Minimum Moves to Move a Box to Their Target Location
<p>A storekeeper is a game in which the player pushes boxes around in a warehouse trying to get them to target locations.</p>

<p>The game is represented by an <code>m x n</code> grid of characters <code>grid</code> where each element is a wall, floor, or box.</p>

<p>Your task is to move the box <code>&#39;B&#39;</code> to the target position <code>&#39;T&#39;</code> under the following rules:</p>

<ul>
	<li>The character <code>&#39;S&#39;</code> represents the player. The player can move up, down, left, right in <code>grid</code> if it is a floor (empty cell).</li>
	<li>The character <code>&#39;.&#39;</code> represents the floor which means a free cell to walk.</li>
	<li>The character<font face="monospace">&nbsp;</font><code>&#39;#&#39;</code><font face="monospace">&nbsp;</font>represents the wall which means an obstacle (impossible to walk there).</li>
	<li>There is only one box <code>&#39;B&#39;</code> and one target cell <code>&#39;T&#39;</code> in the <code>grid</code>.</li>
	<li>The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box. This is a <strong>push</strong>.</li>
	<li>The player cannot walk through the box.</li>
</ul>

<p>Return <em>the minimum number of <strong>pushes</strong> to move the box to the target</em>. If there is no way to reach the target, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1200-1299/1263.Minimum%20Moves%20to%20Move%20a%20Box%20to%20Their%20Target%20Location/images/sample_1_1620.png" style="width: 500px; height: 335px;" />
<pre>
<strong>Input:</strong> grid = [[&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;T&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;B&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;S&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We return only the number of times the box is pushed.</pre>

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

<pre>
<strong>Input:</strong> grid = [[&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;T&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;B&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;S&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;]]
<strong>Output:</strong> -1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;T&quot;,&quot;.&quot;,&quot;.&quot;,&quot;#&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;B&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;S&quot;,&quot;#&quot;],
               [&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> push the box down, left, left, up and up.
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 20</code></li>
	<li><code>grid</code> contains only characters <code>&#39;.&#39;</code>, <code>&#39;#&#39;</code>, <code>&#39;S&#39;</code>, <code>&#39;T&#39;</code>, or <code>&#39;B&#39;</code>.</li>
	<li>There is only one character <code>&#39;S&#39;</code>, <code>&#39;B&#39;</code>, and <code>&#39;T&#39;</code> in the <code>grid</code>.</li>
</ul>
Breadth-First Search; Array; Matrix; Heap (Priority Queue)
func minPushBox(grid [][]byte) int {
	m, n := len(grid), len(grid[0])
	var si, sj, bi, bj int
	for i, row := range grid {
		for j, c := range row {
			if c == 'S' {
				si, sj = i, j
			} else if c == 'B' {
				bi, bj = i, j
			}
		}
	}
	f := func(i, j int) int {
		return i*n + j
	}
	check := func(i, j int) bool {
		return i >= 0 && i < m && j >= 0 && j < n && grid[i][j] != '#'
	}
	q := [][]int{[]int{f(si, sj), f(bi, bj), 0}}
	vis := make([][]bool, m*n)
	for i := range vis {
		vis[i] = make([]bool, m*n)
	}
	vis[f(si, sj)][f(bi, bj)] = true
	dirs := [5]int{-1, 0, 1, 0, -1}
	for len(q) > 0 {
		p := q[0]
		q = q[1:]
		si, sj, bi, bj = p[0]/n, p[0]%n, p[1]/n, p[1]%n
		d := p[2]
		if grid[bi][bj] == 'T' {
			return d
		}
		for k := 0; k < 4; k++ {
			sx, sy := si+dirs[k], sj+dirs[k+1]
			if !check(sx, sy) {
				continue
			}
			if sx == bi && sy == bj {
				bx, by := bi+dirs[k], bj+dirs[k+1]
				if !check(bx, by) || vis[f(sx, sy)][f(bx, by)] {
					continue
				}
				vis[f(sx, sy)][f(bx, by)] = true
				q = append(q, []int{f(sx, sy), f(bx, by), d + 1})
			} else if !vis[f(sx, sy)][f(bi, bj)] {
				vis[f(sx, sy)][f(bi, bj)] = true
				q = append([][]int{[]int{f(sx, sy), f(bi, bj), d}}, q...)
			}
		}
	}
	return -1
}