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51 lines (47 loc) · 1.21 KB
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// 64. Minimum Path Sum
// Medium
// 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.
/**
* @param grid: a list of lists of integers
* @return: An integer, minimizes the sum of all numbers along its path
*/
const minPathSum = grid => {
let m = grid.length
if (!m) return 0
let n = grid[0].length
if (!n) return 0
let i, j
let dpArr = []
for (i = 0; i < m; i++) {
dpArr[i] = []
}
// 初始化起点
dpArr[0][0] = grid[0][0]
// 初始化可能性固定的0行0列
// 0行
for (i = 1; i < n; i++) {
dpArr[0][i] = dpArr[0][i - 1] + grid[0][i]
}
// 0列
for (i = 1; i < m; i++) {
dpArr[i][0] = dpArr[i - 1][0] + grid[i][0]
}
// 多种可能的点
for (i = 1; i < m; i++) {
for (j = 1; j < n; j++) {
dpArr[i][j] = Math.min(dpArr[i][j - 1], dpArr[i - 1][j]) + grid[i][j]
}
}
// 取出最小的解
return dpArr[m - 1][n - 1]
}