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package class18;
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public class Code01_HanoiProblem {
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public static int step1(int[] arr) {
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if (arr == null || arr.length == 0) {
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return -1;
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}
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return process(arr, arr.length - 1, 1, 2, 3);
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}
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// 目标是: 把0~i的圆盘，从from全部挪到to上
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// 返回，根据arr中的状态arr[0..i]，它是最优解的第几步？
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// f(i, 3 , 2, 1) f(i, 1, 3, 2) f(i, 3, 1, 2)
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public static int process(int[] arr, int i, int from, int other, int to) {
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if (i == -1) {
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return 0;
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}
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if (arr[i] != from && arr[i] != to) {
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return -1;
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}
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if (arr[i] == from) { // 第一大步没走完
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return process(arr, i - 1, from, to, other);
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} else { // arr[i] == to
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// 已经走完1，2两步了，
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int rest = process(arr, i - 1, other, from, to); // 第三大步完成的程度
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if (rest == -1) {
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return -1;
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}
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return (1 << i) + rest;
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}
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}
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public static int step2(int[] arr) {
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if (arr == null || arr.length == 0) {
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return -1;
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}
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int from = 1;
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int mid = 2;
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int to = 3;
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int i = arr.length - 1;
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int res = 0;
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int tmp = 0;
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while (i >= 0) {
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if (arr[i] != from && arr[i] != to) {
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return -1;
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}
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if (arr[i] == to) {
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res += 1 << i;
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tmp = from;
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from = mid;
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} else {
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tmp = to;
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to = mid;
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}
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mid = tmp;
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i--;
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}
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return res;
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}
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public static int kth(int[] arr) {
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int N = arr.length;
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return step(arr, N - 1, 1, 3, 2);
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}
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// 0...index这些圆盘，arr[0..index] index+1层塔
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// 在哪？from 去哪？to 另一个是啥？other
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// arr[0..index]这些状态，是index+1层汉诺塔问题的，最优解第几步
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public static int step(int[] arr, int index, int from, int to, int other) {
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if (index == -1) {
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return 0;
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}
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if (arr[index] == other) {
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return -1;
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}
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// arr[index] == from arr[index] == to;
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if (arr[index] == from) {
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return step(arr, index - 1, from, other, to);
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} else {
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int p1 = (1 << index) - 1;
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int p2 = 1;
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int p3 = step(arr, index - 1, other, to, from);
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if (p3 == -1) {
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return -1;
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}
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return p1 + p2 + p3;
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}
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}
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public static void main(String[] args) {
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int[] arr = { 3, 3, 2, 1 };
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System.out.println(step1(arr));
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System.out.println(step2(arr));
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System.out.println(kth(arr));
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}
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}
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