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krahets
2023-11-17 00:35:19 +08:00
parent c7794e1a84
commit 5ae2d5e925
17 changed files with 229 additions and 178 deletions
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docs/chapter_dynamic_programming/dp_solution_pipeline.md
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@@ -326,7 +326,7 @@ $$
```c title="min_path_sum.c"
/* 最小路径和：暴力搜索 */
int minPathSumDFS(int gridCols, int grid[][gridCols], int i, int j) {
int minPathSumDFS(int grid[MAX_SIZE][MAX_SIZE], int i, int j) {
// 若为左上角单元格，则终止搜索
if (i == 0 && j == 0) {
return grid[0][0];
@@ -336,10 +336,10 @@ $$
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 up = minPathSumDFS(gridCols, grid, i - 1, j);
int left = minPathSumDFS(gridCols, grid, i, j - 1);
int up = minPathSumDFS(grid, i - 1, j);
int left = minPathSumDFS(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;
return myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;
}
```
@@ -646,7 +646,7 @@ $$
```c title="min_path_sum.c"
/* 最小路径和：记忆化搜索 */
int minPathSumDFSMem(int gridCols, int grid[][gridCols], int mem[][gridCols], int i, int j) {
int minPathSumDFSMem(int grid[MAX_SIZE][MAX_SIZE], int mem[MAX_SIZE][MAX_SIZE], int i, int j) {
// 若为左上角单元格，则终止搜索
if (i == 0 && j == 0) {
return grid[0][0];
@@ -660,10 +660,10 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
int up = minPathSumDFSMem(gridCols, grid, mem, i - 1, j);
int left = minPathSumDFSMem(gridCols, grid, mem, i, j - 1);
int up = minPathSumDFSMem(grid, mem, i - 1, j);
int left = 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] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;
mem[i][j] = myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;
return mem[i][j];
}
```
@@ -984,9 +984,12 @@ $$
```c title="min_path_sum.c"
/* 最小路径和：动态规划 */
int minPathSumDP(int gridCols, int grid[][gridCols], int n, int m) {
int minPathSumDP(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {
// 初始化 dp 表
int dp[n][m];
int **dp = malloc(n * sizeof(int *));
for (int i = 0; i < n; i++) {
dp[i] = calloc(m, sizeof(int));
}
dp[0][0] = grid[0][0];
// 状态转移：首行
for (int j = 1; j < m; j++) {
@@ -999,10 +1002,15 @@ $$
// 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];
dp[i][j] = myMin(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
}
}
return dp[n - 1][m - 1];
int res = dp[n - 1][m - 1];
// 释放内存
for (int i = 0; i < n; i++) {
free(dp[i]);
}
return res;
}
```
@@ -1344,9 +1352,9 @@ $$
```c title="min_path_sum.c"
/* 最小路径和：空间优化后的动态规划 */
int minPathSumDPComp(int gridCols, int grid[][gridCols], int n, int m) {
int minPathSumDPComp(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {
// 初始化 dp 表
int dp[m];
int *dp = calloc(m, sizeof(int));
// 状态转移：首行
dp[0] = grid[0][0];
for (int j = 1; j < m; j++) {
@@ -1358,10 +1366,13 @@ $$
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];
dp[j] = myMin(dp[j - 1], dp[j]) + grid[i][j];
}
}
return dp[m - 1];
int res = dp[m - 1];
// 释放内存
free(dp);
return res;
}
```