Partition given string in such manner that i’th substring is sum of (i-1)’th and (i-2)’nd substring.
Examples:
Input : "11235813" Output : ["1", "1", "2", "3", "5", "8", "13"] Input : "1111223" Output : ["1", "11", "12", "23"] Input : "1111213" Output : ["11", "1", "12", "13"] Input : "11121114" Output : []
- Iterate through the given string by picking 3 numbers (first, seconds and third) at a time starting from one digit each.
- If first + second = third, recursively call check() with second as first and third as second. The third is picked based on next possible number of digits. (The result of addition of two numbers can have a max. of second’s & third’s digits + 1)
- Else, first increment the third (by adding more digits) till the limit (Here limit is sum of first and second).
- After incrementing third, following cases arise. a) When doesn’t match, increment the second offset. b) When doesn’t match, increment the first offset. c)
- Note: Once a call to check() is made after incrementing the third offset, do not alter the second or first, as those are already finalized.
- When the end of the string is reached and the condition is satisfied, add “second” and “third” to the empty list. While rolling back the recursive stack, prepend the “first” to the list so the order is preserved.
Implementation:
Java
// Java program to check if we can partition a // string in a way that value of i-th string is // sum of (i-1)-th and (i-2)-th substrings. import java.util.LinkedList; public class SumArray { private static LinkedList<Integer> resultList = new LinkedList<>(); private static boolean check(char[] chars, int offset1, int offset2, int offset3, boolean freezeFirstAndSecond) { // Find subarrays according to given offsets int first = intOf(subArr(chars, 0, offset1)); int second = intOf(subArr(chars, offset1, offset2)); int third = intOf(subArr(chars, offset1 + offset2, offset3)); // If condition is satisfied for current subarrays if (first + second == third) { // If whole array is covered. if (offset1 + offset2 + offset3 >= chars.length) { resultList.add(first); resultList.add(second); resultList.add(third); return true; } // Check if remaining array also satisfies the condition boolean result = check(subArr(chars, offset1, chars.length - offset1), offset2, offset3, Math.max(offset2, offset3), true); if (result) { resultList.addFirst(first); } return result; } // If not satisfied, try incrementing third if (isValidOffSet(offset1, offset2, 1 + offset3, chars.length)) { if (check(chars, offset1, offset2, 1 + offset3, false)) return true; } // If first and second have been finalized, do not // alter already computed results if (freezeFirstAndSecond) return false; // If first and second are not finalized if (isValidOffSet(offset1, 1 + offset2, Math.max(offset1, 1 + offset2), chars.length)) { // Try incrementing second if (check(chars, offset1, 1 + offset2, Math.max(offset1, 1 + offset2), false)) return true; } // Try incrementing first if (isValidOffSet(1 + offset1, offset2, Math.max(1 + offset1, offset2), chars.length)) { if (check(chars, 1 + offset1, offset2, Math.max(1 + offset1, offset2), false)) return true; } return false; } // Check if given three offsets are valid (Within array length // and third offset can represent sum of first two) private static boolean isValidOffSet(int offset1, int offset2, int offset3, int length) { return (offset1 + offset2 + offset3 <= length && (offset3 == Math.max(offset1, offset2) || offset3 == 1 + Math.max(offset1, offset2))); } // To get a subarray with starting from given // index and offset private static char[] subArr(char[] chars, int index, int offset) { int trueOffset = Math.min(chars.length - index, offset); char[] destArr = new char[trueOffset]; System.arraycopy(chars, index, destArr, 0, trueOffset); return destArr; } private static int intOf(char... chars) { return Integer.valueOf(new String(chars)); } public static void main(String[] args) { String numStr = "11235813"; char[] chars = numStr.toCharArray(); System.out.println(check(chars, 1, 1, 1, false)); System.out.println(resultList); } } |
C++
#include <iostream>#include <list>#include <algorithm>using namespace std;list<int> resultList;bool check(string chars, int offset1, int offset2, int offset3, bool freezeFirstAndSecond) { // Find substrings according to given offsets string first = chars.substr(0, offset1); string second = chars.substr(offset1, offset2); string third = chars.substr(offset1 + offset2, offset3); // If condition is satisfied for current substrings if (stoi(first) + stoi(second) == stoi(third)) { // If whole string is covered. if (offset1 + offset2 + offset3 >= chars.length()) { resultList.push_back(stoi(first)); resultList.push_back(stoi(second)); resultList.push_back(stoi(third)); return true; } // Check if remaining array also satisfies the condition bool result = check(chars.substr(offset1), offset2, offset3, max(offset2, offset3), true); if (result) { resultList.push_front(stoi(first)); } return result; } // If not satisfied, try incrementing third if (offset1 + offset2 + offset3 <= chars.length() && (offset3 == max(offset1, offset2) || offset3 == 1 + max(offset1, offset2))) { if (check(chars, offset1, offset2, offset3 + 1, false)) return true; } // If first and second have been finalized, do not // alter already computed results if (freezeFirstAndSecond) return false; // If first and second are not finalized if (offset1 + offset2 + offset3 <= chars.length() && (offset3 == max(offset1, offset2) || offset3 == 1 + max(offset1, offset2))) { // Try incrementing second if (check(chars, offset1, offset2 + 1, max(offset1, offset2 + 1), false)) return true; } // Try incrementing first if (offset1 + offset2 + offset3 <= chars.length() && (offset3 == max(offset1, offset2) || offset3 == 1 + max(offset1, offset2))) { if (check(chars, offset1 + 1, offset2, max(offset1 + 1, offset2), false)) return true; } return false;}int main() { string numStr = "11235813"; cout << check(numStr, 1, 1, 1, false) << endl; for (int i : resultList) { cout << i << " "; } return 0;} |
Python3
from typing import ListresultList = []def check(chars: str, offset1: int, offset2: int, offset3: int, freezeFirstAndSecond: bool) -> bool: first = chars[:offset1] second = chars[offset1:offset1+offset2] third = chars[offset1+offset2:offset1+offset2+offset3] if int(first) + int(second) == int(third): if offset1 + offset2 + offset3 >= len(chars): resultList.append(int(first)) resultList.append(int(second)) resultList.append(int(third)) return True result = check(chars[offset1:], offset2, offset3, max(offset2, offset3), True) if result: resultList.insert(0, int(first)) return result if offset1 + offset2 + offset3 <= len(chars) and (offset3 == max(offset1, offset2) or offset3 == 1 + max(offset1, offset2)): if check(chars, offset1, offset2, offset3 + 1, False): return True if freezeFirstAndSecond: return False if offset1 + offset2 + offset3 <= len(chars) and (offset3 == max(offset1, offset2) or offset3 == 1 + max(offset1, offset2)): if check(chars, offset1, offset2 + 1, max(offset1, offset2 + 1), False): return True if offset1 + offset2 + offset3 <= len(chars) and (offset3 == max(offset1, offset2) or offset3 == 1 + max(offset1, offset2)): if check(chars, offset1 + 1, offset2, max(offset1 + 1, offset2), False): return True return Falsedef main() -> None: numStr = "11235813" print(check(numStr, 1, 1, 1, False)) print(resultList)if __name__ == "__main__": main() |
Javascript
// Javascript program for the above approachlet resultList = [];function check(chars, offset1, offset2, offset3, freezeFirstAndSecond) { // Find substrings according to given offsets const first = chars.substring(0, offset1); const second = chars.substring(offset1, offset1 + offset2); const third = chars.substring(offset1 + offset2, offset1 + offset2 + offset3); // If condition is satisfied for current substrings if (parseInt(first) + parseInt(second) === parseInt(third)) { // If whole string is covered. if (offset1 + offset2 + offset3 >= chars.length) { resultList.push(parseInt(first)); resultList.push(parseInt(second)); resultList.push(parseInt(third)); return true; } // Check if remaining array also satisfies the condition const result = check(chars.substring(offset1), offset2, offset3, Math.max(offset2, offset3), true); if (result) { resultList.unshift(parseInt(first)); } return result; } // If not satisfied, try incrementing third if (offset1 + offset2 + offset3 <= chars.length && (offset3 === Math.max(offset1, offset2) || offset3 === 1 + Math.max(offset1, offset2))) { if (check(chars, offset1, offset2, offset3 + 1, false)) { return true; } } // If first and second have been finalized, do not // alter already computed results if (freezeFirstAndSecond) { return false; } // If first and second are not finalized if (offset1 + offset2 + offset3 <= chars.length && (offset3 === Math.max(offset1, offset2) || offset3 === 1 + Math.max(offset1, offset2))) { // Try incrementing second if (check(chars, offset1, offset2 + 1, Math.max(offset1, offset2 + 1), false)) { return true; } } // Try incrementing first if (offset1 + offset2 + offset3 <= chars.length && (offset3 === Math.max(offset1, offset2) || offset3 === 1 + Math.max(offset1, offset2))) { if (check(chars, offset1 + 1, offset2, Math.max(offset1 + 1, offset2), false)) { return true; } } return false;}// Driver code main functionfunction main() { const numStr = "11235813"; console.log(check(numStr, 1, 1, 1, false)); console.log(resultList);}main();// This code is contributed by codebraxnzt |
C#
// C# program for the above approachusing System;using System.Collections.Generic;public class SumArray { private static LinkedList<int> resultList = new LinkedList<int>(); private static bool Check(char[] chars, int offset1, int offset2, int offset3, bool freezeFirstAndSecond) { int first = IntOf(SubArr(chars, 0, offset1)); int second = IntOf(SubArr(chars, offset1, offset2)); int third = IntOf(SubArr(chars, offset1 + offset2, offset3)); if (first + second == third) { if (offset1 + offset2 + offset3 >= chars.Length) { resultList.AddLast(first); resultList.AddLast(second); resultList.AddLast(third); return true; } bool result = Check(SubArr(chars, offset1, chars.Length - offset1), offset2, offset3, Math.Max(offset2, offset3), true); if (result) { resultList.AddFirst(first); } return result; } if (IsValidOffSet(offset1, offset2, 1 + offset3, chars.Length)) { if (Check(chars, offset1, offset2, 1 + offset3, false)) { return true; } } if (freezeFirstAndSecond) { return false; } if (IsValidOffSet(offset1, 1 + offset2, Math.Max(offset1, 1 + offset2), chars.Length)) { if (Check(chars, offset1, 1 + offset2, Math.Max(offset1, 1 + offset2), false)) { return true; } } if (IsValidOffSet(1 + offset1, offset2, Math.Max(1 + offset1, offset2), chars.Length)) { if (Check(chars, 1 + offset1, offset2, Math.Max(1 + offset1, offset2), false)) { return true; } } return false; } private static bool IsValidOffSet(int offset1, int offset2, int offset3, int length) { return (offset1 + offset2 + offset3 <= length && (offset3 == Math.Max(offset1, offset2) || offset3 == 1 + Math.Max(offset1, offset2))); } private static char[] SubArr(char[] chars, int index, int offset) { int trueOffset = Math.Min(chars.Length - index, offset); char[] destArr = new char[trueOffset]; Array.Copy(chars, index, destArr, 0, trueOffset); return destArr; } private static int IntOf(params char[] chars) { return int.Parse(new string(chars)); } public static void Main(string[] args) { string numStr = "11235813"; char[] chars = numStr.ToCharArray(); Console.WriteLine(Check(chars, 1, 1, 1, false)); Console.WriteLine(string.Join(", ", resultList)); }} // This code is contributed by princekumaras |
Output:
true [1, 1, 2, 3, 5, 8, 13]
Time Complexity: O(n)
Auxiliary Space: O(n)
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