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docs/chapter_dynamic_programming/dp_solution_pipeline.md
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@ -122,8 +122,8 @@ $$
if i < 0 or j < 0:
return inf
# 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
left = min_path_sum_dfs(grid, i - 1, j)
up = min_path_sum_dfs(grid, i, j - 1)
up = min_path_sum_dfs(grid, i - 1, j)
left = min_path_sum_dfs(grid, i, j - 1)
# 返回从左上角到 (i, j) 的最小路径代价
return min(left, up) + grid[i][j]
```
@ -142,8 +142,8 @@ $$
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(grid, i - 1, j);
int up = minPathSumDFS(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;
}
@ -163,8 +163,8 @@ $$
return Integer.MAX_VALUE;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
int left = minPathSumDFS(grid, i - 1, j);
int up = minPathSumDFS(grid, i, j - 1);
int up = minPathSumDFS(grid, i - 1, j);
int left = minPathSumDFS(grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return Math.min(left, up) + grid[i][j];
}
@ -184,8 +184,8 @@ $$
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 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 Math.Min(left, up) + grid[i][j];
}
@ -205,8 +205,8 @@ $$
return math.MaxInt
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
left := minPathSumDFS(grid, i-1, j)
up := minPathSumDFS(grid, i, j-1)
up := minPathSumDFS(grid, i-1, j)
left := minPathSumDFS(grid, i, j-1)
// 返回从左上角到 (i, j) 的最小路径代价
return int(math.Min(float64(left), float64(up))) + grid[i][j]
}
@ -226,8 +226,8 @@ $$
return .max
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
let left = minPathSumDFS(grid: grid, i: i - 1, j: j)
let up = minPathSumDFS(grid: grid, i: i, j: j - 1)
let up = minPathSumDFS(grid: grid, i: i - 1, j: j)
let left = minPathSumDFS(grid: grid, i: i, j: j - 1)
// 返回从左上角到 (i, j) 的最小路径代价
return min(left, up) + grid[i][j]
}
@ -247,8 +247,8 @@ $$
return Infinity;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
const left = minPathSumDFS(grid, i - 1, j);
const up = minPathSumDFS(grid, i, j - 1);
const up = minPathSumDFS(grid, i - 1, j);
const left = minPathSumDFS(grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return Math.min(left, up) + grid[i][j];
}
@ -272,8 +272,8 @@ $$
return Infinity;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
const left = minPathSumDFS(grid, i - 1, j);
const up = minPathSumDFS(grid, i, j - 1);
const up = minPathSumDFS(grid, i - 1, j);
const left = 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];
}
@ -294,8 +294,8 @@ $$
return BigInt.from(2).pow(31).toInt();
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
int left = minPathSumDFS(grid, i - 1, j);
int up = minPathSumDFS(grid, i, j - 1);
int up = minPathSumDFS(grid, i - 1, j);
int left = minPathSumDFS(grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return min(left, up) + grid[i][j];
}
@ -315,8 +315,8 @@ $$
return i32::MAX;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
let left = min_path_sum_dfs(grid, i - 1, j);
let up = min_path_sum_dfs(grid, i, j - 1);
let up = min_path_sum_dfs(grid, i - 1, j);
let left = min_path_sum_dfs(grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
std::cmp::min(left, up) + grid[i as usize][j as usize]
}
@ -336,8 +336,8 @@ $$
return INT_MAX;
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
int left = minPathSumDFS(gridCols, grid, i - 1, j);
int up = minPathSumDFS(gridCols, grid, i, j - 1);
int up = minPathSumDFS(gridCols, grid, i - 1, j);
int left = minPathSumDFS(gridCols, grid, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
return min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;
}
@ -357,8 +357,8 @@ $$
return std.math.maxInt(i32);
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
var left = minPathSumDFS(grid, i - 1, j);
var up = minPathSumDFS(grid, i, j - 1);
var up = minPathSumDFS(grid, i - 1, j);
var 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) + grid[@as(usize, @intCast(i))][@as(usize, @intCast(j))];
}
@ -395,8 +395,8 @@ $$
if mem[i][j] != -1:
return mem[i][j]
# 左边和上边单元格的最小路径代价
left = min_path_sum_dfs_mem(grid, mem, i - 1, j)
up = min_path_sum_dfs_mem(grid, mem, i, j - 1)
up = min_path_sum_dfs_mem(grid, mem, i - 1, j)
left = min_path_sum_dfs_mem(grid, mem, i, j - 1)
# 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = min(left, up) + grid[i][j]
return mem[i][j]
@ -420,8 +420,8 @@ $$
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 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;
return mem[i][j];
@ -446,8 +446,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
int left = minPathSumDFSMem(grid, mem, i - 1, j);
int up = minPathSumDFSMem(grid, mem, i, j - 1);
int up = minPathSumDFSMem(grid, mem, i - 1, j);
int left = minPathSumDFSMem(grid, mem, i, j - 1);
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = Math.min(left, up) + grid[i][j];
return mem[i][j];
@ -472,8 +472,8 @@ $$
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 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] = Math.Min(left, up) + grid[i][j];
return mem[i][j];
@ -498,8 +498,8 @@ $$
return mem[i][j]
}
// 左边和上边单元格的最小路径代价
left := minPathSumDFSMem(grid, mem, i-1, j)
up := minPathSumDFSMem(grid, mem, i, j-1)
up := minPathSumDFSMem(grid, mem, i-1, j)
left := minPathSumDFSMem(grid, mem, i, j-1)
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = int(math.Min(float64(left), float64(up))) + grid[i][j]
return mem[i][j]
@ -524,8 +524,8 @@ $$
return mem[i][j]
}
// 左边和上边单元格的最小路径代价
let left = minPathSumDFSMem(grid: grid, mem: &mem, i: i - 1, j: j)
let up = minPathSumDFSMem(grid: grid, mem: &mem, i: i, j: j - 1)
let up = minPathSumDFSMem(grid: grid, mem: &mem, i: i - 1, j: j)
let left = minPathSumDFSMem(grid: grid, mem: &mem, i: i, j: 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) + grid[i][j]
return mem[i][j]
@ -550,8 +550,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
const left = minPathSumDFSMem(grid, mem, i - 1, j);
const up = minPathSumDFSMem(grid, mem, i, j - 1);
const up = minPathSumDFSMem(grid, mem, i - 1, j);
const left = minPathSumDFSMem(grid, mem, i, j - 1);
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = Math.min(left, up) + grid[i][j];
return mem[i][j];
@ -581,8 +581,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
const left = minPathSumDFSMem(grid, mem, i - 1, j);
const up = minPathSumDFSMem(grid, mem, i, j - 1);
const up = minPathSumDFSMem(grid, mem, i - 1, j);
const 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] = Math.min(left, up) + grid[i][j];
return mem[i][j];
@ -608,8 +608,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
int left = minPathSumDFSMem(grid, mem, i - 1, j);
int up = minPathSumDFSMem(grid, mem, i, j - 1);
int up = minPathSumDFSMem(grid, mem, i - 1, j);
int left = minPathSumDFSMem(grid, mem, i, j - 1);
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = min(left, up) + grid[i][j];
return mem[i][j];
@ -634,8 +634,8 @@ $$
return mem[i as usize][j as usize];
}
// 左边和上边单元格的最小路径代价
let left = min_path_sum_dfs_mem(grid, mem, i - 1, j);
let up = min_path_sum_dfs_mem(grid, mem, i, j - 1);
let up = min_path_sum_dfs_mem(grid, mem, i - 1, j);
let left = min_path_sum_dfs_mem(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 as usize][j as usize] = std::cmp::min(left, up) + grid[i as usize][j as usize];
mem[i as usize][j as usize]
@ -660,8 +660,8 @@ $$
return mem[i][j];
}
// 左边和上边单元格的最小路径代价
int left = minPathSumDFSMem(gridCols, grid, mem, i - 1, j);
int up = minPathSumDFSMem(gridCols, grid, mem, i, j - 1);
int up = minPathSumDFSMem(gridCols, grid, mem, i - 1, j);
int left = minPathSumDFSMem(gridCols, grid, mem, i, j - 1);
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[i][j] = min(left, up) != INT_MAX ? min(left, up) + grid[i][j] : INT_MAX;
return mem[i][j];
@ -686,8 +686,8 @@ $$
return mem[@as(usize, @intCast(i))][@as(usize, @intCast(j))];
}
// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
var left = minPathSumDFSMem(grid, mem, i - 1, j);
var up = minPathSumDFSMem(grid, mem, i, j - 1);
var up = minPathSumDFSMem(grid, mem, i - 1, j);
var left = minPathSumDFSMem(grid, mem, i, j - 1);
// 返回从左上角到 (i, j) 的最小路径代价
// 记录并返回左上角到 (i, j) 的最小路径代价
mem[@as(usize, @intCast(i))][@as(usize, @intCast(j))] = @min(left, up) + grid[@as(usize, @intCast(i))][@as(usize, @intCast(j))];