Problem Description
You are given a string S consisting of only lowercase english letters and some queries.
For each query (l,r,k), please output the starting position of the k-th occurence of the substring SlSl+1...Sr in S.
Input
The first line contains an integer T(1≤T≤20), denoting the number of test cases.
The first line of each test case contains two integer N(1≤N≤105),Q(1≤Q≤105), denoting the length of S and the number of queries.
The second line of each test case contains a string S(|S|=N) consisting of only lowercase english letters.
Then Q lines follow, each line contains three integer l,r(1≤l≤r≤N) and k(1≤k≤N), denoting a query.
There are at most 5 testcases which N is greater than 103.
Output
For each query, output the starting position of the k-th occurence of the given substring.
If such position don't exists, output −1 instead.
题意:查找子串第k次出现的位置
题解:后缀数组 + 二分 + 倍增 + 主席树
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
const int inf = 1e9;
struct SA {
int dp[maxn][20], sa[maxn], rak[maxn];
int tx[maxn], height[maxn], lg[maxn];
int n, m, p;
char s[maxn];
struct node {
int x, y, id;
} a[maxn], b[maxn];
void rsort() {
for (int i = 1; i <= m; i++) tx[i] = 0;
for (int i = 1; i <= n; i++) tx[a[i].y]++;
for (int i = 1; i <= m; i++) tx[i] += tx[i - 1];
for (int i = 1; i <= n; i++) b[tx[a[i].y]--] = a[i];
for (int i = 1; i <= m; i++) tx[i] = 0;
for (int i = 1; i <= n; i++) tx[b[i].x]++;
for (int i = 1; i <= m; i++) tx[i] += tx[i - 1];
for (int i = n; i >= 1; i--) a[tx[b[i].x]--] = b[i];
}
void ssort() {
rsort();
p = 0;
for (int i = 1; i <= n; i++) {
if (a[i].x != a[i - 1].x || a[i].y != a[i - 1].y) ++p;
rak[a[i].id] = p;
}
for (int i = 1; i <= n; i++) {
a[i].x = rak[i];
a[i].id = sa[rak[i]] = i;
a[i].y = 0;
}
m = p;
}
void solve() {
m = maxn - 1;
for (int i = 1; i <= m; i++) {
a[i].x = a[i].y = s[i];a[i].id = i;
}
ssort();
for (int j = 1; j <= n; j <<= 1) {
for (int i = 1; i + j <= n; i++) a[i].y = a[i + j].x;
ssort();
if (p == n) break;
}
get_Height();
}
void get_Height() {
int k = 0;
for (int i = 1; i <= n; i++) {
if (k) k--;
int j = sa[rak[i] - 1];
while (i + k <= n && j + k <= n && s[i + k] == s[j + k]) k++;
height[rak[i]] = k;
}
RMQ();
}
void RMQ() {
for (int i = 2; i <= n; i++) lg[i] = lg[i >> 1] + 1;
for (int i = 1; i <= n; i++) dp[i][0] = height[i];
for(int j = 1; j <= lg[n]; j++) {
for(int i = 1; i + (1 << j) - 1 <= n; i++) {
dp[i][j] = min(dp[i][j - 1], dp[i + (1 << (j - 1))][j - 1]);
}
}
}
int lcp(int x, int y) {
int l = rak[x], r = rak[y];
if (l > r) swap(l, r);
l++;
int k = lg[r - l + 1];
return min(dp[l][k], dp[r - (1 << k) + 1][k]);
}
int check(int l, int r) {
if (l == r) return dp[l][0];
if (l > r) swap(l, r);
int k = lg[r - l + 1];
return min(dp[l][k], dp[r - (1 << k) + 1][k]);
}
} sa;
struct Tree {
int lson, rson;
int sum;
} tree[maxn * 40];
int root[maxn], tot;
void insert(int &nowp, int last, int l, int r, int x) {
nowp = ++tot;
tree[nowp] = tree[last];
tree[nowp].sum++;
if (l == r) return;
int mid = (l + r) / 2;
if (mid >= x) {
insert(tree[nowp].lson, tree[last].lson, l, mid, x);
} else {
insert(tree[nowp].rson, tree[last].rson, mid + 1, r, x);
}
}
int query(int lt, int rt, int l, int r, int k) {
if (l == r) {
return l;
}
int lsum = tree[tree[lt].lson].sum;
int rsum = tree[tree[rt].lson].sum;
int mid = (l + r) / 2;
if (rsum - lsum >= k) {
return query(tree[lt].lson, tree[rt].lson, l, mid, k);
} else {
return query(tree[lt].rson, tree[rt].rson, mid + 1, r, k - rsum + lsum);
}
}
int main() {
// freopen("in.in", "r", stdin);
// freopen("out1.out", "w", stdout);
int T, m, l, r, k;
scanf("%d", &T);
while (T--) {
tot = 0;
memset(root, 0, sizeof(root));
scanf("%d%d", &sa.n, &m);
scanf("%s", sa.s + 1);
sa.solve();
for (int i = 1; i <= sa.n; i++) {
insert(root[i], root[i - 1], 1, sa.n, sa.sa[i]);
}
while (m--) {
int mm = inf;
scanf("%d%d%d", &l, &r, &k);
int L = sa.rak[l], R = sa.rak[l];
int ll = sa.rak[l] + 1, rr = sa.n;
int post = sa.rak[l] + 1;
while (ll <= rr) {
int mid = (ll + rr) / 2;
if (sa.check(post, mid) >= r - l + 1) {
R = mid;
ll = mid + 1;
} else {
rr = mid - 1;
}
}
ll = 1, rr = sa.rak[l];
post = sa.rak[l];
while (ll <= rr) {
int mid = (ll + rr) / 2;
int x = sa.check(post, mid);
if (x >= r - l + 1) {
L = mid - 1;
rr = mid - 1;
} else {
ll = mid + 1;
}
}
if (R - L + 1 < k) {
printf("-1\n");
} else {
printf("%d\n", query(root[L - 1], root[R], 1, sa.n, k));
}
}
}
return 0;
} 
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