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.

遞歸：

1 public static int MinimumPathSum(List<List<int>> grid) 2 { 3 int m = grid.Count; 4 int n = grid[0].Count; 5 6 return MinimumPathSumRecursive(grid, m - 1, n - 1); 7 } 8 9 public static int MinimumPathSumRecursive(List<List<int>> grid, int x, int y) 10 { 11 if (x == 0 && y == 0) 12 { 13 return grid[0][0]; 14 } 15 else if (x == 0) 16 { 17 return MinimumPathSumRecursive(grid, 0, y - 1) + grid[0][y]; 18 } 19 else if (y == 0) 20 { 21 return MinimumPathSumRecursive(grid, x - 1, 0) + grid[x][0]; ; 22 } 23 else 24 { 25 return Math.Min(MinimumPathSumRecursive(grid, x - 1, y), MinimumPathSumRecursive(grid, x, y - 1)) + grid[x][y]; 26 } 27 }

DP：

1 public static int MinimumPathSumDP(List<List<int>> grid) 2 { 3 int m = grid.Count; 4 int n = grid[0].Count; 5 6 int[,] ret = new int[m, n]; 7 8 for (int i = 0; i < m; i++) 9 { 10 for (int j = 0; j < n; j++) 11 { 12 if (i == 0 && j == 0) 13 { 14 ret[i, j] = grid[0][0]; 15 continue; 16 } 17 if (i == 0) 18 { 19 ret[i, j] = ret[i, j - 1] + grid[i][j]; 20 continue; 21 } 22 if (j == 0) 23 { 24 ret[i, j] = ret[i - 1, j] + grid[i][j]; 25 continue; 26 } 27 28 if (ret[i - 1, j] <= ret[i, j - 1]) 29 { 30 ret[i, j] = ret[i - 1, j] + grid[i][j]; 31 continue; 32 } 33 else 34 { 35 ret[i, j] = ret[i, j - 1] + grid[i][j]; 36 continue; 37 } 38 39 } 40 } 41 42 return ret[m - 1, n - 1]; 43 }

代碼分析：

　　經典的遞歸(Top-down)，DP(Bottom-up)題。DP一般都比遞歸來的效率高,主要是每次function 調用都新創建一個stack，但是有些問題遞歸用的巧，也是讓人為之一震！

　　

轉載于:https://www.cnblogs.com/etcow/archive/2012/09/29/2707935.html

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