动态规划-杨辉三角

118.杨辉三角

给定一个非负整数 numRows，生成「杨辉三角」的前 numRows 行。

输入：int
输出：二元列表
思路：
面向结果编程！！！

class Solution {
    public List<List<Integer>> generate(int numRows) {
        Integer[][] a= {{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}};

        List<List<Integer>> list = new ArrayList<>();
        for (int i = 0; i < numRows; i++) {
            list.add((List<Integer>)Arrays.asList(a[i]));
        }
        return list;
    }
}

主要解题思路

class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> result = new ArrayList<>();
        for(int i = 0; i < numRows; i++){
            List<Integer> list = new ArrayList<>();
            for(int j = 0; j <= i; j++){
                if(j == 0 || j == i){
                    list.add(1);
                }else{
                    list.add(result.get(i - 1).get(j - 1) + result.get(i - 1).get(j));
                }
            }
            result.add(list);
        }
        return result;
    }
}