[LeetCode] Minimum Number of Valid Strings to Form Target II

3292. Minimum Number of Valid Strings to Form Target II

You are given an array of strings words and a string target.

A string x is called valid if x is a prefix of any string in words.

Return the minimum number of valid strings that can be concatenated to form target. If it is not possible to form target, return -1.

A prefix of a string is a substring that starts from the beginning of the string and extends to any point within it.

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struct Seg {
long long mi, ma, val, lazy;
Seg *left, *right;
Seg(long long l, long long r) : mi(l), ma(r), val(INT_MAX), lazy(INT_MAX), left(nullptr), right(nullptr) {
if(l^r) {
long long m = l + (r - l) / 2;
left = new Seg(l,m);
right = new Seg(m+1,r);
}
}
void propagate() {
if(lazy != INT_MAX) {
val = min(val, lazy);
if(left) left->lazy = min(left->lazy, lazy);
if(right) right->lazy = min(right->lazy, lazy);
lazy = INT_MAX;
}
}
long long query(long long x) {
propagate();
if(mi == x and x == ma) return val;
long long m = mi + (ma - mi) / 2;
if(x <= m) return left->query(x);
return right->query(x);
}
void update(long long l, long long r, long long x) {
propagate();
if(l <= mi and ma <= r) {
lazy = min(lazy, x);
propagate();
return;
}
if(l > ma or r < mi) return;
left->update(l,r,x);
right->update(l,r,x);
val = min(left->val, right->val);
}
};
class Solution {
public:
long long mod = 1e9 + 7, base = 131;
long long query(vector<unordered_set<long long>>& rh, vector<long long>& h, vector<long long>& p, long long pos) {
long long l = pos, r = p.size() - 2, res = -1;
auto qry = [&](long long l, long long r) {
long long len = r - l + 1;
long long val = (h[r+1] - h[l] * p[len] % mod + mod) % mod;
return rh[len-1].count(val);
};
while(l <= r) {
long long m = l + (r - l) / 2;
bool ok = qry(pos,m);
if(ok) {
l = m + 1;
res = max(res, m);
} else r = m - 1;
}
return res;
}
int minValidStrings(vector<string>& words, string target) {
vector<unordered_set<long long>> rh(50505);
for(auto& w : words) {
long long now = 0;
for(int i = 0; i < w.length(); i++) {
now = (now * base + w[i] - 'a') % mod;
rh[i].insert(now);
}
}
vector<long long> hash(target.length() + 1), po(target.length() + 1);
po[0] = 1;
for(int i = 0; i < target.length(); i++) {
po[i+1] = po[i] * base % mod;
hash[i+1] = (hash[i] * base + target[i] - 'a') % mod;
}
Seg* seg = new Seg(0,target.length());
seg->update(0,0,0);
for(int i = 0; i < target.length(); i++) {
long long val = seg->query(i);
if(val == INT_MAX) continue;
long long best = query(rh,hash,po,i);
if(best == -1) continue;
seg->update(i+1,best+1,seg->query(i) + 1);
}
long long res = seg->query(target.length());
return res >= INT_MAX ? -1 : res;
}
};

Author: Song Hayoung
Link: https://songhayoung.github.io/2024/09/15/PS/LeetCode/minimum-number-of-valid-strings-to-form-target-ii/
Copyright Notice: All articles in this blog are licensed under CC BY-NC-SA 4.0 unless stating additionally.