[Leetcode 1631] Youngsang Solution

Leetcode/1631/ysuh/README.md

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+## Link
+[Path With Minimum Effort](https://leetcode.com/problems/path-with-minimum-effort/description/)
+
+## Topic
+- Dijkstra
+- Priority Queue
+
+## Approach
+- We define possible direction in each cell (left, right, up, down)
+- Using relaxation and maximum effort, run dijkstra 
+
+## Note
+- Terminating when arrived at ROW-1, COL-1 idx remarkably shrinks the computation time.

Leetcode/1631/ysuh/solution.cpp

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+class Solution {
+public:
+    int move_hor[4] = {-1, 0, 1, 0};
+    int move_ver[4] = {0, -1, 0, 1};
+    int ROW;
+    int COL;
+    int dijkstra(vector<vector<int>>& heights, vector<vector<int>>& min_effort) {
+        min_effort[0][0] = 0;
+        priority_queue<pair<int, pair<int, int>>> pq;
+        pq.push({0, {0, 0}});
+        while (!pq.empty()) {
+            auto tmp = pq.top();
+            int eff = -tmp.first;
+            int idx_r = tmp.second.first;
+            int idx_c = tmp.second.second;
+            if (idx_r == ROW-1 && idx_c == COL-1) return min_effort[ROW-1][COL-1];
+            pq.pop();
+            for (int i=0; i<4; i++) {
+                int new_row = idx_r + move_hor[i];
+                int new_col = idx_c + move_ver[i];
+                if (new_row < ROW && new_row > -1 && new_col < COL && new_col > -1) {
+                    int cost = max(eff, abs(heights[new_row][new_col] - heights[idx_r][idx_c]));
+                    if (cost < min_effort[new_row][new_col]) {
+                        min_effort[new_row][new_col] = cost;
+                        pq.push({-cost, {new_row, new_col}});
+                    }
+                }
+            }
+        }
+        return min_effort[ROW-1][COL-1];
+
+    }
+    int minimumEffortPath(vector<vector<int>>& heights) {
+        ROW = heights.size();
+        COL = heights[0].size();
+        vector<vector<int>> min_effort(ROW, vector<int>(COL, 1e9));
+        return dijkstra(heights, min_effort);
+    }
+};