介绍

给定一个二维矩阵，其中每一个元素代表通过该格子的代价，计算从左上角到右下角的最小代价及其路径。

演示

实现

JavaScript

// Problem Statement => https://www.youtube.com/watch?v=lBRtnuxg-gU
/*
Find the min cost path from top-left to bottom-right in matrix
>>> minCostPath([[2, 1], [3, 1], [4, 2]])
>>> 6
*/
const minCostPath = (matrix) => {
  const n = matrix.length
  const m = matrix[0].length

  // moves[i][j] => minimum number of moves to reach cell i, j
  const moves = new Array(n)
  for (let i = 0; i < moves.length; i++) moves[i] = new Array(m)

  // base conditions
  moves[0][0] = matrix[0][0] // to reach cell (0, 0) from (0, 0) is of no moves
  for (let i = 1; i < m; i++) moves[0][i] = moves[0][i - 1] + matrix[0][i]
  for (let i = 1; i < n; i++) moves[i][0] = moves[i - 1][0] + matrix[i][0]

  for (let i = 1; i < n; i++) {
    for (let j = 1; j < m; j++) moves[i][j] = Math.min(moves[i - 1][j], moves[i][j - 1]) + matrix[i][j]
  }

  return moves[n - 1][m - 1]
}