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2023-10-08 01:43:28 +08:00
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commit baac2d11a7
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zh/chapter_dynamic_programming/dp_solution_pipeline.md
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@@ -174,7 +174,7 @@ $$
```csharp title="min_path_sum.cs"
/* 最小路径和：暴力搜索 */
int minPathSumDFS(int[][] grid, int i, int j) {
int MinPathSumDFS(int[][] grid, int i, int j) {
// 若为左上角单元格，则终止搜索
if (i == 0 && j == 0) {
return grid[0][0];
@@ -184,8 +184,8 @@ $$
return int.MaxValue;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
int left = minPathSumDFS(grid, i - 1, j);
int up = minPathSumDFS(grid, i, j - 1);
int left = MinPathSumDFS(grid, i - 1, j);
int up = MinPathSumDFS(grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return Math.Min(left, up) + grid[i][j];
}
@@ -325,7 +325,22 @@ $$
=== "C"
```c title="min_path_sum.c"
[class]{}-[func]{minPathSumDFS}
/* 最小路径和：暴力搜索 */
int minPathSumDFS(int gridCols, int grid[][gridCols], int i, int j) {
// 若为左上角单元格，则终止搜索
if (i == 0 && j == 0) {
return grid[0][0];
}
// 若行列索引越界，则返回 +∞ 代价
if (i < 0 || j < 0) {
return INT_MAX;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
int left = minPathSumDFS(gridCols, grid, i - 1, j);
int up = minPathSumDFS(gridCols, grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;
}
```
=== "Zig"
@@ -443,7 +458,7 @@ $$
```csharp title="min_path_sum.cs"
/* 最小路径和：记忆化搜索 */
int minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {
int MinPathSumDFSMem(int[][] grid, int[][] mem, 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];
@@ -457,8 +472,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
int left = minPathSumDFSMem(grid, mem, i - 1, j);
int up = minPathSumDFSMem(grid, mem, i, j - 1);
int left = MinPathSumDFSMem(grid, mem, i - 1, j);
int up = MinPathSumDFSMem(grid, mem, i, j - 1);
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = Math.Min(left, up) + grid[i][j];
return mem[i][j];
@@ -630,7 +645,27 @@ $$
=== "C"
```c title="min_path_sum.c"
[class]{}-[func]{minPathSumDFSMem}
/* 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];
}
```
=== "Zig"
@@ -750,7 +785,7 @@ $$
```csharp title="min_path_sum.cs"
/* 最小路径和：动态规划 */
int minPathSumDP(int[][] grid) {
int MinPathSumDP(int[][] grid) {
int n = grid.Length, m = grid[0].Length;
// 初始化 dp 表
int[,] dp = new int[n, m];
@@ -948,7 +983,27 @@ $$
=== "C"
```c title="min_path_sum.c"
[class]{}-[func]{minPathSumDP}
/* 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];
}
```
=== "Zig"
@@ -1105,7 +1160,7 @@ $$
```csharp title="min_path_sum.cs"
/* 最小路径和：空间优化后的动态规划 */
int minPathSumDPComp(int[][] grid) {
int MinPathSumDPComp(int[][] grid) {
int n = grid.Length, m = grid[0].Length;
// 初始化 dp 表
int[] dp = new int[m];
@@ -1288,7 +1343,26 @@ $$
=== "C"
```c title="min_path_sum.c"
[class]{}-[func]{minPathSumDPComp}
/* 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];
}
```
=== "Zig"