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package leetcode.dp;
/**
* 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。
*
* 来源：力扣（LeetCode）
* 链接：https://leetcode-cn.com/problems/minimum-path-sum
* 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
*/
/*
dp[i][j]表示从开始到（i，j)的最小值。如果是第一行或者第一列。将其累加即可。
如果不是dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
*/
public class N064MinPathSum {
public int minPathSum(int[][] grid) {
if (grid == null || grid.length == 0 || grid[0].length == 0) {
return 0;
}
int row = grid.length;
int col = grid[0].length;
int[][] dp = new int[row][col];
dp[0][0] = grid[0][0];
for (int i = 1; i < row; i++) {
dp[i][0] = grid[i][0] + dp[i - 1][0];
}
for (int i = 1; i < col; i++) {
dp[0][i] = grid[0][i] + dp[0][i - 1];
}
for (int i = 1; i < row; i++) {
for (int j = 1; j < col; j++) {
dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
}
}
return dp[row - 1][col - 1];
}
//空间压缩
public int minPathSum1(int[][] grid) {
if (grid == null || grid.length == 0 || grid[0].length == 0) {
return 0;
}
int row = grid.length;
int col = grid[0].length;
int[] dp = new int[col];
//初始化第一行
dp[0] = grid[0][0];
for (int i = 1; i < col; i++) {
dp[i] = dp[i - 1] + grid[0][i];
}
for (int i = 1; i < row; i++) {
dp[0] = grid[i][0] + dp[0];
for (int j = 1; j < col; j++) {
dp[j] = grid[i][j] + Math.min(dp[j], dp[j - 1]);
}
}
return dp[col - 1];
}
}