# ---
# title: 1605. Find Valid Matrix Given Row and Column Sums
# id: problem1605
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Greedy
# link: <https://leetcode.com/problems/find-valid-matrix-given-row-and-column-sums/description/>
# hidden: true
# ---
# 
# You are given two arrays `rowSum` and `colSum` of non-negative integers where
# `rowSum[i]` is the sum of the elements in the `ith` row and `colSum[j]` is the
# sum of the elements of the `jth` 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.
# 
# Find any matrix of **non-negative** integers of size `rowSum.length x
# colSum.length` that satisfies the `rowSum` and `colSum` requirements.
# 
# Return _a 2D array representing **any** matrix that fulfills the
# requirements_. It's guaranteed that **at least one** matrix that fulfills the
# requirements exists.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: rowSum = [3,8], colSum = [4,7]
#     Output: [[3,0],
#              [1,7]]
#     Explanation:
#     0th row: 3 + 0 = 0 == rowSum[0]
#     1st row: 1 + 7 = 8 == rowSum[1]
#     0th column: 3 + 1 = 4 == colSum[0]
#     1st 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]]
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: rowSum = [5,7,10], colSum = [8,6,8]
#     Output: [[0,5,0],
#              [6,1,0],
#              [2,0,8]]
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: rowSum = [14,9], colSum = [6,9,8]
#     Output: [[0,9,5],
#              [6,0,3]]
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: rowSum = [1,0], colSum = [1]
#     Output: [[1],
#              [0]]
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: rowSum = [0], colSum = [0]
#     Output: [[0]]
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= rowSum.length, colSum.length <= 500`
#   * `0 <= rowSum[i], colSum[i] <= 108`
#   * `sum(rows) == sum(columns)`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
