【LeetCode】【Study Notes】64. Minimum path sum

64. Minimum Path Sum

Given a m x ngrid of non-negative integers grid, find a path from the upper left corner to the lower right corner that minimizes the sum of numbers on the path.

Note: Only move down or right one step at a time.

Example 1:

输入：grid = [[1,3,1],[1,5,1],[4,2,1]]
输出：7
解释：因为路径 1→3→1→1→1 的总和最小。

Example 2:

输入：grid = [[1,2,3],[4,5,6]]
输出：12

hint:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 100

problem solving ideas

dynamic programming

Learning ideas: After watching this video, you won’t feel that dynamic programming is difficult to learn, the minimum path sum, Leetcode64, lecturer version

1. Initialize the dp table

2. Calculate the minimum path sum of horizontal and vertical coordinates

   • Abscissa

     

   • Y-axis

     

3. Calculate the path sum in the remaining spaces

   • compare path and shortest

     

     • likeGreen path and +grid current paththe smallest
       • The orange area is the calculated value
     • likered path and +grid current paththe smallest
       • The orange area is the calculated value

   • Iterate over the remainder of the inner

     

4. Finally, take dp[rowLength-1] [colLength-1]the minimum path

   

Code

var minPathSum = function(grid) {
    
    
  let rowLength=grid.length;
  let colLength=grid[0].length;
  let dp=new Array(colLength);
  for(let index=0;index<rowLength;index++){
    
    
    dp[index]=new Array(colLength);
  }

  dp[0][0]=grid[0][0];
  for(let index=1;index<colLength;index++){
    
    
    dp[0][index]=dp[0][index-1]+grid[0][index];
  }

  for(let index=1;index<rowLength;index++){
    
    
    dp[index][0]=dp[index-1][0]+grid[index][0];
  }

  for(let row=1;row<rowLength;row++){
    
    
    for(let col=1;col<colLength;col++){
    
    
      dp[row][col]=Math.min(dp[row-1][col],dp[row][col-1])+grid[row][col];
    }
  }
  
  return dp[rowLength-1][colLength-1];
};