使网格图至少有一条有效路径的最小代价

Leetcode题目链接

描述

详见中文题目链接。

解答

using PII = pair<int, int>;

class Solution {
private:
    static constexpr int dx[4] = {0, 0, 1, -1};
    static constexpr int dy[4] = {1, -1, 0, 0};

public:
    int minCost(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<int> dist(m * n, 0x3f3f3f3f);
        vector<bool> st(m * n, false);

        priority_queue<PII, vector<PII>, greater<PII>> heap;
        dist[0] = 0;
        heap.emplace(0, 0);

        while (!heap.empty()) {
            auto [distance, vertex] = heap.top();
            heap.pop();

            if (st[vertex]) continue;
            st[vertex] = true;

            int x = vertex / n, y = vertex % n;
            for (int i = 0; i < 4; i++) {
                int newX = x + dx[i];
                int newY = y + dy[i];
                int newVertex = newX * n + newY;
                int newDistance = distance + (grid[x][y] != i + 1);

                if (newX >= 0 && newX < m && newY >= 0 && newY < n && newDistance < dist[newVertex]) {
                    dist[newVertex] = newDistance;
                    heap.emplace(newDistance, newVertex);
                }
            }
        }

        return dist[m * n - 1];
    }
};