Separate the Numbers


Problem Statement :


A numeric string, , is beautiful if it can be split into a sequence of two or more positive integers, , satisfying the following conditions:

 for any  (i.e., each element in the sequence is  more than the previous element).
No  contains a leading zero. For example, we can split  into the sequence , but it is not beautiful because  and  have leading zeroes.
The contents of the sequence cannot be rearranged. For example, we can split  into the sequence , but it is not beautiful because it breaks our first constraint (i.e., ).
The diagram below depicts some beautiful strings:

Perform  queries where each query consists of some integer string . For each query, print whether or not the string is beautiful on a new line. If it is beautiful, print YES x, where  is the first number of the increasing sequence. If there are multiple such values of , choose the smallest. Otherwise, print NO.

Function Description

Complete the separateNumbers function in the editor below.

separateNumbers has the following parameter:

s: an integer value represented as a string
Prints
- string: Print a string as described above. Return nothing.

Input Format

The first line contains an integer q, the number of strings to evaluate.
Each of the next q lines contains an integer string s to query.

Constraints

1  <=   q  <=  10
1  <=  | s |  <=  32



Solution :



title-img


                            Solution in C :

In  C++  :








#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;

int main() {
int q;

cin >> q;

while (q--) {
string s;

cin >> s;

if (s[0] == '0') {
cout << "NO\n";
continue;
}

ll now = 0;

bool st = false;

for (int i = 0; i < (int)s.size(); i++) {
now *= 10;
now += s[i] - '0';

ll res = 0;

if (s[i + 1] == '0') {
continue;
}

int cnt = 1;

for (int j = i + 1; j < (int)s.size(); j++) {
res *= 10;
res += s[j] - '0';

if (res == now + cnt) {
if (j + 1 == (int)s.size()) {
st = true;
break;
}

if (s[j + 1] == '0') {
break;
}

res = 0;
cnt++;
}
}

if (st) {
break;
}
}

if (st) {
cout << "YES " << now << endl;
} else {
cout << "NO\n";
}
}

return 0;
}









In  Java  :






import java.io.*;
import java.util.StringTokenizer;


public class Main {
private void solve() {
int n = rw.nextInt();
main:
for (int i = 0; i < n; ++i) {
String s = rw.next();
if (s.startsWith("0") || s.length() == 1) {
rw.println("NO");
continue;
}
long x, cur;
cy:
for (int j = 1; j <= s.length() / 2; ++j) {
x = Long.parseLong(s.substring(0, j));
cur = x + 1;
int c = j;
while (c < s.length()) {
String p = String.valueOf(cur);
cur += 1;
if (s.startsWith(p, c)) {
c += p.length();
} else {
continue cy;
}
}
rw.println("YES" + " " + x);
continue main;
}
rw.println("NO");
}

}

private RW rw;
private String FILE_NAME = "file";

public static void main(String[] args) {
new Main().run();
}

private void run() {
rw = new RW(FILE_NAME + ".in", FILE_NAME + ".out");
solve();
rw.close();
}

private class RW {
private StringTokenizer st;
private PrintWriter out;
private BufferedReader br;
private boolean eof;

RW(String inputFile, String outputFile) {
br = new BufferedReader(new InputStreamReader(System.in));
out = new PrintWriter(new OutputStreamWriter(System.out));

File f = new File(inputFile);
if (f.exists() && f.canRead()) {
try {
br = new BufferedReader(new FileReader(inputFile));
out = new PrintWriter(new FileWriter(outputFile));
} catch (IOException e) {
e.printStackTrace();
}
}
}

private String nextLine() {
String s = "";
try {
s = br.readLine();
} catch (IOException e) {
e.printStackTrace();
}
return s;
}

private String next() {
while (st == null || !st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (IOException e) {
eof = true;
return "-1";
}
}
return st.nextToken();
}

private long nextLong() {
return Long.parseLong(next());
}

private int nextInt() {
return Integer.parseInt(next());
}

private void println() {
out.println();
}

private void println(Object o) {
out.println(o);
}

private void print(Object o) {
out.print(o);
}

private void close() {
try {
br.close();
} catch (IOException e) {
e.printStackTrace();
}
out.close();
}
}
}









In    C  :






#include <stdio.h>
#include <string.h>


typedef unsigned long long int Long;
char s[33];
int q;
Long x;

int isZeroLead(int i) { return s[i] == '0'; }
Long read(int i, int sz) {
    char *pt = s + i;
    Long ans = 0;
    while(sz-- && *pt) {
        ans = ans*10 + (*pt - '0');
        pt++;
    }
    return ans;
}

int digs(Long x) {
    int ll = 0;
    while(x) {
        ll++;
        x /= 10;
    }
    return ll;
}

int check(Long fst, int len) {
    Long last = fst, curr;
    int lsz = digs(fst);
    for(int i = lsz; i < len; i += lsz) {
        if(isZeroLead(i)) return 0;
        if(digs(last + 1) != digs(last)) { lsz++; }
        
        curr = read(i, lsz);
        if(curr - last != 1) return 0;
        last = curr;
    }
    
    return 1;
}

int main() {
    scanf("%d",&q);
    while(q--) {
        scanf("%s", s);
        Long x = -1, fst;
        for(int i = 1, len = strlen(s); i <= (len>>1); i++) {
            fst = read(0, i);
            if(check(fst, len)) {
                x = fst;
                break;
            }
        }
        
        if(x == -1) puts("NO");
        else printf("YES %lld\n", x);
    }
    
    return 0;
}








In   Python3 :






for _ in range(int(input())):
    s = input().strip()
    n = len(s)
    x = ''
    for i in s[:-1]:
        x += i
        y = int(x)
        z = ''
        while len(z) < n:
            z += str(y)
            y += 1
        if n == len(z) and z == s:
            print("YES", x)
            break
    else:
        print("NO")
                        








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