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Merged
NASU41 merged 2 commits into from
Sep 10, 2020
Merged

#6 Z Algorithmの追加' #24

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71b71c8
'Z Algorithmの追加'
Sep 9, 2020
5cbf3b5
'importを削除してFQCN指定にする'
Sep 9, 2020
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25 changes: 23 additions & 2 deletions StringAlgorithm/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,7 @@ public static int[] suffixArray(int[] s)
public static int[] suffixArray(int[] s, int upper)
```

長さ $n$ の文字列 `s` のSuffix Arrayとして、長さ $n$ のint配列を返す。 Suffix Array `sa`は $(0,1,\ldots ,n-1)$ の順列であって、各 $i=0,1,\cdots , n-2$ について `S[sa[i]..n) < s[sa[i+1]..n)` を満たすもの。
長さ $n$ の文字列 `s` のSuffix Arrayとして、長さ $n$ のint配列を返す。 Suffix Array `sa`は $(0,1,\ldots ,n-1)$ の順列であって、各 $i=0,1,\cdots , n-2$ について `s[sa[i]..n) < s[sa[i+1]..n)` を満たすもの。

### 制約

Expand Down Expand Up @@ -53,5 +53,26 @@ public static int[] lcpArray(int[] s, int[] sa)

- $O(n)$

## 使用例
### 使用例
[[https://atcoder.jp/contests/practice2/submissions/16585271]]

## zAlgorithm

```Java
// (1)
public static int[] zAlgorithm(java.lang.String s)
// (2)
public static int[] zAlgorithm(char[] s)
// (3)
public static int[] zAlgorithm(int[] s)
```

入力の長さを $n$ として、長さ $n$ の配列を返す。 $i$番目の要素は `s[0..n)` と `s[i..n)` のLCP(Longest Common Prefix)の長さ。

### 制約

- $0\le n\le 10^8$

### 計算量

- $O(n)$
50 changes: 39 additions & 11 deletions StringAlgorithm/StringAlgorithm.java
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Original file line number Diff line number Diff line change
@@ -1,15 +1,11 @@
import java.util.Arrays;
import java.util.Comparator;
import java.util.function.Consumer;

class StringAlgorithm {
private static int[] saNaive(int[] s) {
int n = s.length;
Integer[] _sa = new Integer[n];
for (int i = 0; i < n; i++) {
_sa[i] = i;
}
Arrays.sort(_sa, (l, r) -> {
java.util.Arrays.sort(_sa, (l, r) -> {
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] - s[r];
l++;
Expand All @@ -36,13 +32,13 @@ private static int[] saDoubling(int[] s) {
for (int k = 1; k < n; k *= 2) {
final int _k = k;
final int[] _rnk = rnk;
Comparator<Integer> cmp = (x, y) -> {
java.util.Comparator<Integer> cmp = (x, y) -> {
if (_rnk[x] != _rnk[y]) return _rnk[x] - _rnk[y];
int rx = x + _k < n ? _rnk[x + _k] : -1;
int ry = y + _k < n ? _rnk[y + _k] : -1;
return rx - ry;
};
Arrays.sort(_sa, cmp);
java.util.Arrays.sort(_sa, cmp);
tmp[_sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[_sa[i]] = tmp[_sa[i - 1]] + (cmp.compare(_sa[i - 1], _sa[i]) < 0 ? 1 : 0);
Expand Down Expand Up @@ -102,8 +98,8 @@ private static int[] sais(int[] s, int upper) {
if (i < upper) sumL[i + 1] += sumS[i];
}

Consumer<int[]> induce = lms -> {
Arrays.fill(sa, -1);
java.util.function.Consumer<int[]> induce = lms -> {
java.util.Arrays.fill(sa, -1);
int[] buf = new int[upper + 1];
System.arraycopy(sumS, 0, buf, 0, upper + 1);
for (int d : lms) {
Expand All @@ -128,7 +124,7 @@ private static int[] sais(int[] s, int upper) {
};

int[] lmsMap = new int[n + 1];
Arrays.fill(lmsMap, -1);
java.util.Arrays.fill(lmsMap, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
Expand Down Expand Up @@ -205,7 +201,7 @@ public static int[] suffixArray(int[] s) {
for (int i = 0; i < n; i++) {
idx[i] = i;
}
Arrays.sort(idx, (l, r) -> s[l] - s[r]);
java.util.Arrays.sort(idx, (l, r) -> s[l] - s[r]);
int[] s2 = new int[n];
int now = 0;
for (int i = 0; i < n; i++) {
Expand Down Expand Up @@ -265,4 +261,36 @@ public static int[] lcpArray(char[] s, int[] sa) {
public static int[] lcpArray(java.lang.String s, int[] sa) {
return lcpArray(s.toCharArray(), sa);
}

public static int[] zAlgorithm(int[] s) {
int n = s.length;
if (n == 0) return new int[0];
int[] z = new int[n];
for (int i = 1, j = 0; i < n; i++) {
int k = j + z[j] <= i ? 0 : Math.min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
z[i] = k;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}

public static int[] zAlgorithm(char[] s) {
int n = s.length;
if (n == 0) return new int[0];
int[] z = new int[n];
for (int i = 1, j = 0; i < n; i++) {
int k = j + z[j] <= i ? 0 : Math.min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
z[i] = k;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}

public static int[] zAlgorithm(String s) {
return zAlgorithm(s.toCharArray());
}
}