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package class18;
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public class Code01_RobotWalk {
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public static int ways1(int N, int start, int aim, int K) {
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if (N < 2 || start < 1 || start > N || aim < 1 || aim > N || K < 1) {
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return -1;
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}
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return process1(start, K, aim, N);
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}
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// 机器人当前来到的位置是cur，
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// 机器人还有rest步需要去走，
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// 最终的目标是aim，
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// 有哪些位置？1~N
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// 返回：机器人从cur出发，走过rest步之后，最终停在aim的方法数，是多少？
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public static int process1(int cur, int rest, int aim, int N) {
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if (rest == 0) { // 如果已经不需要走了，走完了！
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return cur == aim ? 1 : 0;
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}
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// (cur, rest)
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if (cur == 1) { // 1 -> 2
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return process1(2, rest - 1, aim, N);
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}
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// (cur, rest)
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if (cur == N) { // N-1 <- N
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return process1(N - 1, rest - 1, aim, N);
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}
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// (cur, rest)
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return process1(cur - 1, rest - 1, aim, N) + process1(cur + 1, rest - 1, aim, N);
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}
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public static int ways2(int N, int start, int aim, int K) {
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if (N < 2 || start < 1 || start > N || aim < 1 || aim > N || K < 1) {
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return -1;
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}
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int[][] dp = new int[N + 1][K + 1];
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for (int i = 0; i <= N; i++) {
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for (int j = 0; j <= K; j++) {
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dp[i][j] = -1;
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}
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}
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// dp就是缓存表
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// dp[cur][rest] == -1 -> process1(cur, rest)之前没算过！
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// dp[cur][rest] != -1 -> process1(cur, rest)之前算过！返回值，dp[cur][rest]
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// N+1 * K+1
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return process2(start, K, aim, N, dp);
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}
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// cur 范: 1 ~ N
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// rest 范：0 ~ K
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public static int process2(int cur, int rest, int aim, int N, int[][] dp) {
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if (dp[cur][rest] != -1) {
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return dp[cur][rest];
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}
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// 之前没算过！
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int ans = 0;
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if (rest == 0) {
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ans = cur == aim ? 1 : 0;
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} else if (cur == 1) {
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ans = process2(2, rest - 1, aim, N, dp);
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} else if (cur == N) {
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ans = process2(N - 1, rest - 1, aim, N, dp);
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} else {
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ans = process2(cur - 1, rest - 1, aim, N, dp) + process2(cur + 1, rest - 1, aim, N, dp);
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}
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dp[cur][rest] = ans;
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return ans;
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}
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public static int ways3(int N, int start, int aim, int K) {
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if (N < 2 || start < 1 || start > N || aim < 1 || aim > N || K < 1) {
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return -1;
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}
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int[][] dp = new int[N + 1][K + 1];
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dp[aim][0] = 1;
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for (int rest = 1; rest <= K; rest++) {
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dp[1][rest] = dp[2][rest - 1];
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for (int cur = 2; cur < N; cur++) {
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dp[cur][rest] = dp[cur - 1][rest - 1] + dp[cur + 1][rest - 1];
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}
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dp[N][rest] = dp[N - 1][rest - 1];
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}
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return dp[start][K];
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}
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public static void main(String[] args) {
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System.out.println(ways1(5, 2, 4, 6));
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System.out.println(ways2(5, 2, 4, 6));
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System.out.println(ways3(5, 2, 4, 6));
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}
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}
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