|
|
|
|
@ -0,0 +1,284 @@
|
|
|
|
|
package class44;
|
|
|
|
|
|
|
|
|
|
// 最长公共子串问题是面试常见题目之一
|
|
|
|
|
// 假设str1长度N，str2长度M
|
|
|
|
|
// 因为最优解的难度所限，一般在面试场上回答出O(N*M)的解法已经是比较优秀了
|
|
|
|
|
// 因为得到O(N*M)的解法，就已经需要用到动态规划了
|
|
|
|
|
// 但其实这个问题的最优解是O(N+M)，为了达到这个复杂度可是不容易
|
|
|
|
|
// 首先需要用到DC3算法得到后缀数组(sa)
|
|
|
|
|
// 进而用sa数组去生成height数组
|
|
|
|
|
// 而且在生成的时候，还有一个不回退的优化，都非常不容易理解
|
|
|
|
|
// 这就是后缀数组在面试算法中的地位 : 德高望重的噩梦
|
|
|
|
|
public class Code04_LongestCommonSubstringConquerByHeight {
|
|
|
|
|
|
|
|
|
|
public static int lcs1(String s1, String s2) {
|
|
|
|
|
if (s1 == null || s2 == null || s1.length() == 0 || s2.length() == 0) {
|
|
|
|
|
return 0;
|
|
|
|
|
}
|
|
|
|
|
char[] str1 = s1.toCharArray();
|
|
|
|
|
char[] str2 = s2.toCharArray();
|
|
|
|
|
int row = 0;
|
|
|
|
|
int col = str2.length - 1;
|
|
|
|
|
int max = 0;
|
|
|
|
|
while (row < str1.length) {
|
|
|
|
|
int i = row;
|
|
|
|
|
int j = col;
|
|
|
|
|
int len = 0;
|
|
|
|
|
while (i < str1.length && j < str2.length) {
|
|
|
|
|
if (str1[i] != str2[j]) {
|
|
|
|
|
len = 0;
|
|
|
|
|
} else {
|
|
|
|
|
len++;
|
|
|
|
|
}
|
|
|
|
|
if (len > max) {
|
|
|
|
|
max = len;
|
|
|
|
|
}
|
|
|
|
|
i++;
|
|
|
|
|
j++;
|
|
|
|
|
}
|
|
|
|
|
if (col > 0) {
|
|
|
|
|
col--;
|
|
|
|
|
} else {
|
|
|
|
|
row++;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return max;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static int lcs2(String s1, String s2) {
|
|
|
|
|
if (s1 == null || s2 == null || s1.length() == 0 || s2.length() == 0) {
|
|
|
|
|
return 0;
|
|
|
|
|
}
|
|
|
|
|
char[] str1 = s1.toCharArray();
|
|
|
|
|
char[] str2 = s2.toCharArray();
|
|
|
|
|
int N = str1.length;
|
|
|
|
|
int M = str2.length;
|
|
|
|
|
int min = str1[0];
|
|
|
|
|
int max = str1[0];
|
|
|
|
|
for (int i = 1; i < N; i++) {
|
|
|
|
|
min = Math.min(min, str1[i]);
|
|
|
|
|
max = Math.max(max, str1[i]);
|
|
|
|
|
}
|
|
|
|
|
for (int i = 0; i < M; i++) {
|
|
|
|
|
min = Math.min(min, str2[i]);
|
|
|
|
|
max = Math.max(max, str2[i]);
|
|
|
|
|
}
|
|
|
|
|
int[] all = new int[N + M + 1];
|
|
|
|
|
int index = 0;
|
|
|
|
|
for (int i = 0; i < N; i++) {
|
|
|
|
|
all[index++] = str1[i] - min + 2;
|
|
|
|
|
}
|
|
|
|
|
all[index++] = 1;
|
|
|
|
|
for (int i = 0; i < M; i++) {
|
|
|
|
|
all[index++] = str2[i] - min + 2;
|
|
|
|
|
}
|
|
|
|
|
DC3 dc3 = new DC3(all, max - min + 2);
|
|
|
|
|
int n = all.length;
|
|
|
|
|
int[] sa = dc3.sa;
|
|
|
|
|
int[] height = dc3.height;
|
|
|
|
|
int ans = 0;
|
|
|
|
|
for (int i = 1; i < n; i++) {
|
|
|
|
|
int up = sa[i - 1];
|
|
|
|
|
int down = sa[i];
|
|
|
|
|
if (Math.min(up, down) < N && Math.max(up, down) > N) {
|
|
|
|
|
ans = Math.max(ans, height[i]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static class DC3 {
|
|
|
|
|
|
|
|
|
|
public int[] sa;
|
|
|
|
|
|
|
|
|
|
public int[] rank;
|
|
|
|
|
|
|
|
|
|
public int[] height;
|
|
|
|
|
|
|
|
|
|
public DC3(int[] nums, int max) {
|
|
|
|
|
sa = sa(nums, max);
|
|
|
|
|
rank = rank();
|
|
|
|
|
height = height(nums);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private int[] sa(int[] nums, int max) {
|
|
|
|
|
int n = nums.length;
|
|
|
|
|
int[] arr = new int[n + 3];
|
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
|
|
|
arr[i] = nums[i];
|
|
|
|
|
}
|
|
|
|
|
return skew(arr, n, max);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private int[] skew(int[] nums, int n, int K) {
|
|
|
|
|
int n0 = (n + 2) / 3, n1 = (n + 1) / 3, n2 = n / 3, n02 = n0 + n2;
|
|
|
|
|
int[] s12 = new int[n02 + 3], sa12 = new int[n02 + 3];
|
|
|
|
|
for (int i = 0, j = 0; i < n + (n0 - n1); ++i) {
|
|
|
|
|
if (0 != i % 3) {
|
|
|
|
|
s12[j++] = i;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
radixPass(nums, s12, sa12, 2, n02, K);
|
|
|
|
|
radixPass(nums, sa12, s12, 1, n02, K);
|
|
|
|
|
radixPass(nums, s12, sa12, 0, n02, K);
|
|
|
|
|
int name = 0, c0 = -1, c1 = -1, c2 = -1;
|
|
|
|
|
for (int i = 0; i < n02; ++i) {
|
|
|
|
|
if (c0 != nums[sa12[i]] || c1 != nums[sa12[i] + 1] || c2 != nums[sa12[i] + 2]) {
|
|
|
|
|
name++;
|
|
|
|
|
c0 = nums[sa12[i]];
|
|
|
|
|
c1 = nums[sa12[i] + 1];
|
|
|
|
|
c2 = nums[sa12[i] + 2];
|
|
|
|
|
}
|
|
|
|
|
if (1 == sa12[i] % 3) {
|
|
|
|
|
s12[sa12[i] / 3] = name;
|
|
|
|
|
} else {
|
|
|
|
|
s12[sa12[i] / 3 + n0] = name;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
if (name < n02) {
|
|
|
|
|
sa12 = skew(s12, n02, name);
|
|
|
|
|
for (int i = 0; i < n02; i++) {
|
|
|
|
|
s12[sa12[i]] = i + 1;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
for (int i = 0; i < n02; i++) {
|
|
|
|
|
sa12[s12[i] - 1] = i;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
int[] s0 = new int[n0], sa0 = new int[n0];
|
|
|
|
|
for (int i = 0, j = 0; i < n02; i++) {
|
|
|
|
|
if (sa12[i] < n0) {
|
|
|
|
|
s0[j++] = 3 * sa12[i];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
radixPass(nums, s0, sa0, 0, n0, K);
|
|
|
|
|
int[] sa = new int[n];
|
|
|
|
|
for (int p = 0, t = n0 - n1, k = 0; k < n; k++) {
|
|
|
|
|
int i = sa12[t] < n0 ? sa12[t] * 3 + 1 : (sa12[t] - n0) * 3 + 2;
|
|
|
|
|
int j = sa0[p];
|
|
|
|
|
if (sa12[t] < n0 ? leq(nums[i], s12[sa12[t] + n0], nums[j], s12[j / 3])
|
|
|
|
|
: leq(nums[i], nums[i + 1], s12[sa12[t] - n0 + 1], nums[j], nums[j + 1], s12[j / 3 + n0])) {
|
|
|
|
|
sa[k] = i;
|
|
|
|
|
t++;
|
|
|
|
|
if (t == n02) {
|
|
|
|
|
for (k++; p < n0; p++, k++) {
|
|
|
|
|
sa[k] = sa0[p];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
sa[k] = j;
|
|
|
|
|
p++;
|
|
|
|
|
if (p == n0) {
|
|
|
|
|
for (k++; t < n02; t++, k++) {
|
|
|
|
|
sa[k] = sa12[t] < n0 ? sa12[t] * 3 + 1 : (sa12[t] - n0) * 3 + 2;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return sa;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private void radixPass(int[] nums, int[] input, int[] output, int offset, int n, int k) {
|
|
|
|
|
int[] cnt = new int[k + 1];
|
|
|
|
|
for (int i = 0; i < n; ++i) {
|
|
|
|
|
cnt[nums[input[i] + offset]]++;
|
|
|
|
|
}
|
|
|
|
|
for (int i = 0, sum = 0; i < cnt.length; ++i) {
|
|
|
|
|
int t = cnt[i];
|
|
|
|
|
cnt[i] = sum;
|
|
|
|
|
sum += t;
|
|
|
|
|
}
|
|
|
|
|
for (int i = 0; i < n; ++i) {
|
|
|
|
|
output[cnt[nums[input[i] + offset]]++] = input[i];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private boolean leq(int a1, int a2, int b1, int b2) {
|
|
|
|
|
return a1 < b1 || (a1 == b1 && a2 <= b2);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private boolean leq(int a1, int a2, int a3, int b1, int b2, int b3) {
|
|
|
|
|
return a1 < b1 || (a1 == b1 && leq(a2, a3, b2, b3));
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private int[] rank() {
|
|
|
|
|
int n = sa.length;
|
|
|
|
|
int[] ans = new int[n];
|
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
|
|
|
ans[sa[i]] = i;
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
private int[] height(int[] s) {
|
|
|
|
|
int n = s.length;
|
|
|
|
|
int[] ans = new int[n];
|
|
|
|
|
for (int i = 0, k = 0; i < n; ++i) {
|
|
|
|
|
if (rank[i] != 0) {
|
|
|
|
|
if (k > 0) {
|
|
|
|
|
--k;
|
|
|
|
|
}
|
|
|
|
|
int j = sa[rank[i] - 1];
|
|
|
|
|
while (i + k < n && j + k < n && s[i + k] == s[j + k]) {
|
|
|
|
|
++k;
|
|
|
|
|
}
|
|
|
|
|
ans[rank[i]] = k;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// for test
|
|
|
|
|
public static String randomNumberString(int len, int range) {
|
|
|
|
|
char[] str = new char[len];
|
|
|
|
|
for (int i = 0; i < len; i++) {
|
|
|
|
|
str[i] = (char) ((int) (Math.random() * range) + 'a');
|
|
|
|
|
}
|
|
|
|
|
return String.valueOf(str);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static void main(String[] args) {
|
|
|
|
|
int len = 30;
|
|
|
|
|
int range = 5;
|
|
|
|
|
int testTime = 100000;
|
|
|
|
|
System.out.println("功能测试开始");
|
|
|
|
|
for (int i = 0; i < testTime; i++) {
|
|
|
|
|
int N1 = (int) (Math.random() * len);
|
|
|
|
|
int N2 = (int) (Math.random() * len);
|
|
|
|
|
String str1 = randomNumberString(N1, range);
|
|
|
|
|
String str2 = randomNumberString(N2, range);
|
|
|
|
|
int ans1 = lcs1(str1, str2);
|
|
|
|
|
int ans2 = lcs2(str1, str2);
|
|
|
|
|
if (ans1 != ans2) {
|
|
|
|
|
System.out.println("Oops!");
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
System.out.println("功能测试结束");
|
|
|
|
|
System.out.println("==========");
|
|
|
|
|
|
|
|
|
|
System.out.println("性能测试开始");
|
|
|
|
|
len = 80000;
|
|
|
|
|
range = 26;
|
|
|
|
|
long start;
|
|
|
|
|
long end;
|
|
|
|
|
|
|
|
|
|
String str1 = randomNumberString(len, range);
|
|
|
|
|
String str2 = randomNumberString(len, range);
|
|
|
|
|
|
|
|
|
|
start = System.currentTimeMillis();
|
|
|
|
|
int ans1 = lcs1(str1, str2);
|
|
|
|
|
end = System.currentTimeMillis();
|
|
|
|
|
System.out.println("方法1结果 : " + ans1 + " , 运行时间 : " + (end - start) + " ms");
|
|
|
|
|
|
|
|
|
|
start = System.currentTimeMillis();
|
|
|
|
|
int ans2 = lcs2(str1, str2);
|
|
|
|
|
end = System.currentTimeMillis();
|
|
|
|
|
System.out.println("方法2结果 : " + ans2 + " , 运行时间 : " + (end - start) + " ms");
|
|
|
|
|
|
|
|
|
|
System.out.println("性能测试结束");
|
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|
algorithmzuo
4 years ago