Dados dos números como strings. Los números pueden ser muy grandes (pueden no caber en long long int), la tarea es encontrar la diferencia entre estos dos números.
Ejemplos:
Input : str1 = "11443333311111111100", str2 = "1144422222221111" Output : 11442188888888889989 Input :str1 = "122387876566565674", str2 = "31435454654554" Output : 122356441111911120
Esto se basa simplemente en las matemáticas escolares. Recorremos ambas strings desde el final, una a una restamos dígitos.
- Invierte ambas cuerdas.
- Siga restando dígitos uno por uno desde el índice 0′ (en strings invertidas) hasta el final de una string más pequeña, agregue la diferencia si es positiva al final del resultado. Si la diferencia (diff) es negativa, agregue 10 y realice un seguimiento del acarreo como 1, si es positivo, entonces el acarreo es 0.
- Finalmente, invierte el resultado.
A continuación se muestra la implementación de la idea anterior:
C++
// C++ program to find difference of two large numbers. #include <bits/stdc++.h> using namespace std; // Returns true if str1 is smaller than str2. bool isSmaller(string str1, string str2) { // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) if (str1[i] < str2[i]) return true; else if (str1[i] > str2[i]) return false; return false; } // Function for find difference of larger numbers string findDiff(string str1, string str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller(str1, str2)) swap(str1, str2); // Take an empty string for storing result string str = ""; // Calculate length of both string int n1 = str1.length(), n2 = str2.length(); // Reverse both of strings reverse(str1.begin(), str1.end()); reverse(str2.begin(), str2.end()); int carry = 0; // Run loop till small string length // and subtract digit of str1 to str2 for (int i = 0; i < n2; i++) { // Do school mathematics, compute difference of // current digits int sub = ((str1[i] - '0') - (str2[i] - '0') - carry); // If subtraction is less than zero // we add then we add 10 into sub and // take carry as 1 for calculating next step if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str.push_back(sub + '0'); } // subtract remaining digits of larger number for (int i = n2; i < n1; i++) { int sub = ((str1[i] - '0') - carry); // if the sub value is -ve, then make it positive if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str.push_back(sub + '0'); } // reverse resultant string reverse(str.begin(), str.end()); return str; } // Driver code int main() { string str1 = "978"; string str2 = "12977"; // Function call cout << findDiff(str1, str2) << endl; string s1 = "100"; string s2 = "1000000"; // Function call cout << findDiff(s1, s2); return 0; }
Java
// Java program to find difference of two large numbers. import java.util.*; class GFG { // Returns true if str1 is smaller than str2. static boolean isSmaller(String str1, String str2) { // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) if (str1.charAt(i) < str2.charAt(i)) return true; else if (str1.charAt(i) > str2.charAt(i)) return false; return false; } // Function for find difference of larger numbers static String findDiff(String str1, String str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller(str1, str2)) { String t = str1; str1 = str2; str2 = t; } // Take an empty string for storing result String str = ""; // Calculate length of both string int n1 = str1.length(), n2 = str2.length(); // Reverse both of strings str1 = new StringBuilder(str1).reverse().toString(); str2 = new StringBuilder(str2).reverse().toString(); int carry = 0; // Run loop till small string length // and subtract digit of str1 to str2 for (int i = 0; i < n2; i++) { // Do school mathematics, compute difference of // current digits int sub = ((int)(str1.charAt(i) - '0') - (int)(str2.charAt(i) - '0') - carry); // If subtraction is less than zero // we add then we add 10 into sub and // take carry as 1 for calculating next step if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += (char)(sub + '0'); } // subtract remaining digits of larger number for (int i = n2; i < n1; i++) { int sub = ((int)(str1.charAt(i) - '0') - carry); // if the sub value is -ve, then make it // positive if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += (char)(sub + '0'); } // reverse resultant string return new StringBuilder(str).reverse().toString(); } // Driver code public static void main(String[] args) { String str1 = "978"; String str2 = "12977"; // Function call System.out.println(findDiff(str1, str2)); String s1 = "100"; String s2 = "1000000"; // Function call System.out.println(findDiff(s1, s2)); } } // This code is contributed by mits
Python3
# Python 3 program to find difference of two large numbers. # Returns true if str1 is smaller than str2. def isSmaller(str1, str2): # Calculate lengths of both string n1 = len(str1) n2 = len(str2) if (n1 < n2): return True if (n2 < n1): return False for i in range(n1): if (str1[i] < str2[i]): return True elif (str1[i] > str2[i]): return False return False # Function for find difference of larger numbers def findDiff(str1, str2): # Before proceeding further, make sure str1 # is not smaller if (isSmaller(str1, str2)): temp = str1 str1 = str2 str2 = temp # Take an empty string for storing result str3 = "" # Calculate length of both string n1 = len(str1) n2 = len(str2) # Reverse both of strings str1 = str1[::-1] str2 = str2[::-1] carry = 0 # Run loop till small string length # and subtract digit of str1 to str2 for i in range(n2): # Do school mathematics, compute difference of # current digits sub = ((ord(str1[i])-ord('0'))-(ord(str2[i])-ord('0'))-carry) # If subtraction is less than zero # we add then we add 10 into sub and # take carry as 1 for calculating next step if (sub < 0): sub = sub + 10 carry = 1 else: carry = 0 str3 = str3+str(sub) # subtract remaining digits of larger number for i in range(n2, n1): sub = ((ord(str1[i])-ord('0')) - carry) # if the sub value is -ve, then make it positive if (sub < 0): sub = sub + 10 carry = 1 else: carry = 0 str3 = str3+str(sub) # reverse resultant string str3 = str3[::-1] return str3 # Driver code if __name__ == "__main__": str1 = "978" str2 = "12977" # Function call print(findDiff(str1, str2)) s1 = "100" s2 = "1000000" # Function call print(findDiff(s1, s2)) # This code is contributed by ChitraNayal
C#
// C# program to find difference of two large numbers. using System; using System.Collections; class GFG { // Returns true if str1 is smaller than str2. static bool isSmaller(string str1, string str2) { // Calculate lengths of both string int n1 = str1.Length, n2 = str2.Length; if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) if (str1[i] < str2[i]) return true; else if (str1[i] > str2[i]) return false; return false; } // Function for find difference of larger numbers static string findDiff(string str1, string str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller(str1, str2)) { string t = str1; str1 = str2; str2 = t; } // Take an empty string for storing result string str = ""; // Calculate length of both string int n1 = str1.Length, n2 = str2.Length; // Reverse both of strings char[] ch1 = str1.ToCharArray(); Array.Reverse(ch1); str1 = new string(ch1); char[] ch2 = str2.ToCharArray(); Array.Reverse(ch2); str2 = new string(ch2); int carry = 0; // Run loop till small string length // and subtract digit of str1 to str2 for (int i = 0; i < n2; i++) { // Do school mathematics, compute difference of // current digits int sub = ((int)(str1[i] - '0') - (int)(str2[i] - '0') - carry); // If subtraction is less than zero // we add then we add 10 into sub and // take carry as 1 for calculating next step if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += (char)(sub + '0'); } // subtract remaining digits of larger number for (int i = n2; i < n1; i++) { int sub = ((int)(str1[i] - '0') - carry); // if the sub value is -ve, then make it // positive if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += (char)(sub + '0'); } // reverse resultant string char[] ch3 = str.ToCharArray(); Array.Reverse(ch3); return new string(ch3); } // Driver code public static void Main() { string str1 = "978"; string str2 = "12977"; // Function call Console.WriteLine(findDiff(str1, str2)); string s1 = "100"; string s2 = "1000000"; // Function call Console.WriteLine(findDiff(s1, s2)); } } // This code is contributed by mits
PHP
<?php // PHP program to find difference of two large numbers. // Returns true if str1 is smaller than str2. function isSmaller($str1, $str2) { // Calculate lengths of both string $n1 = strlen($str1); $n2 = strlen($str2); if ($n1 < $n2) return true; if ($n2 < $n1) return false; for ($i=0; $i<$n1; $i++) if ($str1[$i] < $str2[$i]) return true; else if ($str1[$i] > $str2[$i]) return false; return false; } // Function for find difference of larger numbers function findDiff($str1, $str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller($str1, $str2)){ $t=$str1; $str1=$str2; $str2=$t; } // Take an empty string for storing result $str = ""; // Calculate length of both string $n1 = strlen($str1); $n2 = strlen($str2); // Reverse both of strings $str1=strrev($str1); $str2=strrev($str2); $carry = 0; // Run loop till small string length // and subtract digit of str1 to str2 for ($i=0; $i<$n2; $i++) { // Do school mathematics, compute difference of // current digits $sub=((ord($str1[$i])-ord('0'))-(ord($str2[$i])-ord('0'))-$carry); // If subtraction is less than zero // we add then we add 10 into sub and // take carry as 1 for calculating next step if ($sub < 0) { $sub = $sub + 10; $carry = 1; } else $carry = 0; $str.=chr($sub+48); } // subtract remaining digits of larger number for ($i=$n2; $i<$n1; $i++) { $sub = ((ord($str1[$i])-ord('0')) - $carry); // if the sub value is -ve, then make it positive if ($sub < 0) { $sub = $sub + 10; $carry = 1; } else $carry = 0; $str.=chr($sub+48); } // reverse resultant string $str=strrev($str); return $str; } // Driver code $str1 = "978"; $str2 = "12977"; // Function call echo findDiff($str1, $str2)."\n"; $s1 = "100"; $s2 = "1000000"; // Function call echo findDiff($s1,$s2); // This code is contributed by mits ?>
Javascript
<script> // Javascript program to find difference // of two large numbers. // Returns true if str1 is smaller than str2. function isSmaller(str1,str2) { // Calculate lengths of both string let n1 = str1.length, n2 = str2.length; if (n1 < n2) return true; if (n2 < n1) return false; for (let i = 0; i < n1; i++) if (str1[i] < str2[i]) return true; else if (str1[i] > str2[i]) return false; return false; } // Function for find difference // of larger numbers function findDiff(str1,str2) { // Before proceeding further, // make sure str1 // is not smaller if (isSmaller(str1, str2)) { let t = str1; str1 = str2; str2 = t; } // Take an empty string for storing result let str = ""; // Calculate length of both string let n1 = str1.length, n2 = str2.length; // Reverse both of strings str1 = str1.split("").reverse().join("") str2 = str2.split("").reverse().join("") let carry = 0; // Run loop till small string length // and subtract digit of str1 to str2 for (let i = 0; i < n2; i++) { // Do school mathematics, // compute difference of // current digits let sub = ((str1[i].charCodeAt(0) - '0'.charCodeAt(0)) - (str2[i].charCodeAt(0) - '0'.charCodeAt(0)) - carry); // If subtraction is less than zero // we add then we add 10 into sub and // take carry as 1 for calculating next step if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += String.fromCharCode(sub + '0'.charCodeAt(0)); } // subtract remaining digits of larger number for (let i = n2; i < n1; i++) { let sub = ((str1[i].charCodeAt(0) - '0'.charCodeAt(0)) - carry); // if the sub value is -ve, then make it // positive if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += String.fromCharCode(sub + '0'.charCodeAt(0)); } // reverse resultant string return str.split("").reverse().join("") } // Driver code let str1 = "978"; let str2 = "12977"; document.write(findDiff(str1, str2)+"<br>"); let s1 = "100"; let s2 = "1000000"; document.write(findDiff(s1, s2)+"<br>"); // This code is contributed by rag2127 </script>
11999 0999900
Complejidad temporal: O(n1 + n2)
Espacio auxiliar: O(max(n1, n2))
Solución optimizada:
podemos evitar las dos primeras operaciones inversas de strings atravesándolas desde el final.
A continuación se muestra la solución optimizada.
C++
// C++ program to find difference of two large numbers. #include <bits/stdc++.h> using namespace std; // Returns true if str1 is smaller than str2, // else false. bool isSmaller(string str1, string str2) { // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) { if (str1[i] < str2[i]) return true; else if (str1[i] > str2[i]) return false; } return false; } // Function for finding difference of larger numbers string findDiff(string str1, string str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller(str1, str2)) swap(str1, str2); // Take an empty string for storing result string str = ""; // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); int diff = n1 - n2; // Initially take carry zero int carry = 0; // Traverse from end of both strings for (int i = n2 - 1; i >= 0; i--) { // Do school mathematics, compute difference of // current digits and carry int sub = ((str1[i + diff] - '0') - (str2[i] - '0') - carry); if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str.push_back(sub + '0'); } // subtract remaining digits of str1[] for (int i = n1 - n2 - 1; i >= 0; i--) { if (str1[i] == '0' && carry) { str.push_back('9'); continue; } int sub = ((str1[i] - '0') - carry); if (i > 0 || sub > 0) // remove preceding 0's str.push_back(sub + '0'); carry = 0; } // reverse resultant string reverse(str.begin(), str.end()); return str; } // Driver code int main() { string str1 = "88"; string str2 = "1079"; // Function call cout << findDiff(str1, str2); return 0; }
Java
// Java program to find difference of two large numbers. class GFG { // Returns true if str1 is smaller than str2, // else false. static boolean isSmaller(String str1, String str2) { // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) { if (str1.charAt(i) < str2.charAt(i)) return true; else if (str1.charAt(i) > str2.charAt(i)) return false; } return false; } // Function for finding difference of larger numbers static String findDiff(String str1, String str2) { // Before proceeding further, make sure str1 // is not smaller if (isSmaller(str1, str2)) { String t = str1; str1 = str2; str2 = t; } // Take an empty string for storing result String str = ""; // Calculate lengths of both string int n1 = str1.length(), n2 = str2.length(); int diff = n1 - n2; // Initially take carry zero int carry = 0; // Traverse from end of both strings for (int i = n2 - 1; i >= 0; i--) { // Do school mathematics, compute difference of // current digits and carry int sub = (((int)str1.charAt(i + diff) - (int)'0') - ((int)str2.charAt(i) - (int)'0') - carry); if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += String.valueOf(sub); } // subtract remaining digits of str1[] for (int i = n1 - n2 - 1; i >= 0; i--) { if (str1.charAt(i) == '0' && carry > 0) { str += "9"; continue; } int sub = (((int)str1.charAt(i) - (int)'0') - carry); if (i > 0 || sub > 0) // remove preceding 0's str += String.valueOf(sub); carry = 0; } // reverse resultant string return new StringBuilder(str).reverse().toString(); } // Driver code public static void main(String[] args) { String str1 = "88"; String str2 = "1079"; // Function call System.out.println(findDiff(str1, str2)); } } // This code is contributed by mits
Python3
# Python3 program to find difference # of two large numbers. # Returns true if str1 is smaller than # str2, else false. def isSmaller(str1, str2): # Calculate lengths of both string n1 = len(str1) n2 = len(str2) if (n1 < n2): return True if (n2 < n1): return False for i in range(n1): if (str1[i] < str2[i]): return True elif (str1[i] > str2[i]): return False return False # Function for finding difference # of larger numbers def findDiff(str1, str2): # Before proceeding further, # make sure str1 is not smaller if (isSmaller(str1, str2)): str1, str2 = str2, str1 # Take an empty string for # storing result Str = "" # Calculate lengths of both string n1 = len(str1) n2 = len(str2) diff = n1 - n2 # Initially take carry zero carry = 0 # Traverse from end of both strings for i in range(n2 - 1, -1, -1): # Do school mathematics, compute # difference of current digits # and carry sub = ((ord(str1[i + diff]) - ord('0')) - (ord(str2[i]) - ord('0')) - carry) if (sub < 0): sub += 10 carry = 1 else: carry = 0 Str += chr(sub + ord('0')) # Subtract remaining digits of str1[] for i in range(n1 - n2 - 1, -1, -1): if (str1[i] == '0' and carry): Str += '9' continue sub = (ord(str1[i]) - ord('0')) - carry # Remove preceding 0's if (i > 0 or sub > 0): Str += chr(sub + ord('0')) carry = 0 # Reverse resultant string Str = Str[::-1] return Str # Driver code str1 = "88" str2 = "1079" # Function call print(findDiff(str1, str2)) # This code is contributed by avanitrachhadiya2155
C#
// C# program to find difference of // two large numbers. using System; class GFG { // Returns true if str1 is smaller // than str2, else false. static bool isSmaller(string str1, string str2) { // Calculate lengths of both string int n1 = str1.Length, n2 = str2.Length; if (n1 < n2) return true; if (n2 < n1) return false; for (int i = 0; i < n1; i++) { if (str1[i] < str2[i]) return true; else if (str1[i] > str2[i]) return false; } return false; } // Function for finding difference of // larger numbers static string findDiff(string str1, string str2) { // Before proceeding further, // make sure str1 is not smaller if (isSmaller(str1, str2)) { string t = str1; str1 = str2; str2 = t; } // Take an empty string for // storing result String str = ""; // Calculate lengths of both string int n1 = str1.Length, n2 = str2.Length; int diff = n1 - n2; // Initially take carry zero int carry = 0; // Traverse from end of both strings for (int i = n2 - 1; i >= 0; i--) { // Do school mathematics, compute // difference of current digits and carry int sub = (((int)str1[i + diff] - (int)'0') - ((int)str2[i] - (int)'0') - carry); if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += sub.ToString(); } // subtract remaining digits of str1[] for (int i = n1 - n2 - 1; i >= 0; i--) { if (str1[i] == '0' && carry > 0) { str += "9"; continue; } int sub = (((int)str1[i] - (int)'0') - carry); if (i > 0 || sub > 0) // remove preceding 0's str += sub.ToString(); carry = 0; } // reverse resultant string char[] aa = str.ToCharArray(); Array.Reverse(aa); return new string(aa); } // Driver code public static void Main() { String str1 = "88"; String str2 = "1079"; // Function call Console.WriteLine(findDiff(str1, str2)); } } // This code is contributed by mits
PHP
<?php // PHP program to find difference of two // large numbers. // Returns true if str1 is smaller than // str2, else false. function isSmaller($str1, $str2) { // Calculate lengths of both string $n1 = strlen($str1); $n2 = strlen($str2); if ($n1 < $n2) return true; if ($n2 < $n1) return false; for ($i = 0; $i < $n1; $i++) { if ($str1[$i] < $str2[$i]) return true; else if ($str1[$i] > $str2[$i]) return false; } return false; } // Function for finding difference // of larger numbers function findDiff($str1, $str2) { // Before proceeding further, make // sure str1 is not smaller if (isSmaller($str1, $str2)) { $t = $str1; $str1 = $str2; $str2 = $t; } // Take an empty string for storing result $str = ""; // Calculate lengths of both string $n1 = strlen($str1); $n2 = strlen($str2); $diff = $n1 - $n2; // Initially take carry zero $carry = 0; // Traverse from end of both strings for ($i = $n2 - 1; $i >= 0; $i--) { // Do school mathematics, compute // difference of current digits and carry $sub = ((ord($str1[$i + $diff]) - ord('0')) - (ord($str2[$i]) - ord('0')) - $carry); if ($sub < 0) { $sub = $sub + 10; $carry = 1; } else $carry = 0; $str.=chr($sub + ord("0")); } // subtract remaining digits of str1[] for ($i = $n1 - $n2 - 1; $i >= 0; $i--) { if ($str1[$i] == '0' && $carry > 0) { $str.="9"; continue; } $sub = (ord($str1[$i]) - ord('0') - $carry); if ($i > 0 || $sub > 0) // remove preceding 0's $str.=chr($sub + ord("0")); $carry = 0; } // reverse resultant string return strrev($str); } // Driver code $str1 = "88"; $str2 = "1079"; // Function call print(findDiff($str1, $str2)); // This code is contributed by chandan_jnu ?>
Javascript
<script> // JavaScript program to find difference // of two large numbers. // Returns true if str1 is smaller // than str2, else false. function isSmaller(str1, str2) { // Calculate lengths of both string let n1 = str1.length, n2 = str2.length; if (n1 < n2) return true; if (n2 < n1) return false; for (let i = 0; i < n1; i++) { if (str1[i].charCodeAt() < str2[i].charCodeAt()) return true; else if (str1[i].charCodeAt() > str2[i].charCodeAt()) return false; } return false; } // Function for finding difference of // larger numbers function findDiff(str1, str2) { // Before proceeding further, // make sure str1 is not smaller if (isSmaller(str1, str2)) { let t = str1; str1 = str2; str2 = t; } // Take an empty string for // storing result let str = ""; // Calculate lengths of both string let n1 = str1.length, n2 = str2.length; let diff = n1 - n2; // Initially take carry zero let carry = 0; // Traverse from end of both strings for (let i = n2 - 1; i >= 0; i--) { // Do school mathematics, compute // difference of current digits and carry let sub = ((str1[i + diff].charCodeAt() - '0'.charCodeAt()) - (str2[i].charCodeAt() - '0'.charCodeAt()) - carry); if (sub < 0) { sub = sub + 10; carry = 1; } else carry = 0; str += sub.toString(); } // subtract remaining digits of str1[] for (let i = n1 - n2 - 1; i >= 0; i--) { if (str1[i] == '0' && carry > 0) { str += "9"; continue; } let sub = ((str1[i].charCodeAt() - '0'.charCodeAt()) - carry); if (i > 0 || sub > 0) // remove preceding 0's str += sub.toString(); carry = 0; } // reverse resultant string let aa = str.split(''); aa.reverse(); return aa.join(""); } let str1 = "88"; let str2 = "1079"; // Function call document.write(findDiff(str1, str2)); </script>
991
Complejidad del tiempo : O(n1 + n2)
Espacio auxiliar: O(max(n1, n2))
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA