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.
给定一个包含非负整数的 m x n 网格，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
说明：每次只能向下或者向右移动一步。
示例:
输入: [ [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。
20ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 guard grid.count > 0 else { 4 return 0 5 } 6 let m = grid.count 7 let n = grid[0].count 8 var dp = Array(repeating:0, count: n) 9 dp[0] = grid[0][0] 10 for i in 1..<n { 11 dp[i] = dp[i - 1] + grid[0][i] 12 } 13 for i in 1..<m { 14 for j in 0..<n { 15 if j == 0 { 16 dp[j] += grid[i][0] 17 } else { 18 dp[j] = min(dp[j], dp[j - 1]) + grid[i][j] 19 } 20 } 21 } 22 return dp[n - 1] 23 } 24 }
24ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 guard grid.count>0 else { return 0} 4 var rows = grid.count 5 var cols = grid[0].count 6 var dp = Array(repeating:Array(repeating:0,count:cols),count:rows) 7 8 9 dp[0][0] = grid[0][0] 10 var row = 0, col = 0 11 for row in 1..<rows { 12 dp[row][0] = dp[row-1][0] + grid[row][0] 13 } 14 15 for col in 1..<cols { 16 dp[0][col] = dp[0][col-1] + grid[0][col] 17 } 18 19 for row in 1..<rows { 20 for col in 1..<cols { 21 dp[row][col] = min(dp[row-1][col],dp[row][col-1]) + grid[row][col] 22 } 23 } 24 25 26 return dp[rows-1][cols-1] 27 28 } 29 }
24ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 guard grid.count > 0 else { 4 return 0 5 } 6 var row = [Int].init(repeating: 0, count: grid[0].count+1) 7 for i in 1..<row.count { 8 row[i] = row[i-1] + grid[0][i-1] 9 } 10 11 for i in 1..<grid.count { 12 row[1] = row[1] + grid[i][0] 13 for j in 1..<grid[0].count { 14 row[j+1] = row[j] > row[j+1] ? row[j+1] + grid[i][j] : row[j] + grid[i][j] 15 } 16 } 17 let resultIndex = grid[0].count 18 return row[resultIndex] 19 } 20 }
28ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 var grid = grid 4 let m = grid.count 5 let n = grid.first!.count 6 func top(_ row: Int, _ column: Int) -> Int { 7 return row-1 >= 0 ? grid[row-1][column] : 100500 8 } 9 func left(_ row: Int, _ column: Int) -> Int { 10 return column-1 >= 0 ? grid[row][column-1] : 100500 11 } 12 for row in 0..<m { 13 for column in 0..<n { 14 if row == 0 && column == 0 { continue } 15 grid[row][column] += min(top(row, column), left(row, column)) 16 } 17 } 18 return grid.last!.last! 19 } 20 }
44ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 var rows = Array.init(repeating: 0, count: grid[0].count) 4 var result = Array.init(repeating: rows, count: grid.count) 5 6 result[0][0] = grid[0][0] 7 8 for i in 1..<grid.count { 9 result[i][0] = grid[i][0] + result[i - 1][0] 10 } 11 12 for i in 1..<grid[0].count { 13 result[0][i] = grid[0][i] + result[0][i - 1] 14 } 15 16 for row in 1..<grid.count { 17 for col in 1..<grid[row].count { 18 let a = result[row - 1][col] 19 let b = result[row][col - 1] 20 21 result[row][col] = min(a, b) + grid[row][col] 22 } 23 } 24 25 return result[grid.count - 1][grid[0].count - 1] 26 } 27 28 func res(_ row:Int, _ col: Int, _ grid:[[Int]]) -> Int { 29 if row == 0 && col == 0 { 30 return grid[0][0] 31 } else if row == 0 { 32 return res(0, col - 1, grid) + grid[row][col] 33 } else if col == 0{ 34 return res(row - 1, 0, grid) + grid[row][col] 35 } else { 36 let a = res(row - 1, col, grid); 37 let b = res(row, col - 1, grid); 38 return min(a, b) + grid[row][col] 39 } 40 } 41 }
48ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 var grid = grid 4 let n = grid.count 5 let m = grid[0].count 6 7 for i in 1..<n { 8 grid[i][0] += grid[i-1][0] 9 } 10 11 for j in 1..<m { 12 grid[0][j] += grid[0][j-1] 13 } 14 15 for i in 1..<n { 16 for j in 1..<m { 17 grid[i][j] += min(grid[i-1][j], grid[i][j-1]) 18 } 19 } 20 21 for i in 0..<n { 22 for j in 0..<m { 23 print(grid[i][j], terminator: " ") 24 } 25 print() 26 } 27 28 return grid[n-1][m-1] 29 } 30 }
56ms
1 class Solution { 2 func minPathSum(_ grid: [[Int]]) -> Int { 3 if grid.count == 0 || grid.first!.count == 0 { 4 return 0 5 } 6 var memo: [Int] = Array(repeating: 0, count: grid.count * grid.first!.count) 7 for y in 0..<grid.count { 8 for x in 0..<grid.first!.count { 9 let value = grid[y][x] 10 let index = indexFrom(y, x, grid) 11 let topIndex = indexFrom(y - 1, x, grid) 12 let leftIndex = indexFrom(y, x - 1, grid) 13 if x == 0 && y == 0 { 14 memo[index] = value 15 } else if x == 0 { // 第一列, 仅由其上方位置值决定 16 memo[index] = value + memo[topIndex] 17 } else if y == 0 { // 第一行, 同理 18 memo[index] = value + memo[leftIndex] 19 } else { 20 memo[index] = min(value + memo[leftIndex], value + memo[topIndex]) 21 } 22 } 23 } 24 25 return memo.last! 26 } 27 28 /// 二维数组序号转一维数组的Index 29 private func indexFrom(_ y: Int, _ x: Int, _ grid: [[Int]]) -> Int { 30 return y * grid.first!.count + x 31 } 32 }