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| 1 | +/* |
| 2 | + * @lc app=leetcode.cn id=120 lang=golang |
| 3 | + * |
| 4 | + * [120] 三角形最小路径和 |
| 5 | + * |
| 6 | + * https://leetcode-cn.com/problems/triangle/description/ |
| 7 | + * |
| 8 | + * algorithms |
| 9 | + * Medium (68.47%) |
| 10 | + * Likes: 1012 |
| 11 | + * Dislikes: 0 |
| 12 | + * Total Accepted: 225.7K |
| 13 | + * Total Submissions: 329.3K |
| 14 | + * Testcase Example: '[[2],[3,4],[6,5,7],[4,1,8,3]]' |
| 15 | + * |
| 16 | + * 给定一个三角形 triangle ,找出自顶向下的最小路径和。 |
| 17 | + * |
| 18 | + * 每一步只能移动到下一行中相邻的结点上。相邻的结点 在这里指的是 下标 与 上一层结点下标 相同或者等于 上一层结点下标 + 1 |
| 19 | + * 的两个结点。也就是说,如果正位于当前行的下标 i ,那么下一步可以移动到下一行的下标 i 或 i + 1 。 |
| 20 | + * |
| 21 | + * |
| 22 | + * |
| 23 | + * 示例 1: |
| 24 | + * |
| 25 | + * |
| 26 | + * 输入:triangle = [[2],[3,4],[6,5,7],[4,1,8,3]] |
| 27 | + * 输出:11 |
| 28 | + * 解释:如下面简图所示: |
| 29 | + * 2 |
| 30 | + * 3 4 |
| 31 | + * 6 5 7 |
| 32 | + * 4 1 8 3 |
| 33 | + * 自顶向下的最小路径和为 11(即,2 + 3 + 5 + 1 = 11)。 |
| 34 | + * |
| 35 | + * |
| 36 | + * 示例 2: |
| 37 | + * |
| 38 | + * |
| 39 | + * 输入:triangle = [[-10]] |
| 40 | + * 输出:-10 |
| 41 | + * |
| 42 | + * |
| 43 | + * |
| 44 | + * |
| 45 | + * 提示: |
| 46 | + * |
| 47 | + * |
| 48 | + * 1 |
| 49 | + * triangle[0].length == 1 |
| 50 | + * triangle[i].length == triangle[i - 1].length + 1 |
| 51 | + * -10^4 |
| 52 | + * |
| 53 | + * |
| 54 | + * |
| 55 | + * |
| 56 | + * 进阶: |
| 57 | + * |
| 58 | + * |
| 59 | + * 你可以只使用 O(n) 的额外空间(n 为三角形的总行数)来解决这个问题吗? |
| 60 | + * |
| 61 | + * |
| 62 | + */ |
| 63 | + |
| 64 | +// @lc code=start |
| 65 | +func minimumTotal(triangle [][]int) int { |
| 66 | + |
| 67 | + row := len(triangle) |
| 68 | + |
| 69 | + dp := make([][]int, row) |
| 70 | + for i := 0; i < row; i++ { |
| 71 | + dp[i] = make([]int, len(triangle[i])) |
| 72 | + } |
| 73 | + |
| 74 | + dp[0][0] = triangle[0][0] |
| 75 | + for i := 1; i < row; i++ { |
| 76 | + for j := 0; j < len(triangle[i]); j++ { |
| 77 | + if j == 0 { |
| 78 | + dp[i][0] = dp[i-1][0] + triangle[i][0] |
| 79 | + } else if j == len(triangle[i])-1 { |
| 80 | + dp[i][j] = dp[i-1][j-1] + triangle[i][j] |
| 81 | + } else { |
| 82 | + dp[i][j] = min(dp[i-1][j], dp[i-1][j-1]) + triangle[i][j] |
| 83 | + } |
| 84 | + } |
| 85 | + } |
| 86 | + |
| 87 | + return minNum(dp[row-1]) |
| 88 | +} |
| 89 | + |
| 90 | +func min(x, y int) int { |
| 91 | + if x < y { |
| 92 | + return x |
| 93 | + } |
| 94 | + return y |
| 95 | +} |
| 96 | + |
| 97 | +func minNum(arr []int) int { |
| 98 | + ans := arr[0] |
| 99 | + |
| 100 | + for i := 1; i < len(arr); i++ { |
| 101 | + if arr[i] < ans { |
| 102 | + ans = arr[i] |
| 103 | + } |
| 104 | + } |
| 105 | + return ans |
| 106 | +} |
| 107 | + |
| 108 | +// @lc code=end |
| 109 | + |
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