16.算法习题之KMP算法

KMP算法核心

1）如何理解next数组

2）如何利用next数组加速匹配过程，优化时的两个实质！

习题1 假设字符串str长度为N，字符串match长度为M，M <= N 想确定str中是否有某个子串是等于match的。时间复杂度O(N)

public static int getIndexOf(String s1, String s2) {
		if (s1 == null || s2 == null || s2.length() < 1 || s1.length() < s2.length()) {
			return -1;
		}
		char[] str1 = s1.toCharArray();
		char[] str2 = s2.toCharArray();
		int x = 0;
		int y = 0;
		// O(M) m <= n
		int[] next = getNextArray(str2);
		// O(N)
		while (x < str1.length && y < str2.length) {
			if (str1[x] == str2[y]) {
				x++;
				y++;
			} else if (next[y] == -1) { // y == 0
				x++;
			} else {
				y = next[y];
			}
		}
		return y == str2.length ? x - y : -1;
	}

	public static int[] getNextArray(char[] str2) {
		if (str2.length == 1) {
			return new int[] { -1 };
		}
		int[] next = new int[str2.length];
		next[0] = -1;
		next[1] = 0;
		int i = 2; // 目前在哪个位置上求next数组的值
		int cn = 0; // 当前是哪个位置的值再和i-1位置的字符比较
		while (i < next.length) {
			if (str2[i - 1] == str2[cn]) { // 配成功的时候
				next[i++] = ++cn;
			} else if (cn > 0) {
				cn = next[cn];
			} else {
				next[i++] = 0;
			}
		}
		return next;
	}

	// for test
	public static String getRandomString(int possibilities, int size) {
		char[] ans = new char[(int) (Math.random() * size) + 1];
		for (int i = 0; i < ans.length; i++) {
			ans[i] = (char) ((int) (Math.random() * possibilities) + 'a');
		}
		return String.valueOf(ans);
	}

	public static void main(String[] args) {
		int possibilities = 5;
		int strSize = 20;
		int matchSize = 5;
		int testTimes = 5000000;
		System.out.println("test begin");
		for (int i = 0; i < testTimes; i++) {
			String str = getRandomString(possibilities, strSize);
			String match = getRandomString(possibilities, matchSize);
			if (getIndexOf(str, match) != str.indexOf(match)) {
				System.out.println("Oops!");
			}
		}
		System.out.println("test finish");
	}

习题2 给定两棵二叉树的头节点head1和head2 想知道head1中是否有某个子树的结构和head2完全一样

public static class Node {
		public int value;
		public Node left;
		public Node right;

		public Node(int v) {
			value = v;
		}
	}

	public static boolean containsTree1(Node big, Node small) {
		if (small == null) {
			return true;
		}
		if (big == null) {
			return false;
		}
		if (isSameValueStructure(big, small)) {
			return true;
		}
		return containsTree1(big.left, small) || containsTree1(big.right, small);
	}

	public static boolean isSameValueStructure(Node head1, Node head2) {
		if (head1 == null && head2 != null) {
			return false;
		}
		if (head1 != null && head2 == null) {
			return false;
		}
		if (head1 == null && head2 == null) {
			return true;
		}
		if (head1.value != head2.value) {
			return false;
		}
		return isSameValueStructure(head1.left, head2.left) 
				&& isSameValueStructure(head1.right, head2.right);
	}

	public static boolean containsTree2(Node big, Node small) {
		if (small == null) {
			return true;
		}
		if (big == null) {
			return false;
		}
		ArrayList<String> b = preSerial(big);
		ArrayList<String> s = preSerial(small);
		String[] str = new String[b.size()];
		for (int i = 0; i < str.length; i++) {
			str[i] = b.get(i);
		}

		String[] match = new String[s.size()];
		for (int i = 0; i < match.length; i++) {
			match[i] = s.get(i);
		}
		return getIndexOf(str, match) != -1;
	}

	public static ArrayList<String> preSerial(Node head) {
		ArrayList<String> ans = new ArrayList<>();
		pres(head, ans);
		return ans;
	}

	public static void pres(Node head, ArrayList<String> ans) {
		if (head == null) {
			ans.add(null);
		} else {
			ans.add(String.valueOf(head.value));
			pres(head.left, ans);
			pres(head.right, ans);
		}
	}

	public static int getIndexOf(String[] str1, String[] str2) {
		if (str1 == null || str2 == null || str1.length < 1 || str1.length < str2.length) {
			return -1;
		}
		int x = 0;
		int y = 0;
		int[] next = getNextArray(str2);
		while (x < str1.length && y < str2.length) {
			if (isEqual(str1[x], str2[y])) {
				x++;
				y++;
			} else if (next[y] == -1) {
				x++;
			} else {
				y = next[y];
			}
		}
		return y == str2.length ? x - y : -1;
	}

	public static int[] getNextArray(String[] ms) {
		if (ms.length == 1) {
			return new int[] { -1 };
		}
		int[] next = new int[ms.length];
		next[0] = -1;
		next[1] = 0;
		int i = 2;
		int cn = 0;
		while (i < next.length) {
			if (isEqual(ms[i - 1], ms[cn])) {
				next[i++] = ++cn;
			} else if (cn > 0) {
				cn = next[cn];
			} else {
				next[i++] = 0;
			}
		}
		return next;
	}

	public static boolean isEqual(String a, String b) {
		if (a == null && b == null) {
			return true;
		} else {
			if (a == null || b == null) {
				return false;
			} else {
				return a.equals(b);
			}
		}
	}

	// for test
	public static Node generateRandomBST(int maxLevel, int maxValue) {
		return generate(1, maxLevel, maxValue);
	}

	// for test
	public static Node generate(int level, int maxLevel, int maxValue) {
		if (level > maxLevel || Math.random() < 0.5) {
			return null;
		}
		Node head = new Node((int) (Math.random() * maxValue));
		head.left = generate(level + 1, maxLevel, maxValue);
		head.right = generate(level + 1, maxLevel, maxValue);
		return head;
	}

	public static void main(String[] args) {
		int bigTreeLevel = 7;
		int smallTreeLevel = 4;
		int nodeMaxValue = 5;
		int testTimes = 100000;
		System.out.println("test begin");
		for (int i = 0; i < testTimes; i++) {
			Node big = generateRandomBST(bigTreeLevel, nodeMaxValue);
			Node small = generateRandomBST(smallTreeLevel, nodeMaxValue);
			boolean ans1 = containsTree1(big, small);
			boolean ans2 = containsTree2(big, small);
			if (ans1 != ans2) {
				System.out.println("Oops!");
			}
		}
		System.out.println("test finish!");

	}

习题3 判断str1和str2是否是旋转字符串

public static boolean isRotation(String a, String b) {
		if (a == null || b == null || a.length() != b.length()) {
			return false;
		}
		String b2 = b + b;
		return getIndexOf(b2, a) != -1;
	}

	// KMP Algorithm
	public static int getIndexOf(String s, String m) {
		if (s.length() < m.length()) {
			return -1;
		}
		char[] ss = s.toCharArray();
		char[] ms = m.toCharArray();
		int si = 0;
		int mi = 0;
		int[] next = getNextArray(ms);
		while (si < ss.length && mi < ms.length) {
			if (ss[si] == ms[mi]) {
				si++;
				mi++;
			} else if (next[mi] == -1) {
				si++;
			} else {
				mi = next[mi];
			}
		}
		return mi == ms.length ? si - mi : -1;
	}

	public static int[] getNextArray(char[] ms) {
		if (ms.length == 1) {
			return new int[] { -1 };
		}
		int[] next = new int[ms.length];
		next[0] = -1;
		next[1] = 0;
		int pos = 2;
		int cn = 0;
		while (pos < next.length) {
			if (ms[pos - 1] == ms[cn]) {
				next[pos++] = ++cn;
			} else if (cn > 0) {
				cn = next[cn];
			} else {
				next[pos++] = 0;
			}
		}
		return next;
	}

	public static void main(String[] args) {
		String str1 = "yunzuocheng";
		String str2 = "zuochengyun";
		System.out.println(isRotation(str1, str2));

	}