64. Minimum Path Sum.md

64. Minimum Path Sum

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leetcode-cn Daily Challenge on July 23th, 2020.

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Difficulty : Medium

Related Topics : Array、Dynamic Programming

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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.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

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same as 62. Unique Paths !

Solution

• mine
  • Java

    • Dynamic Programming

      Runtime: 2 ms, faster than 88.22%, Memory Usage: 42.2 MB, less than 70.01% of Java online submissions

      // O(R*C)time O(1)space
      public int minPathSum(int[][] grid) {
          if (grid == null || grid.length == 0 || grid[0].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++) {
                  if (i == 0 && j == 0) {
                      continue;
                  } else if (i == 0) {
                      grid[i][j] += grid[i][j - 1];
                  } else if (j == 0) {
                      grid[i][j] += grid[i - 1][j];
                  } else {
                      grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]);
                  }
              }
          }
          return grid[r - 1][c - 1];
      }
      

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