LeetCode Online Judge 题目C# 练习 - Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Note: You can only move either down or right at any point in time.

递归：

public static int MinimumPathSum(List<List<int>> grid)
{
int m = grid.Count;
int n = grid[0].Count;

return MinimumPathSumRecursive(grid, m - 1, n - 1);
}

public static int MinimumPathSumRecursive(List<List<int>> grid, int x, int y)
{
if (x == 0 && y == 0)
{
return grid[0][0];
}
else if (x == 0)
{
return MinimumPathSumRecursive(grid, 0, y - 1) + grid[0][y];
}
else if (y == 0)
{
return MinimumPathSumRecursive(grid, x - 1, 0) + grid[x][0]; ;
}
else
{
return Math.Min(MinimumPathSumRecursive(grid, x - 1, y), MinimumPathSumRecursive(grid, x, y - 1)) + grid[x][y];
}
}

DP：

public static int MinimumPathSumDP(List<List<int>> grid)
{
int m = grid.Count;
int n = grid[0].Count;

int[,] ret = new int[m, n];

for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (i == 0 && j == 0)
{
ret[i, j] = grid[0][0];
continue;
}
if (i == 0)
{
ret[i, j] = ret[i, j - 1] + grid[i][j];
continue;
}
if (j == 0)
{
ret[i, j] = ret[i - 1, j] + grid[i][j];
continue;
}

if (ret[i - 1, j] <= ret[i, j - 1])
{
ret[i, j] = ret[i - 1, j] + grid[i][j];
continue;
}
else
{
ret[i, j] = ret[i, j - 1] + grid[i][j];
continue;
}

}
}

return ret[m - 1, n - 1];
}

代码分析：

　　经典的递归(Top-down)，DP(Bottom-up)题。DP一般都比递归来的效率高,主要是每次function 调用都新创建一个stack，但是有些问题递归用的巧，也是让人为之一震！