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leetcode-problemset/leetcode-cn/problem (Chinese)/给定行和列的和求可行矩阵 [find-valid-matrix-given-row-and-column-sums].html

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<p>给你两个非负整数数组&nbsp;<code>rowSum</code>&nbsp;<code>colSum</code>&nbsp;,其中&nbsp;<code>rowSum[i]</code>&nbsp;是二维矩阵中第 <code>i</code>&nbsp;行元素的和, <code>colSum[j]</code>&nbsp;是第 <code>j</code>&nbsp;列元素的和。换言之你不知道矩阵里的每个元素,但是你知道每一行和每一列的和。</p>
<p>请找到大小为&nbsp;<code>rowSum.length x colSum.length</code>&nbsp;的任意 <strong>非负整数</strong>&nbsp;矩阵,且该矩阵满足&nbsp;<code>rowSum</code>&nbsp;<code>colSum</code>&nbsp;的要求。</p>
<p>请你返回任意一个满足题目要求的二维矩阵,题目保证存在 <strong>至少一个</strong>&nbsp;可行矩阵。</p>
<p>&nbsp;</p>
<p><strong>示例 1</strong></p>
<pre>
<strong>输入:</strong>rowSum = [3,8], colSum = [4,7]
<strong>输出:</strong>[[3,0],
[1,7]]
<strong>解释:</strong>
第 0 行3 + 0 = 3 == rowSum[0]
第 1 行1 + 7 = 8 == rowSum[1]
第 0 列3 + 1 = 4 == colSum[0]
第 1 列0 + 7 = 7 == colSum[1]
行和列的和都满足题目要求,且所有矩阵元素都是非负的。
另一个可行的矩阵为:[[1,2],
[3,5]]
</pre>
<p><strong>示例 2</strong></p>
<pre>
<strong>输入:</strong>rowSum = [5,7,10], colSum = [8,6,8]
<strong>输出:</strong>[[0,5,0],
[6,1,0],
[2,0,8]]
</pre>
<p><strong>示例 3</strong></p>
<pre>
<strong>输入:</strong>rowSum = [14,9], colSum = [6,9,8]
<strong>输出:</strong>[[0,9,5],
[6,0,3]]
</pre>
<p><strong>示例 4</strong></p>
<pre>
<strong>输入:</strong>rowSum = [1,0], colSum = [1]
<strong>输出:</strong>[[1],
[0]]
</pre>
<p><strong>示例 5</strong></p>
<pre>
<strong>输入:</strong>rowSum = [0], colSum = [0]
<strong>输出:</strong>[[0]]
</pre>
<p>&nbsp;</p>
<p><strong>提示:</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(rowSum) == sum(colSum)</code></li>
</ul>