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| 1 | +Problem Description |
| 2 | + |
| 3 | +/* |
| 4 | +Given a 2D integer array A of size M x N, you need to find a path from top left to bottom right which minimizes the sum of all numbers along its path. |
| 5 | +
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| 6 | +NOTE: You can only move either down or right at any point in time. |
| 7 | +
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| 8 | +
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| 9 | +
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| 10 | +Input Format |
| 11 | +First and only argument is an 2D integer array A of size M x N. |
| 12 | +
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| 13 | +
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| 14 | +
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| 15 | +Output Format |
| 16 | +Return a single integer denoting the minimum sum of a path from cell (1, 1) to cell (M, N). |
| 17 | +
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| 18 | +
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| 19 | +
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| 20 | +Example Input |
| 21 | +Input 1: |
| 22 | +
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| 23 | +A = [ [1, 3, 2] |
| 24 | +[4, 3, 1] |
| 25 | +[5, 6, 1] |
| 26 | +] |
| 27 | +
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| 28 | +
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| 29 | +Example Output |
| 30 | +Output 1: |
| 31 | +
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| 32 | +9 |
| 33 | +
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| 34 | +
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| 35 | +Example Explanation |
| 36 | +Explanation 1: |
| 37 | +
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| 38 | +The path is 1 -> 3 -> 2 -> 1 -> 1 |
| 39 | +So ( 1 + 3 + 2 + 1 + 1) = 8 |
| 40 | +*/ |
| 41 | + |
| 42 | +public class Solution { |
| 43 | +public int minPathSum(ArrayList<ArrayList<Integer>> A) { |
| 44 | +int m = A.size(); |
| 45 | +int n = A.get(0).size(); |
| 46 | +int[][] path = new int[m][n]; |
| 47 | +path[0][0] = A.get(0).get(0); |
| 48 | +for(int i = 0; i<m; i++) |
| 49 | +{ |
| 50 | +for(int j = 0; j<n; j++) |
| 51 | +{ |
| 52 | +if(i == 0 && j == 0) |
| 53 | +continue; |
| 54 | +if(i== 0 ) |
| 55 | +path[i][j] = A.get(i).get(j) + path[i][j-1]; |
| 56 | +else if(j == 0) |
| 57 | +path[i][j] = A.get(i).get(j) + path[i-1][j]; |
| 58 | +else |
| 59 | +path[i][j] = Math.min(path[i-1][j], path[i][j-1]) + A.get(i).get(j); |
| 60 | +} |
| 61 | +} |
| 62 | +return path[m-1][n-1]; |
| 63 | +} |
| 64 | +} |
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