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文章觀看次數: 702
LeetCode題目翻譯 英文原文如下
Given an integer numRows , return the first numRows of Pascal’s triangle .
In Pascal’s triangle , each number is the sum of the two numbers directly above it as shown:
中文翻譯
給予一個整數 numRows ,回傳巴斯卡三角形的前numRows 列
在巴斯卡三角形裡,每一個數字都會是前兩個數字的加總,如下圖所示(上面那張gif)
題目限制則為最高列數為30
來看下官方的範例
可以直接看向上面的那個gif,陣列的各個子陣列分別就對應到了三角形的各列
分別是1到5列,跟只有1列的區別
解題思路 看到兩數相加等於下一數的,是不是感覺到很熟悉呢
還記得之前提過的 LeetCode #70 爬梯子 的費波那契數 嗎? 巴斯卡三角形 其實就是他的變形呢!
這次也採用與上次類似的作法,不過因為要儲存在陣列裡面
所以可以省下一點暫存的麻煩,直接拿陣列值就好
來看一下程式吧
C# 解決方案 方案1
public class Solution {
public IList<IList<int>> Generate(int numRows) {
List<List<int>>res = new List<List<int>>();
res.Add(new List<int>(){1}); //巧婦難為無米之炊,第一列的值容我寫死
if(numRows!=1) //超過第一列才要計算,合情合理吧?
{
for(int i = 1;i<numRows;i++)
{
List<int>tmp = new List<int>(); //暫存子陣列
for(int j=0;j<=i;j++)
{
int num;
if(j==0 || j==i) //每列第一跟最後的數字都是1,沒甚麼好說的
{
num = 1;
}
else
{
num = res[i-1][j-1]+res[i-1][j];
}
tmp.Add(num);
}
res.Add(tmp); //加回母陣列
}
}
return res.ToArray();
}
}
注意上面的 i 代表的是每一列,j 則是每列中的各個數字
可以看到計算就是拿上面一列的,自已index前一個跟自己index的加總,就會是目前欄位的值
Java解 決方案方案1
class Solution {
public List<List<Integer>> generate(int numRows) {
List<List<Integer>>res = new ArrayList<List<Integer>>();
res.add(Arrays.asList(new Integer[]{1}));
if(numRows!=1)
{
for(int i = 1;i<numRows;i++)
{
List<Integer>tmp = new ArrayList<Integer>();
for(int j=0;j<=i;j++)
{
int num;
if(j==0 || j==i)
{
num = 1;
}
else
{
num = res.get(i-1).get(j-1)+res.get(i-1).get(j);
}
tmp.add(num);
}
res.add(tmp);
}
}
return res;
}
}
運行時間 : 1ms
Python3 解決方案方案1
class Solution:
def generate(self, numRows: int) -> List[List[int]]:
res = [];
res.append([1]);
if numRows!=1:
for i in range(1,numRows):
tmp = [];
for j in range(0,i+1):
if j==0 or j==i :
tmp.append(1);
else:
tmp.append(res[i-1][j-1]+res[i-1][j]);
res.append(tmp);
return res;
JavaScript 解決方案方案1
/**
* @param {number} numRows
* @return {number[][]}
*/
var generate = function(numRows) {
var res = [];
res[0] = [1];
if(numRows!=1)
{
for(let i = 1;i<numRows;i++)
{
let tmp = [];
for(let j=0;j<=i;j++)
{
var num;
if(j==0 || j==i)
{
num = 1;
}
else
{
num = res[i-1][j-1]+res[i-1][j];
}
tmp[j] = num;
}
res[i] = tmp;
}
}
return res;
};
結論 整體上來說,這題算是比較沒有難度的
但在寫過費波那契數 後,不由得感嘆數學家的腦袋
不過是東方還西方,聰明人的想法往往很相似啊
"你知道嗎? 巴斯克起司蛋糕是從巴斯克地區(西班牙及法國)來的喔"
維基百科說的 ⬆原來巴斯克是地名啊…
附上個巴斯卡三角形的好朋友,巴斯克起司蛋糕?
圖片來源 : 蛋糕 – Photo by Syauqy Ayyash on Unsplash
題目連結 : Pascal’s Triangle – LeetCode
🧡如果這篇文章有幫上你的一點點忙,那是我的榮幸
🧡可以的話,幫我的FaceBook 粉絲專頁按個讚,我會很感謝的
✅如有任何疑問,歡迎透過留言或messenger讓我知道 !
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