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算法题/find-valid-matrix-given-row-and-column-sums.html

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+<p>You are given two arrays <code>rowSum</code> and <code>colSum</code> of non-negative integers where <code>rowSum[i]</code> is the sum of the elements in the <code>i<sup>th</sup></code> row and <code>colSum[j]</code> is the sum of the elements of the <code>j<sup>th</sup></code> column of a 2D matrix. In other words, you do not know the elements of the matrix, but you do know the sums of each row and column.</p>
+
+<p>Find any matrix of <strong>non-negative</strong> integers of size <code>rowSum.length x colSum.length</code> that satisfies the <code>rowSum</code> and <code>colSum</code> requirements.</p>
+
+<p>Return <em>a 2D array representing <strong>any</strong> matrix that fulfills the requirements</em>. It&#39;s guaranteed that <strong>at least one </strong>matrix that fulfills the requirements exists.</p>
+
+<p>&nbsp;</p>
+<p><strong>Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> rowSum = [3,8], colSum = [4,7]
+<strong>Output:</strong> [[3,0],
+         [1,7]]
+<strong>Explanation:</strong> 
+0<sup>th</sup> row: 3 + 0 = 3 == rowSum[0]
+1<sup>st</sup> row: 1 + 7 = 8 == rowSum[1]
+0<sup>th</sup> column: 3 + 1 = 4 == colSum[0]
+1<sup>st</sup> column: 0 + 7 = 7 == colSum[1]
+The row and column sums match, and all matrix elements are non-negative.
+Another possible matrix is: [[1,2],
+                             [3,5]]
+</pre>
+
+<p><strong>Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> rowSum = [5,7,10], colSum = [8,6,8]
+<strong>Output:</strong> [[0,5,0],
+         [6,1,0],
+         [2,0,8]]
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= rowSum.length, colSum.length &lt;= 500</code></li>
+	<li><code>0 &lt;= rowSum[i], colSum[i] &lt;= 10<sup>8</sup></code></li>
+	<li><code>sum(rows) == sum(columns)</code></li>
+</ul>