Determining DNA Health
Problem Statement :
DNA is a nucleic acid present in the bodies of living things. Each piece of DNA contains a number of genes, some of which are beneficial and increase the DNA's total health. Each gene has a health value, and the total health of a DNA is the sum of the health values of all the beneficial genes that occur as a substring in the DNA. We represent genes and DNA as non-empty strings of lowercase English alphabetic letters, and the same gene may appear multiple times as a susbtring of a DNA. Given the following: An array of beneficial gene strings, . Note that these gene sequences are not guaranteed to be distinct. An array of gene health values, , where each is the health value for gene . A set of DNA strands where the definition of each strand has three components, , , and , where string is a DNA for which genes are healthy. Find and print the respective total healths of the unhealthiest (minimum total health) and healthiest (maximum total health) strands of DNA as two space-separated values on a single line. Input Format The first line contains an integer, , denoting the total number of genes. The second line contains space-separated strings describing the respective values of (i.e., the elements of ). The third line contains space-separated integers describing the respective values of (i.e., the elements of ). The fourth line contains an integer, , denoting the number of strands of DNA to process. Each of the subsequent lines describes a DNA strand in the form start end d, denoting that the healthy genes for DNA strand are and their respective correlated health values are . Output Format Print two space-separated integers describing the respective total health of the unhealthiest and the healthiest strands of DNA.
Solution :
Solution in C :
In C++ :
/*AMETHYSTS*/
#pragma comment(linker, "/STACK:1000000000")
#include <cstdio>
#include <iostream>
#include <ctime>
#include <string>
#include <vector>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <set>
#include <cstdlib>
#include <ctime>
#include <cassert>
#include <bitset>
#include <fstream>
#include <deque>
#include <stack>
#include <climits>
#include <string>
#include <queue>
#include <memory.h>
#include <map>
#include <unordered_map>
#define ll long long
#define ld double
#define pii pair <ll, ll>
#define mp make_pair
using namespace std;
const int maxn = (int)1e5 + 10, maxm = (int)2e6 + 10;
char s[maxm];
int len;
struct point {
int ed[26];
int lnk;
int par;
int c;
vector <int> pos;
point() {
memset(ed, -1, sizeof ed);
lnk = -1;
par = -1;
c = -1;
}
};
point mas[maxm];
int posit = 0;
int my_new() {
return posit++;
}
void add(int it, int pos, int num) {
if (pos == len) {
mas[it].pos.push_back(num);
return;
}
int c = s[pos] - 'a';
if (mas[it].ed[c] == -1) {
mas[it].ed[c] = my_new();
int nit = mas[it].ed[c];
mas[nit].par = it;
mas[nit].c = c;
}
add(mas[it].ed[c], pos + 1, num);
}
int h[maxn];
int l[maxn], r[maxn];
vector <int> z[maxm];
int getlnk(int it);
int go(int it, int c) {
if (mas[it].ed[c] != -1) {
return mas[it].ed[c];
}
if (it == 0) {
mas[it].ed[c] = 0;
} else {
mas[it].ed[c] = go(getlnk(it), c);
}
return mas[it].ed[c];
}
int getlnk(int it) {
if (mas[it].lnk != -1) {
return mas[it].lnk;
}
if (it == 0 || mas[it].par == 0) {
mas[it].lnk = 0;
} else {
mas[it].lnk = go(getlnk(mas[it].par), mas[it].c);
}
return mas[it].lnk;
}
vector <int> ed[maxm];
ll ans[maxn];
ll tr[maxn];
void change(int pos, int x) {
for ( ; pos < maxn; pos |= pos + 1) {
tr[pos] += x;
}
}
ll getsum(int pos) {
ll ans = 0;
for ( ; pos >= 0; pos = (pos & (pos + 1)) - 1) {
ans += tr[pos];
}
return ans;
}
ll gores(int l, int r) {
return getsum(r) - getsum(l - 1);
}
void dfs(int v) {
for (int i = 0; i < (int)mas[v].pos.size(); i++) {
int g = mas[v].pos[i];
change(g, h[g]);
}
for (int i = 0; i < (int)z[v].size(); i++) {
int num = z[v][i];
int lm = l[num];
int rm = r[num];
ans[num] += gores(lm, rm);
}
for (int i = 0; i < (int)ed[v].size(); i++) {
int u = ed[v][i];
dfs(u);
}
for (int i = 0; i < (int)mas[v].pos.size(); i++) {
int g = mas[v].pos[i];
change(g, -h[g]);
}
}
int main() {
int n;
cin >> n;
int tr = my_new();
for (int i = 0; i < n; i++) {
scanf("%s", s);
len = strlen(s);
add(tr, 0, i);
}
for (int i = 0; i < n; i++) {
scanf("%d", &h[i]);
}
int q;
scanf("%d", &q);
for (int i = 0; i < q; i++) {
scanf("%d %d %s", &l[i], &r[i], s);
len = strlen(s);
int it = tr;
for (int j = 0; j < len; j++) {
it = go(it, s[j] - 'a');
z[it].push_back(i);
}
}
ll mins = (ll)1e18;
ll maxs = 0;
for (int i = 1; i < posit; i++) {
ed[getlnk(i)].push_back(i);
}
dfs(0);
for (int i = 0; i < q; i++) {
mins = min(mins, ans[i]);
maxs = max(maxs, ans[i]);
}
cout << mins << ' ' << maxs << endl;
return 0;
}
In Java :
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>
#include <cassert>
#include <cmath>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <cstdlib>
using namespace std;
#define INF 1e+9
#define mp make_pair
#define pb push_back
#define fi first
#define fs first
#define se second
#define i64 long long
#define li long long
#define lint long long
#define pii pair<int, int>
#define vi vector<int>
#define forn(i, n) for (int i = 0; i < (int)n; i++)
#define fore(i, b, e) for (int i = (int)b; i <= (int)e; i++)
struct vertex {
int next[26];
vi numbers;
int p;
char pch;
int link;
int go[26];
};
const int maxn = 2e6+5;
vertex t[maxn];
int sz;
int cost[maxn];
void init() {
t[0].p = t[0].link = -1;
memset (t[0].next, 255, sizeof t[0].next);
memset (t[0].go, 255, sizeof t[0].go);
sz = 1;
}
void add_string (const string & s, int num) {
int v = 0;
for (size_t i=0; i<s.length(); ++i) {
int c = s[i]-'a';
if (t[v].next[c] == -1) {
memset (t[sz].next, 255, sizeof t[sz].next);
memset (t[sz].go, 255, sizeof t[sz].go);
t[sz].link = -1;
t[sz].p = v;
t[sz].pch = c;
t[v].next[c] = sz++;
}
v = t[v].next[c];
}
t[v].numbers.pb(num);
}
int go (int v, int c);
int get_link (int v) {
if (t[v].link == -1) {
if (v == 0 || t[v].p == 0)
t[v].link = 0;
else
t[v].link = go (get_link (t[v].p), t[v].pch);
}
return t[v].link;
}
int go (int v, int c) {
if (t[v].go[c] == -1) {
if (t[v].next[c] != -1)
t[v].go[c] = t[v].next[c];
else
t[v].go[c] = v==0 ? 0 : go (get_link (v), c);
}
return t[v].go[c];
}
int main() {
#ifdef LOCAL
freopen("inp", "r", stdin);
//freopen("outp", "w", stdout);
#else
// freopen(TASKNAME ".in", "r", stdin);
// freopen(TASKNAME ".out", "w", stdout);
#endif
init();
int n;
scanf("%d", &n);
forn(j, n) {
string s;
cin >> s;
// cout << "s = " << s << endl;
add_string(s, j);
}
forn(j, n)
scanf("%d", &cost[j]);
int q;
scanf("%d", &q);
i64 minn = 0;
i64 maxx = 0;
forn(query, q) {
int L, R;
scanf("%d%d", &L, &R);
string s;
cin >> s;
int cur = 0;
i64 sum = 0;
for (char c : s) {
cur = go(cur, (int)(c - 'a'));
//printf("cur = %d\n", cur);
int tmp = cur;
while(tmp != 0) {
for (int x : t[tmp].numbers) {
if (x >= L && x <= R)
sum += cost[x];
//printf("%c x = %d sum = %lld\n", c, x, sum);
}
tmp = get_link(tmp);
}
}
if (query == 0 || sum > maxx)
maxx = sum;
if (query == 0 || sum < minn)
minn = sum;
}
cout << minn << " " << maxx;
}
In C :
#define _XOPEN_SOURCE 500
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <stdbool.h>
struct node {
unsigned int count;
unsigned int next;
unsigned long *value;
unsigned int *index;
struct node *child['z' - 'a' + 1];
};
void init_node(struct node *n)
{
n->value = 0;
memset(n->child, 0, sizeof(n->child));
return;
}
struct node *insert_node(struct node *r, char *s)
{
int i;
int j;
struct node *n;
n = r;
for (i = 0; s[i] != 0; i++) {
j = s[i] - 'a';
if (n->child[j] == NULL) {
n->child[j] = malloc(sizeof(struct node));
init_node(n->child[j]);
}
n = n->child[j];
}
return n;
}
int main()
{
int dc;
int f;
char **g;
int gc;
int *h;
int i;
int j;
int k;
int l;
unsigned long max;
unsigned long min;
struct node **n;
struct node *p;
char *s;
struct node *t;
unsigned long x;
s = malloc(sizeof(char) * (4 * 1024 * 1024));
scanf("%d", &gc);
g = malloc(sizeof(char *) * gc);
for (i = 0; i < gc; i++) {
scanf("%s", s);
g[i] = strdup(s);
}
h = malloc(sizeof(int) * gc);
for (i = 0; i < gc; i++) {
scanf("%d", &h[i]);
}
t = malloc(sizeof(struct node));
init_node(t);
n = malloc(sizeof(struct node *) * gc);
for (i = 0; i < gc; i++) {
n[i] = insert_node(t, g[i]);
}
for (i = 0; i < gc; i++) {
n[i]->count++;
}
for (i = 0; i < gc; i++) {
if (n[i]->next == 0) {
n[i]->value = malloc(sizeof(unsigned long) * n[i]->count);
n[i]->index = malloc(sizeof(unsigned int) * n[i]->count);
}
n[i]->value[n[i]->next] = h[i];
n[i]->index[n[i]->next] = i;
n[i]->next++;
}
scanf("%d", &dc);
min = -1;
max = 0;
while (dc > 0) {
scanf("%d %d %s", &f, &l, s);
x = 0;
for (i = 0; s[i] != 0; i++) {
p = t;
for (j = i; s[j] != 0; j++) {
p = p->child[s[j] - 'a'];
if (p == NULL) {
break;
}
for (k = 0; k < p->count; k++) {
if (p->index[k] < f) {
continue;
}
if (p->index[k] > l) {
break;
}
x += p->value[k];
}
}
}
if ((min == -1) || (x < min)) {
min = x;
}
if (x > max) {
max = x;
}
dc--;
}
printf("%ld %ld\n", min, max);
return 0;
}
In Python3 :
#!/bin/python3
'''Compact prefix trie'''
import bisect
bisect_left = bisect.bisect_left
bisect_right = bisect.bisect_right
class ScoreTable:
def __init__(self):
self.scoreIndexes = []
self.scoreSums = []
def append(self, i, s):
self.scoreIndexes.append(i)
partial = self.scoreSums[-1] if len(self.scoreSums) > 0 else 0
self.scoreSums.append(s + partial)
def getScore(self, start, end):
lo = bisect_left(self.scoreIndexes, start)
hi = bisect_right(self.scoreIndexes, end)
if hi == lo:
return 0
elif lo == 0:
return self.scoreSums[hi-1]
else:
return self.scoreSums[hi-1] - self.scoreSums[lo-1]
def longestCommonPrefix(s, t):
stop = min(len(s), len(t))
i = 0
while i < stop and s[i] == t[i]:
i += 1
return s[:i]
class TrieNode:
def __init__(self, label):
self.label = label
self.child = {}
self.scores = None
def __str__(self):
return '{' + ','.join([c + ':' + str(n) for c,n in self.child.items()]) + '}'
def insert(self, k, ix, score):
'''Insert the key k into the trie rooted at this node.'''
i = 0
node = self
while i < len(k):
if k[i] in node.child:
child = node.child[k[i]]
lcp = longestCommonPrefix(k[i:], child.label)
if len(lcp) < len(child.label):
# Split child node at longest common prefix
suffix = child.label[len(lcp):]
child.label = suffix
prefNode = TrieNode(lcp)
prefNode.child[suffix[0]] = child
node.child[lcp[0]] = prefNode
child = prefNode
node = child
i += len(lcp)
else:
newNode = TrieNode(k[i:])
node.child[k[i]] = newNode
node = newNode
i = len(k)
if not node.scores:
node.scores = ScoreTable()
node.scores.append(ix, score)
def traverse(self):
yield self
for node in self.child.values():
yield from node.traverse()
def countNodes(t):
return sum(1 for _ in t.traverse())
def soloChildren(t):
return sum(1 for n in t.traverse() if len(n.child) == 1)
def buildGeneTrie(genes, healths):
# Build compact prefix trie.
trie = TrieNode('')
for i in range(len(genes)):
trie.insert(genes[i], i, healths[i])
return trie
def checkDNA(geneTrie, dna, start, end):
# print('scoring', dna, start, end)
score = 0
z = len(dna)
for i in range(z):
node = geneTrie
j = i
while j < z and dna[j] in node.child:
node = node.child[dna[j]]
x = len(node.label)
if node.label != dna[j:j+x]: break
if node.scores:
score += node.scores.getScore(start, end)
j += x
# print('final score:', score)
return score
def main():
n_ = int(input())
genes = input().split()
healths = list(map(int, input().split()))
# print('building trie...')
geneTrie = buildGeneTrie(genes, healths)
# print(countNodes(geneTrie), 'nodes')
# print(soloChildren(geneTrie), 'nodes with only one child')
# print(geneTrie)
best = 0
worst = float('inf')
s = int(input())
for _ in range(s):
first,last,d = input().split()
first,last = int(first), int(last)
score = checkDNA(geneTrie, d, first, last)
# if score < worst: print('***', d, first, last, score)
best = max(best, score)
worst = min(worst, score)
print(worst, best)
if __name__ == '__main__':
main()
# import cProfile
# cProfile.run('main()', sort='cumtime')
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