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English Version

题目描述

给定一个非负整数 numRows生成「杨辉三角」的前 numRows 行。

在「杨辉三角」中,每个数是它左上方和右上方的数的和。

 

示例 1:

输入: numRows = 5
输出: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

示例 2:

输入: numRows = 1
输出: [[1]]

 

提示:

  • 1 <= numRows <= 30

解法

先设置每一行首尾元素为 1,其它元素为 0。然后根据杨辉三角,设置每一行其它元素即可。

Python3

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        ans = []
        for i in range(numRows):
            t = [
                1 if j == 0 or j == i else ans[-1][j] + ans[-1][j - 1]
                for j in range(i + 1)
            ]
            ans.append(t)
        return ans

Java

class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> ans = new ArrayList<>();
        for (int i = 0; i < numRows; ++i) {
            List<Integer> t = new ArrayList<>();
            for (int j = 0; j < i + 1; ++j) {
                int v = j == 0 || j == i ? 1 : ans.get(i - 1).get(j) + ans.get(i - 1).get(j - 1);
                t.add(v);
            }
            ans.add(t);
        }
        return ans;
    }
}

TypeScript

function generate(numRows: number): number[][] {
    if (numRows == 0) return [];
    let ans = [[1]];
    for (let i = 1; i < numRows; ++i) {
        ans.push(new Array(i + 1).fill(1));
        let half = i >> 1;
        for (let j = 1; j <= half; ++j) {
            let cur = ans[i - 1][j - 1] + ans[i - 1][j];
            ans[i][j] = cur;
            ans[i][i - j] = cur;
        }
    }
    return ans;
}

C++

class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> ans;
        for (int i = 0; i < numRows; ++i) {
            vector<int> t(i + 1, 1);
            for (int j = 1; j < i; ++j) t[j] = ans[i - 1][j] + ans[i - 1][j - 1];
            ans.push_back(t);
        }
        return ans;
    }
};

Go

func generate(numRows int) [][]int {
	ans := make([][]int, numRows)
	for i := range ans {
		t := make([]int, i+1)
		t[0], t[i] = 1, 1
		for j := 1; j < i; j++ {
			t[j] = ans[i-1][j] + ans[i-1][j-1]
		}
		ans[i] = t
	}
	return ans
}

JavaScript

const generate = function (numRows) {
    let arr = [];
    for (let i = 0; i < numRows; i++) {
        let row = [];
        row[0] = 1;
        row[i] = 1;
        for (let j = 1; j < row.length - 1; j++) {
            row[j] = arr[i - 1][j - 1] + arr[i - 1][j];
        }
        arr.push(row);
    }
    return arr;
};

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