From 1364bc52e71a606c2ec5eb522be73e86e5fb53d4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=8E=8B=E4=BD=9C=E5=8B=8B?= <59754483+Zuoxun@users.noreply.github.com> Date: Sat, 7 Oct 2023 21:36:52 +0800 Subject: [PATCH] Add Min path sum in C code (#831) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Update vector.h 增加功能列表： 获取向量的第 i 个元素 设置向量的第 i 个元素 向量扩容 向量缩容 向量插入元素 向量删除元素 向量交换元素 向量是否为空 向量是否已满 向量是否相等 对向量内部进行排序（升序/降序） 对向量某段数据排序（升序/降序） * Create hanota.c * 新增binary_search_recur.c * Update vector.h * Delete codes/c/chapter_divide_and_conquer directory * Update vector.h * Create binary_search_recur.c * Delete codes/chapter_divide_and_conquer directory * Update vector.h * old vector.h * Create min_path_sum.c * Update min_path_sum.c * Update min_path_sum.c * Create CMakeLists.txt * Update min_path_sum.c --------- Co-authored-by: Yudong Jin --- .../CMakeLists.txt | 1 + .../min_path_sum.c | 120 ++++++++++++++++++ 2 files changed, 121 insertions(+) create mode 100644 codes/c/chapter_dynamic_programming/min_path_sum.c diff --git a/codes/c/chapter_dynamic_programming/CMakeLists.txt b/codes/c/chapter_dynamic_programming/CMakeLists.txt index fd58c2ea9..b54139627 100644 --- a/codes/c/chapter_dynamic_programming/CMakeLists.txt +++ b/codes/c/chapter_dynamic_programming/CMakeLists.txt @@ -1,2 +1,3 @@ +add_executable(min_path_sum min_path_sum.c) add_executable(knapsack knapsack.c) add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c) diff --git a/codes/c/chapter_dynamic_programming/min_path_sum.c b/codes/c/chapter_dynamic_programming/min_path_sum.c new file mode 100644 index 000000000..4a6526b93 --- /dev/null +++ b/codes/c/chapter_dynamic_programming/min_path_sum.c @@ -0,0 +1,120 @@ +/** + * File: min_path_sum.c + * Created Time: 2023-10-02 + * Author: Zuoxun (845242523@qq.com) + */ + +#include "../utils/common.h" + +/* 求最小值 */ +int min(int a, int b) { + return a < b ? a : b; +} + +/* 最小路径和：暴力搜索 */ +int minPathSumDFS(int gridCols, int grid[][gridCols], int i, int j) { + // 若为左上角单元格，则终止搜索 + if (i == 0 && j == 0) { + return grid[0][0]; + } + // 若行列索引越界，则返回 +∞ 代价 + if (i < 0 || j < 0) { + return INT_MAX; + } + // 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价 + int left = minPathSumDFS(gridCols, grid, i - 1, j); + int up = minPathSumDFS(gridCols, grid, i, j - 1); + // 返回从左上角到 (i, j) 的最小路径代价 + return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX; +} + +/* 最小路径和：记忆化搜索 */ +int minPathSumDFSMem(int gridCols, int grid[][gridCols], int mem[][gridCols], int i, int j) { + // 若为左上角单元格，则终止搜索 + if (i == 0 && j == 0) { + return grid[0][0]; + } + // 若行列索引越界，则返回 +∞ 代价 + if (i < 0 || j < 0) { + return INT_MAX; + } + // 若已有记录，则直接返回 + if (mem[i][j] != -1) { + return mem[i][j]; + } + // 左边和上边单元格的最小路径代价 + int left = minPathSumDFSMem(gridCols, grid, mem, i - 1, j); + int up = minPathSumDFSMem(gridCols, grid, mem, i, j - 1); + // 记录并返回左上角到 (i, j) 的最小路径代价 + mem[i][j] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX; + return mem[i][j]; +} + +/* 最小路径和：动态规划 */ +int minPathSumDP(int gridCols, int grid[][gridCols], int n, int m) { + // 初始化 dp 表 + int dp[n][m]; + dp[0][0] = grid[0][0]; + // 状态转移：首行 + for (int j = 1; j < m; j++) { + dp[0][j] = dp[0][j - 1] + grid[0][j]; + } + // 状态转移：首列 + for (int i = 1; i < n; i++) { + dp[i][0] = dp[i - 1][0] + grid[i][0]; + } + // 状态转移：其余行列 + for (int i = 1; i < n; i++) { + for (int j = 1; j < m; j++) { + dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]; + } + } + return dp[n - 1][m - 1]; +} + +/* 最小路径和：空间优化后的动态规划 */ +int minPathSumDPComp(int gridCols, int grid[][gridCols], int n, int m) { + // 初始化 dp 表 + int dp[m]; + // 状态转移：首行 + dp[0] = grid[0][0]; + for (int j = 1; j < m; j++) { + dp[j] = dp[j - 1] + grid[0][j]; + } + // 状态转移：其余行 + for (int i = 1; i < n; i++) { + // 状态转移：首列 + dp[0] = dp[0] + grid[i][0]; + // 状态转移：其余列 + for (int j = 1; j < m; j++) { + dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]; + } + } + return dp[m - 1]; +} + +/* Driver Code */ +int main() { + int grid[][4] = {{1, 3, 1, 5}, {2, 2, 4, 2}, {5, 3, 2, 1}, {4, 3, 5, 2}}; + int n = sizeof(grid) / sizeof(grid[0]), m = sizeof(grid[0]) / sizeof(grid[0][0]); + + // 暴力搜索 + int res = minPathSumDFS(m, grid, n - 1, m - 1); + printf("从左上角到右下角的最小路径和为 %d\n", res); + + // 记忆化搜索 + int mem[n][m]; + memset(mem, -1, sizeof(mem)); + res = minPathSumDFSMem(m, grid, mem, n - 1, m - 1); + printf("从左上角到右下角的最小路径和为 %d\n", res); + + // 动态规划 + res = minPathSumDP(m, grid, n, m); + printf("从左上角到右下角的最小路径和为 %d\n", res); + + // 空间优化后的动态规划 + res = minPathSumDPComp(m, grid, n, m); + printf("从左上角到右下角的最小路径和为 %d\n", res); + + return 0; +}