118-PascalsTriangle.go

package main

// 118. Pascal’s Triangle
// 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:
// <img src="https://upload.wikimedia.org/wikipedia/commons/0/0d/PascalTriangleAnimated2.gif" />

// Example 1:
// Input: numRows = 5
// Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

// Example 2:
// Input: numRows = 1
// Output: [[1]]

// Constraints:
//     1 <= numRows <= 30

// # 解题思路
//     给定一个 n，要求打印杨辉三角的前 n 行

import "fmt"

func generate(numRows int) [][]int {
    res := [][]int{}
    for i := 0; i < numRows; i++ { // 循环 numRows
        row := []int{}
        for j := 0; j < i+1; j++ { // 每次 循环 i + 1
            if j == 0 || j == i { // 如果是开头或者最后 都是 1
                row = append(row, 1)
            } else if i > 1 { // 0,1 都是 1,2以后开始计算
                // result[i-1][j-1]  上前
                // result[i-1][j] 上
                row = append(row, res[i-1][j-1] + res[i-1][j])
            }
        }
        res = append(res, row)
    }
    return res
}

// best solution
func generate1(numRows int) [][]int {
    res := make([][]int,numRows)
    res[0] = make([]int, 1)
    res[0] = append([]int{1}) // 直接加上0的 少一次循环

    for i := 1; i < numRows; i++ {
        res[i] = append(res[i], 1) // 开头是 1
        for j := 1; j < len(res[i-1]); j++ { // 只循环 1 - 上一层长度
            res[i] = append(res[i], res[i-1][j-1] + res[i-1][j])
        }
        res[i] = append(res[i], 1) // 结尾也 1
    }
    return res
}

func main() {
    // Example 1:
    // Input: numRows = 5
    // Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
    fmt.Printf("generate(5) = %v\n",generate(5)) // [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
    // Example 2:
    // Input: numRows = 1
    // Output: [[1]]
    fmt.Printf("generate(1) = %v\n",generate(1)) // [[1]]

    fmt.Printf("generate(8) = %v\n",generate(8)) // [[1] [1 1] [1 2 1] [1 3 3 1] [1 4 6 4 1] [1 5 10 10 5 1] [1 6 15 20 15 6 1] [1 7 21 35 35 21 7 1]]
    fmt.Printf("generate(30) = %v\n",generate(30)) //

    fmt.Printf("generate1(1) = %v\n",generate1(1)) // [[1]]
    fmt.Printf("generate1(5) = %v\n",generate1(5)) // [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
    fmt.Printf("generate1(8) = %v\n",generate1(8)) // [[1] [1 1] [1 2 1] [1 3 3 1] [1 4 6 4 1] [1 5 10 10 5 1] [1 6 15 20 15 6 1] [1 7 21 35 35 21 7 1]]
    fmt.Printf("generate1(30) = %v\n",generate1(30)) // [[1] [1 1] [1 2 1] [1 3 3 1] [1 4 6 4 1] [1 5 10 10 5 1] [1 6 15 20 15 6 1] [1 7 21 35 35 21 7 1] [1 8 28 56 70 56 28 8 1] [1 9 36 84 126 126 84 36 9 1] [1 10 45 120 210 252 210 120 45 10 1] [1 11 55 165 330 462 462 330 165 55 11 1] [1 12 66 220 495 792 924 792 495 220 66 12 1] [1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1] [1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1] [1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1] [1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1] [1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1] [1 18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816 153 18 1] [1 19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876 969 171 19 1] [1 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1] [1 21 210 1330 5985 20349 54264 116280 203490 293930 352716 352716 293930 203490 116280 54264 20349 5985 1330 210 21 1] [1 22 231 1540 7315 26334 74613 170544 319770 497420 646646 705432 646646 497420 319770 170544 74613 26334 7315 1540 231 22 1] [1 23 253 1771 8855 33649 100947 245157 490314 817190 1144066 1352078 1352078 1144066 817190 490314 245157 100947 33649 8855 1771 253 23 1] [1 24 276 2024 10626 42504 134596 346104 735471 1307504 1961256 2496144 2704156 2496144 1961256 1307504 735471 346104 134596 42504 10626 2024 276 24 1] [1 25 300 2300 12650 53130 177100 480700 1081575 2042975 3268760 4457400 5200300 5200300 4457400 3268760 2042975 1081575 480700 177100 53130 12650 2300 300 25 1] [1 26 325 2600 14950 65780 230230 657800 1562275 3124550 5311735 7726160 9657700 10400600 9657700 7726160 5311735 3124550 1562275 657800 230230 65780 14950 2600 325 26 1] [1 27 351 2925 17550 80730 296010 888030 2220075 4686825 8436285 13037895 17383860 20058300 20058300 17383860 13037895 8436285 4686825 2220075 888030 296010 80730 17550 2925 351 27 1] [1 28 378 3276 20475 98280 376740 1184040 3108105 6906900 13123110 21474180 30421755 37442160 40116600 37442160 30421755 21474180 13123110 6906900 3108105 1184040 376740 98280 20475 3276 378 28 1] [1 29 406 3654 23751 118755 475020 1560780 4292145 10015005 20030010 34597290 51895935 67863915 77558760 77558760 67863915 51895935 34597290 20030010 10015005 4292145 1560780 475020 118755 23751 3654 406 29 1]]
}