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package class_2022_04_2_week;
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import java.util.PriorityQueue;
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// 来自网易
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// 3.27笔试
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// 一个二维矩阵，上面只有 0 和 1，只能上下左右移动
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// 如果移动前后的元素值相同，则耗费 1 ，否则耗费 2。
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// 问从左上到右下的最小耗费
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public class Code02_MinDistanceFromLeftUpToRightDown {
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// 一个错误的贪心
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// 网上帖子最流行的解答，看似对，其实不行
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public static int bestWalk1(int[][] map) {
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int n = map.length;
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int m = map[0].length;
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int[][] dp = new int[n][m];
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for (int i = 1; i < m; i++) {
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dp[0][i] = dp[0][i - 1] + (map[0][i - 1] == map[0][i] ? 1 : 2);
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}
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for (int i = 1; i < n; i++) {
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dp[i][0] = dp[i - 1][0] + (map[i - 1][0] == map[i][0] ? 1 : 2);
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}
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for (int i = 1; i < n; i++) {
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for (int j = 1; j < m; j++) {
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dp[i][j] = dp[i - 1][j] + (map[i - 1][j] == map[i][j] ? 1 : 2);
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dp[i][j] = Math.min(dp[i][j], dp[i][j - 1] + (map[i][j - 1] == map[i][j] ? 1 : 2));
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}
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}
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return dp[n - 1][m - 1];
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}
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// 正确的解法
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// Dijskra
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public static int bestWalk2(int[][] map) {
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int n = map.length;
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int m = map[0].length;
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// 小根堆：[代价，行，列]
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// 根据代价，谁代价小，谁放在堆的上面
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PriorityQueue<int[]> heap = new PriorityQueue<>((a, b) -> a[0] - b[0]);
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// poped[i][j] == true 已经弹出过了！不要再处理，直接忽略！
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// poped[i][j] == false 之间(i,j)没弹出过！要处理
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boolean[][] poped = new boolean[n][m];
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heap.add(new int[] { 0, 0, 0 });
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int ans = 0;
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while (!heap.isEmpty()) {
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// 当前弹出了，[代价，行，列]，当前位置
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int[] cur = heap.poll();
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int dis = cur[0];
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int row = cur[1];
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int col = cur[2];
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if (poped[row][col]) {
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continue;
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}
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// 第一次弹出！
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poped[row][col] = true;
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if (row == n - 1 && col == m - 1) {
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ans = dis;
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break;
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}
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add(dis, row - 1, col, map[row][col], n, m, map, poped, heap);
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add(dis, row + 1, col, map[row][col], n, m, map, poped, heap);
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add(dis, row, col - 1, map[row][col], n, m, map, poped, heap);
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add(dis, row, col + 1, map[row][col], n, m, map, poped, heap);
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}
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return ans;
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}
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// preDistance ： 之前的距离
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// int row, int col ： 当前要加入的是什么位置
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// preValue : 前一个格子是什么值，
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// int n, int m ：边界，固定参数
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// map: 每一个格子的值，都在map里
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// boolean[][] poped : 当前位置如果是弹出过的位置，要忽略！
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// PriorityQueue<int[]> heap : 小根堆
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public static void add(int preDistance,
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int row, int col, int preValue, int n, int m,
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int[][] map, boolean[][] poped,
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PriorityQueue<int[]> heap) {
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if (row >= 0 && row < n && col >= 0 && col < m
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&& !poped[row][col]) {
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heap.add(new int[] {
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preDistance + (map[row][col] == preValue ? 1 : 2),
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row, col });
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}
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}
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// 为了测试
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public static int[][] randomMatrix(int n, int m) {
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int[][] ans = new int[n][m];
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < m; j++) {
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ans[i][j] = (int) (Math.random() * 2);
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}
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}
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return ans;
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}
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// 为了测试
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public static void main(String[] args) {
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int n = 100;
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int m = 100;
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int testTime = 10000;
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System.out.println("测试开始");
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for (int i = 0; i < testTime; i++) {
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int[][] map = randomMatrix(n, m);
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int ans1 = bestWalk1(map);
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int ans2 = bestWalk2(map);
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if (ans1 != ans2) {
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System.out.println("出错了!");
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for (int[] arr : map) {
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for (int num : arr) {
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System.out.print(num + " ");
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}
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System.out.println();
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}
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System.out.println(ans1);
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System.out.println(ans2);
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break;
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}
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}
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System.out.println("测试结束");
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}
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}
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