是leetcode的題目,題目如下(直接複製的):
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 = 3 == 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]]
心得:
看來看去這一題主要是要知道這個問題的解法,就像魔術方塊有公式解,
這個問題應該也有類似的公式解,應該不是考推導而是考公式解如何轉化成Code。
一開始我是沒碰過這個問題的,所以卡了一下,要推導出公式還是有點難度的QQ
所以看了一下Hint,Hint中提到大概做法,可能是公式之一吧,其實也是有點懷疑真的嗎XD?
Hint 1
Find the smallest rowSum or colSum, and let it be x. Place that number in the grid, and subtract x from rowSum and colSum. Continue until all the sums are satisfied.
一步一步測試後確認可行。就像魔術方塊公式解也有多種,應該也是有更簡化的方法的,這邊就不繼續研究了。
最後如下;
1 | class Solution { |