public int minPathSum(int[][] grid) {

int m = grid.length;

int n = grid[0].length;

int[][] dp = new int[m][n];

for (int i = 0; i < m; i++)

for (int j = 0; j < n; j++)

dp[i][j] = Integer.MAX_VALUE;

dp[0][0] = grid[0][0];

for (int i = 1; i < m; i++)

dp[i][0] = grid[i][0] + dp[i - 1][0];

for (int i = 1; i < n; i++)

dp[0][i] = grid[0][i] + dp[0][i - 1];

for (int i = 0; i < m; i++) {

for (int j = 0; j < n; j++) {

dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];

}

}

return dp[m-1][n-1];

}

/**

public int minPathSum1(int[][] grid) {

if(grid.length == 0) return 0;

int r = grid.length;

int c = grid[0].length;

for(int i=0;i<r; i++) {

for(int j=0; j<c; j++) {

int leftSum = (j>0) ? grid[i][j-1] : Integer.MAX_VALUE;

int topSum = (i>0) ? grid[i-1][j] : Integer.MAX_VALUE;

if(i==0 && j==0) continue;

grid[i][j] += Math.min(leftSum, topSum);

}

}

return grid[r-1][c-1];

}

/**

public int minPathSum2(int[][] grid) {

int[][] memo = new int[grid.length][grid[0].length];

return minPathSumHelper(grid, 0, 0, memo);

}

public int minPathSumHelper(int[][] grid, int row, int col, int[][] memo) {

if(row == grid.length-1 && col == grid[0].length-1) return grid[row][col];

if(memo[row][col] != 0) return memo[row][col];

int rowInc = Integer.MAX_VALUE, colInc = Integer.MAX_VALUE;

if(row < grid.length-1) rowInc = minPathSumHelper(grid, row+1, col, memo);

if(col < grid[0].length-1) colInc = minPathSumHelper(grid, row, col+1, memo);

memo[row][col] = Math.min(rowInc, colInc) + grid[row][col];

return memo[row][col];

}

/**

public int minPathSum3(int[][] grid) {

int[][] dp = new int[grid.length][grid[0].length];

return minPathSum(grid, 0, 0, dp);

}

public int minPathSum(int[][] grid, int i, int j, int[][] dp) {

if (i == grid.length || j == grid[0].length) {

return Integer.MAX_VALUE;

}

if (i == grid.length - 1 && j == grid[0].length - 1) {

return grid[i][j];

}

if (dp[i][j] != 0) {

return dp[i][j];

}

int min = grid[i][j];

min += Math.min(minPathSum(grid, i, j + 1, dp), minPathSum(grid, i + 1, j, dp));

dp[i][j] = min;

return min;

}

public int minPathSum4(int[][] grid) {

int M = grid.length;

if (M == 0) return 0;

int N = grid[0].length;

if (N == 0) return 0;

for (int j=1; j<N; j++) grid[0][j] += grid[0][j-1];

for (int i=1; i<M; i++) grid[i][0] += grid[i-1][0];

for (int i=1; i<M; i++) {

for (int j=1; j<N; j++) {

grid[i][j] += Math.min(grid[i-1][j], grid[i][j-1]);

}

}

return grid[M-1][N-1];

}