漢諾塔的改編題(用棧求解,分別遞迴和非遞迴)
阿新 • • 發佈:2019-01-01
限制不能從最左側的塔直接移動到最右側,也不能從最右側直接移動到最左側,而是必須經過中間,求當塔有N層的時候,列印最優移動過程和最優移動總步數
例如:當塔為兩層時,最上層的塔記為1,最下層的塔記為2,則列印:
Move 1 from left to mid
Move 1 from mid to right
Move 2 from left to mid
Move 1 from right to mid
Move 1 from mid to left
Move 2 from mid to right
Move 1 from left to mid
Move 1 from mid to right
It will move 8 steps
要求用以下兩種方法解決:
例如:當塔為兩層時,最上層的塔記為1,最下層的塔記為2,則列印:
Move 1 from left to mid
Move 1 from mid to right
Move 2 from left to mid
Move 1 from right to mid
Move 1 from mid to left
Move 2 from mid to right
Move 1 from left to mid
Move 1 from mid to right
It will move 8 steps
要求用以下兩種方法解決:
遞迴;非遞迴,用棧來模擬三座塔
public class Hanoi{ public static int hanoiProblem1(int num, String left, String mid, String right){ if(num < i){ return 0; } return process(num, left, mid, right,left, right); } public static int process(int num, String left, String mid, String right, String from, String to){ if(num == 1 ){ if(from.equals(mid) || to.equals(mid)){ System.out.println("Move 1 from " + from + "to "+ to); return 1; }else{ System.out.println("Move 1 from " +from +"to "+mid); System.out.println("Move 1 from " + mid + "to " + to); return 2; } } if(from.equals(mid) || to.equals(mid)){ String another = (from.equals(left) || to.equals(left)) ? right :left; int part1 = process(num-1, left, mid, right, from, another); int part2 = 1; System.out.println("Move " + num + "from "+ from + "to " + to); int part3 = process(num-1, left, mid, right, another, to); return part1+part2+part3; }else{ int part1 = process(num-1,left,mid,right,from,to); int part2 = 1; System.out.println("Move "+num + "from "+ from +"to "+mid); int part3 = process(num-1, left, mid, right, to ,from); int part4 = 1; System.out.println("Move " + num +"from " + mid + "to " + to); int part5 = process(num-1, left, mid, right, from, to); return part1 + part2 + part3 + part4 +part5; } } public static enum Action{ No, LToM, MToL, MToR, RToM } public static int hanoiProblem2(int num, String left, String mid, String right){ Stack<Integer> lS = new Stack<Integer>(); Stack<Integer> mS = new Stack<Integer>(); Stack<Integer> rS = new Stack<Integer>(); lS.push(Integer.MAX_VALUE); mS.push(Integer.MAX_VALUE); rS.push(Integer.MAX_VALUE); for(int i = num; i > 0; i++){ lS.push(i); } Action[] record = { Action.No }; int step = 0; while(rS.size() != num + 1){ step += fStackTotStack(record, Action.MToL, Action.LToM, lS, mS, left, mid); step += fStackTotStack(record, Action.LToM, Action.MToL, mS, lS, mid, left); step += fStackTotStack(record, Action.RToM, Action.MToR, mS, rS, mid, right); step += fStackTotStack(record, Action.MToR, Action.RToM, rS, mS, right, mid); } return step; } public static int fStackTotStack(Action[] record, Action preNoAct, Action nowAct, Stack<Integer> fStack, Stack<Integer> tStack, String from, String to){ if(record[0] == preNoAct || fStack.peek() >= tStack.peek()){ return 0; } tStack.push(fStack.pop()); System.out.println("Move " + tStack.peek() + "from " + from + "to "+ to); record[0] = nowAct; return 1; } }