From bcdc69de4252f476da296d3095af61ab9210a7be Mon Sep 17 00:00:00 2001 From: SunnyQJm Date: Tue, 7 Apr 2020 12:31:09 +0800 Subject: [PATCH] add: homework6 --- .../image-20200328175231308.png | Bin 0 -> 19999 bytes .../image-20200328215223724.png | Bin 0 -> 20075 bytes .../image-20200328220025887.png | Bin 0 -> 19524 bytes .../image-20200407102849523.png | Bin 0 -> 19920 bytes .../image-20200407105454180.png | Bin 0 -> 19744 bytes .../image-20200407122505839.png | Bin 0 -> 19109 bytes AlgorithmHomework6.md | 123 ++++++++++++++++++ 7 files changed, 123 insertions(+) create mode 100644 AlgorithmHomework6.assets/image-20200328175231308.png create mode 100644 AlgorithmHomework6.assets/image-20200328215223724.png create mode 100644 AlgorithmHomework6.assets/image-20200328220025887.png create mode 100644 AlgorithmHomework6.assets/image-20200407102849523.png create mode 100644 AlgorithmHomework6.assets/image-20200407105454180.png create mode 100644 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- 首先判断长度为1的子串,再判断长度为2的子串,再判断长度为3的子串,以此类推。 + + - **Leetcode提交结果:** + + ![image-20200407102849523](AlgorithmHomework6.assets/image-20200407102849523.png) + + - **代码:** + + ```python + class Solution: + def longestPalindrome(self, s: str) -> str: + arr = [[False] * len(s) for i in range(len(s))] + for i in range(len(s)): + arr[i][i] = True + maxLen, maxStrStart, maxStrEnd = 1, 0, 1 + for span in range(1, len(s)): + left, right = 0, span + while right < len(s): + arr[left][right] = True if s[left] == s[right] and (span == 1 or arr[left + 1][right - 1]) else False + if arr[left][right] and right - left + 1 > maxLen: + maxLen, maxStrStart, maxStrEnd = right - left + 1, left, right + 1 + left, right = left + 1, right + 1 + return s[maxStrStart: maxStrEnd] + ``` + +- ### Leetcode problem 64 + + > [最小路径和](https://leetcode-cn.com/problems/minimum-path-sum/) + + - **算法思路:** + + - 采用动态规划的思想,自右下角向左上脚遍历。 + + - 首先将最下面一排的路径开销自右往左以此叠加,把最右边一排的路径开销自下往上以此叠加,接着其它情况使用与下述状态转换方程: + + $$ + P(i, j) = \left\{ \begin{array}{ll} + P(i, j) + P(i + 1, j) & \textrm{if $ P(i, j + 1) >= P(j + 1) $}\\ + P(i, j) + P(i, j + 1) & \textrm{if $ P(i, j + 1) < P(j + 1) $}\\ + \end{array} \right. + $$ + + - **Leetcode提交结果:** + + ![image-20200407105454180](AlgorithmHomework6.assets/image-20200407105454180.png) + + - **代码:** + + ```python + class Solution: + def minPathSum(self, grid: List[List[int]]) -> int: + rowNum, colNum = len(grid), len(grid[0]) + for col in range(colNum - 2, -1, -1): + grid[rowNum - 1][col] = grid[rowNum - 1][col] + grid[rowNum - 1][col + 1] + for row in range(rowNum - 2, -1, -1): + grid[row][colNum - 1] = grid[row][colNum - 1] + grid[row + 1][colNum - 1] + for col in range(colNum - 2, -1, -1): + for row in range(rowNum - 2, -1, -1): + grid[row][col] = grid[row][col] + min(grid[row + 1][col], grid[row][col + 1]) + return grid[0][0] + ``` + +- ### Leetcode problem 120 + + > [三角形最小路径和](https://leetcode-cn.com/problems/triangle/) + + - **算法思路:** + + - 用动态规划的思想,自底向上一次计算到当前访问节点到叶子节点的最短路径; + + - 状态转移方程如下: + + $$ + P(row, index) = \left\{ \begin{array}{ll} + P(row, index) & \textrm{if $ row == len(triangle) - 1 $}\\ + P(row, index) + min(P(row + 1, index), P(row + 1, index + 1))& \textrm{if $ P(i, j + 1) < P(j + 1) $}\\ + \end{array} \right. + $$ + + - **Leetcode提交结果:** + + ![image-20200407122505839](AlgorithmHomework6.assets/image-20200407122505839.png) + + - **代码:** + + ```python + class Solution: + def minimumTotal(self, triangle: List[List[int]]) -> int: + for row in range(len(triangle) - 2, -1, -1): + for index in range(len(triangle[row])): + triangle[row][index] = triangle[row][index] + min(triangle[row + 1][index], triangle[row + 1][index + 1]) + return triangle[0][0] + ``` + + \ No newline at end of file