1; i2++ {
			ans = min(ans, f(0, 0, i1, n-1)+f(i1+1, 0, i2, n-1)+f(i2+1, 0, m-1, n-1))
		}
	}

	for j1 := 0; j1 < n-1; j1++ {
		for j2 := j1 + 1; j2 < n-1; j2++ {
			ans = min(ans, f(0, 0, m-1, j1)+f(0, j1+1, m-1, j2)+f(0, j2+1, m-1, n-1))
		}
	}

	for i := 0; i < m-1; i++ {
		for j := 0; j < n-1; j++ {
			ans = min(ans, f(0, 0, i, j)+f(0, j+1, i, n-1)+f(i+1, 0, m-1, n-1))
			ans = min(ans, f(0, 0, i, n-1)+f(i+1, 0, m-1, j)+f(i+1, j+1, m-1, n-1))
			ans = min(ans, f(0, 0, i, j)+f(i+1, 0, m-1, j)+f(0, j+1, m-1, n-1))
			ans = min(ans, f(0, 0, m-1, j)+f(0, j+1, i, n-1)+f(i+1, j+1, m-1, n-1))
		}
	}

	return ans
}