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/*
* 64. Minimum Path Sum
* Target: Find a path from top left to bottom right which minimizes the sum of all numbers along its path.
* Difficulty：Medium
* Classification：Array, DP
* Best solution: solution 2.
* Note: Same as LC_62.
*/
/*
* Solution 1
* 2019-06-27 Runtime: 15 ms
* Algorithm: => Recursion and use HashMap.
* Time complexity: ? Space complexity: ?
*/
class Solution {
public int minPathSum(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
HashMap<String, Integer> visited = new HashMap<>();
return getPathSum(0, 0, m - 1, n - 1, grid, visited);
}
private int getPathSum(int x, int y, int m, int n, int[][] grid, HashMap<String, Integer> visited) {
if (x == m && y == n) {
return grid[m][n];
}
int n1 = Integer.MAX_VALUE;
int n2 = Integer.MAX_VALUE;
String key = x + 1 + "@" + y;
if (!visited.containsKey(key)) {
if (x + 1 <= m) {
n1 = getPathSum(x + 1, y, m, n, grid, visited);
}
} else {
n1 = visited.get(key);
}
key = x + "@" + (y + 1);
if (!visited.containsKey(key)) {
if (y + 1 <= n) {
n2 = getPathSum(x, y + 1, m, n, grid, visited);
}
} else {
n2 = visited.get(key);
}
key = x + "@" + y;
visited.put(key, Math.min(n1, n2) + grid[x][y]);
return Math.min(n1, n2) + grid[x][y];
}
}
/*
* Solution 2
* 2019-06-27 Runtime: 2 ms
* Algorithm: => Iteration. Same as DP.
* Time complexity: O(m*n) Space complexity: O(1)
*/
class Solution {
public int minPathSum(int[][] grid) {
int len1 = grid.length;
int len2 = grid[0].length;
// update first column
for (int i = 1; i < len1; i++) {
grid[i][0] = grid[i][0] + grid[i - 1][0];
}
// update first row
for (int j = 1; j < len2; j++) {
grid[0][j] = grid[0][j] + grid[0][j - 1];
}
for (int i = 1; i < len1; i++) {
for (int j = 1; j < len2; j++) {
grid[i][j] = Math.min(grid[i][j] + grid[i][j - 1], grid[i][j] + grid[i - 1][j]);
}
}
return grid[len1 - 1][len2 - 1];
}
}