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//题号：64
//
//给定一个包含非负整数的 m x n 网格 grid ，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 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。
//
//
// 示例 2：
//
//
//输入：grid = [[1,2,3],[4,5,6]]
//输出：12
//
//
//
//
// 提示：
//
//
// m == grid.length
// n == grid[i].length
// 1 <= m, n <= 200
// 0 <= grid[i][j] <= 100
//
// Related Topics 数组 动态规划
// 👍 805 👎 0
public class MinimumPathSum {
public static void main(String[] args) {
Solution solution = new MinimumPathSum().new Solution();
solution.minPathSum(new int[][]{{1, 3, 1}, {1, 5, 1}, {4, 2, 1}});
}
//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
public int minPathSum(int[][] grid) {
/**
* 动态规划
*
* 1、重复性，子问题:program(i,j)=Math(subProgram(i-1,j),subProgram(i,j-1))+grid[i][j];
* 2、状态数组：dp[i][j]
* 3、状态转移方程：dp[i][j]=Math.min(dp[i-1][j]+dp[i][j-1])+grid[i][j]
*
* 时间复杂度O(n^2),空间复杂度O(1)
*
*/
for (int i = 0; i < grid.length; i++) {
for (int j = 0; j < grid[i].length; j++) {
if (i > 0 && j > 0) {
grid[i][j] = Math.min(grid[i - 1][j], grid[i][j - 1])+grid[i][j];
} else if (i > 0) {
grid[i][j] = grid[i - 1][j] + grid[i][j];
} else if (j > 0) {
grid[i][j] = grid[i][j - 1] + grid[i][j];
}
}
}
return grid[grid.length - 1][grid[0].length - 1];
/**
* 不同判断方式
*/
// for (int i = 0; i < grid.length; i++) {
// for (int j = 0; j < grid[0].length; j++) {
// if (i==0 && j==0) continue;
// if (i == 0) {
// grid[i][j] = grid[i][j - 1] + grid[i][j];
// } else if (j == 0) {
// grid[i][j] = grid[i - 1][j] + grid[i][j];
// } else {
// grid[i][j] = Math.min(grid[i - 1][j], grid[i][j - 1]) + grid[i][j];
// }
// }
// }
// return grid[grid.length - 1][grid[0].length - 1];
}
}
//leetcode submit region end(Prohibit modification and deletion)
}