[ZOJ 3817 Chinese Knot] 字符串hash+DP
题目
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3817
分析
字符串hash+DP
将knot loop上的字符串从两个方向hash，对给定的字符串s从前往后hashLeft
然后设f[i][j]表示从s的第i个字符往后的部分从第j个中心点在其所在的loop上能不能匹配
则f[i][j]容易递推
然后枚举knot loop上的一个位置，利用f[i][j]可以很容易的判断是否有解和找出解
代码
/**************************************************
* Problem: ZOJ 3817
* Author: clavichord93
* State: Accepted
**************************************************/
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
using namespace std;
const int MAX_N = 100005;
int n;
char s[4][MAX_N];
long long hashLeft[MAX_N][4];
long long hashRight[MAX_N][4];
int m;
char pattern[MAX_N];
long long hash[MAX_N];
long long pow31[MAX_N * 4];
bool f[MAX_N][8];
int ans[MAX_N];
void findPath(int i, int j, int dir) {
for (int cur = 1; cur <= m; cur++) {
ans[cur] = i * n + j;
if (!dir) {
j++;
if (j == n + 1) {
for (int k = 0; k < 8; k++) {
if (k != 2 * i + 1 && f[cur + 1][k]) {
dir = k & 1;
i = k / 2;
j = dir ? n : 1;
break;
}
}
}
}
else {
j--;
if (j == 0) {
for (int k = 0; k < 8; k++) {
if (k != 2 * i && f[cur + 1][k]) {
dir = k & 1;
i = k / 2;
j = dir ? n : 1;
break;
}
}
}
}
}
printf("%d", ans[1]);
for (int i = 2; i <= m; i++) {
printf(" %d", ans[i]);
}
printf("\n");
}
int main() {
#ifdef LOCAL_JUDGE
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#endif
pow31[0] = 1;
for (int i = 1; i <= 400000; i++) {
pow31[i] = pow31[i - 1] * 31;
}
int T;
scanf("%d", &T);
for (int cas = 1; cas <= T; cas++) {
memset(hash, 0, sizeof(hash));
memset(hashLeft, 0, sizeof(hashLeft));
memset(hashRight, 0, sizeof(hashRight));
memset(f, 0, sizeof(f));
scanf("%d %d", &n, &m);
for (int i = 0; i < 4; i++) {
scanf("%s", s[i] + 1);
for (int j = 1; j <= n; j++) {
hashLeft[j][i] = hashLeft[j - 1][i] + s[i][j] * pow31[j - 1];
}
for (int j = n; j >= 1; j--) {
hashRight[n - j + 1][i] = hashRight[n - j][i] + s[i][j] * pow31[n - j];
}
}
scanf("%s", pattern + 1);
for (int i = 1; i <= m; i++) {
hash[i] = hash[i - 1] + pattern[i] * pow31[i - 1];
}
for (int i = m; i >= 1; i--) {
for (int j = 0; j < 4; j++) {
int length = m - i + 1;
if (length <= n) {
long long hashPattern = hash[m] - hash[i - 1];
long long hashValueL = hashLeft[length][j] * pow31[i - 1];
if (hashValueL == hashPattern) {
f[i][2 * j] = 1;
}
long long hashValueR = hashRight[length][j] * pow31[i - 1];
if (hashValueR == hashPattern) {
f[i][2 * j + 1] = 1;
}
}
else {
long long hashPattern = hash[i + n - 1] - hash[i - 1];
long long hashValueL = hashLeft[n][j] * pow31[i - 1];
if (hashValueL == hashPattern) {
for (int k = 0; k < 8; k++) {
if (k != 2 * j + 1 && f[i + n][k]) {
f[i][2 * j] = 1;
break;
}
}
}
long long hashValueR = hashRight[n][j] * pow31[i - 1];
if (hashValueR == hashPattern) {
for (int k = 0; k < 8; k++) {
if (k != 2 * j && f[i + n][k]) {
f[i][2 * j + 1] = 1;
break;
}
}
}
}
}
}
//for (int i = 1; i <= m; i++) {
//for (int j = 0; j < 8; j++) {
//printf("%d ", f[i][j]);
//}
//printf("\n");
//}
bool ans = 0;
for (int i = 0; i < 4; i++) {
for (int j = 1; j <= n; j++) {
int length = n - j + 1;
if (length >= m) {
long long hashValue = hashLeft[j + m - 1][i] - hashLeft[j - 1][i];
long long hashPattern = hash[m] * pow31[j - 1];
if (hashValue == hashPattern) {
ans = 1;
findPath(i, j, 0);
}
}
else {
long long hashValue = hashLeft[n][i] - hashLeft[j - 1][i];
long long hashPattern = hash[length] * pow31[j - 1];
if (hashValue == hashPattern) {
for (int k = 0; k < 8; k++) {
if (k != 2 * i + 1 && f[length + 1][k]) {
ans = 1;
findPath(i, j, 0);
break;
}
}
}
}
if (ans) {
break;
}
length = j;
if (length >= m) {
long long hashValue = hashRight[n - j + m][i] - hashRight[n - j][i];
long long hashPattern = hash[m] * pow31[n - j];
if (hashValue == hashPattern) {
ans = 1;
findPath(i, j, 1);
}
}
else {
long long hashValue = hashRight[n][i] - hashRight[n - j][i];
long long hashPattern = hash[length] * pow31[n - j];
if (hashValue == hashPattern) {
for (int k = 0; k < 8; k++) {
if (k != 2 * i && f[length + 1][k]) {
ans = 1;
findPath(i, j, 1);
break;
}
}
}
}
if (ans) {
break;
}
}
if (ans) {
break;
}
}
if (!ans) {
printf("No solution!\n");
}
}
return 0;
}