Given N Complex Numbers in the form of Strings, the task is to print the multiplication of these N complex numbers.
Examples:
Input: N = 3, V = { 3 + 1i, 2 + 1i, 5 + -7i }
Output: 10+-60i
Explanation:
Firstly, we will multiply (3+1i) and (2+1i) to yield 5+5i. In the next step, we will multiply 5+5i and -5+-7i to yield the final result 10+-60i.Input: N = 3, V = { “7+4i”, “-12+1i”, “-16+-7i”, “12+18i” }
Output: -9444+35442i
Approach
- Firstly, start iterating from the beginning and take the first 2 Strings and erase both of them.
- Next, convert the string into a number with appropriate signs. Store the Real Part and the Imaginary Part of the String in separate variables. Take a as the real part of the first string while b as the imaginary part of the first string. Take c as the real part of the second string while d as the imaginary part of the second string.
- Next we will calculate the resultant values for the real by calculating the product of a and c and subtracting it with the product of b and subtracting with the product of b and d. For the Imaginary Part, we will calculate the sum of the product of a and d, along with the product of the b and c.
- We will then generate a temporary string to take the sum of real and imaginary values that has been calculated earlier.
- We will push the resultant string into the vector. Repeat the above steps until there is only one remaining element in the vector.
- Return the last remaining element in the vector, which is the desired answer.
Below is the implementation of our above approach:
C++
// C++ Program to multiply// N complex Numbers#include <bits/stdc++.h>using namespace std;#define ll long long// Function which returns the// string in digit formatvector<long long int> findnum(string s1){ vector<long long int> v; // a : real // b : imaginary int a = 0, b = 0; int sa = 0, sb = 0, i = 0; // sa : sign of a // sb : sign of b if (s1[0] == '-') { sa = 1; i = 1; } // Extract the real number while (isdigit(s1[i])) { a = a * 10 + (int(s1[i]) - 48); i++; } if (s1[i] == '+') { sb = 0; i += 1; } if (s1[i] == '-') { sb = 1; i += 1; } // Extract the imaginary part while (i < s1.length() && isdigit(s1[i])) { b = b * 10 + (int(s1[i]) - 48); i++; } if (sa) a *= -1; if (sb) b *= -1; v.push_back(a); v.push_back(b); return v;}string complexNumberMultiply(vector<string> v){ // if size==1 means we reached at result while (v.size() != 1) { // Extract the first two elements vector<ll> v1 = findnum(v[0]); vector<ll> v2 = findnum(v[1]); // Remove them v.erase(v.begin()); v.erase(v.begin()); // Calculate and store the real part ll r = (v1[0] * v2[0] - v1[1] * v2[1]); // Calculate and store the imaginary part ll img = v1[0] * v2[1] + v1[1] * v2[0]; string res = ""; // Append the real part res += to_string(r); res += '+'; // Append the imaginary part res += to_string(img) + 'i'; // Insert into vector v.insert(v.begin(), res); } return v[0];}// Driver Functionint main(){ int n = 3; vector<string> v = { "3+1i", "2+1i", "-5+-7i" }; cout << complexNumberMultiply(v) << "\n"; return 0;} |
Java
// Java Program to multiply// N complex Numbersimport java.util.*;class GFG{ // Function which returns the // string in digit format static ArrayList<Integer> findnum(String s1) { ArrayList<Integer> v = new ArrayList<Integer>(); // a : real // b : imaginary int a = 0, b = 0; int sa = 0, sb = 0, i = 0; // sa : sign of a // sb : sign of b if (s1.charAt(0) == '-') { sa = 1; i = 1; } // Extract the real number while (Character.isDigit(s1.charAt(i))) { a = a * 10 + (s1.charAt(i) - '0'); i++; } if (s1.charAt(i) == '+') { sb = 0; i += 1; } if (s1.charAt(i) == '-') { sb = 1; i += 1; } // Extract the imaginary part while (i < s1.length() && Character.isDigit(s1.charAt(i))) { b = b * 10 + (s1.charAt(i) - '0'); i++; } if (sa != 0) a *= -1; if (sb != 0) b *= -1; v.add(a); v.add(b); return v; } static String complexNumberMultiply(ArrayList<String> v) { // if size==1 means we reached at result while (v.size() != 1) { // Extract the first two elements ArrayList<Integer> v1 = findnum(v.get(0)); ArrayList<Integer> v2 = findnum(v.get(1)); // Remove them v.remove(0); v.remove(0); // Calculate and store the real part int r = (v1.get(0) * v2.get(0) - v1.get(1) * v2.get(1)); // Calculate and store the imaginary part int img = v1.get(0) * v2.get(1) + v1.get(1) * v2.get(0); String res = ""; // Append the real part res += String.valueOf(r); res += '+'; // Append the imaginary part res += String.valueOf(img) + 'i'; // Insert into List v.add(0, res); } return v.get(0); } // Driver Function public static void main(String[] args) { int n = 3; ArrayList<String> v = new ArrayList<String>(); v.add("3+1i"); v.add("2+1i"); v.add("-5+-7i"); System.out.println(complexNumberMultiply(v)); }}// This code is contributed by phasing17 |
Python3
# Python3 program to multiply# N complex Numbers# Function which returns the# in digit formatdef findnum(s1): v = [] # a : real # b : imaginary a = 0 b = 0 sa = 0 sb = 0 i = 0 # sa : sign of a # sb : sign of b if (s1[0] == '-'): sa = 1 i = 1 # Extract the real number while (s1[i].isdigit()): a = a * 10 + (int(s1[i])) i += 1 if (s1[i] == '+'): sb = 0 i += 1 if (s1[i] == '-'): sb = 1 i += 1 # Extract the imaginary part while (i < len(s1) and s1[i].isdigit()): b = b * 10 + (int(s1[i])) i += 1 if (sa): a *= -1 if (sb): b *= -1 v.append(a) v.append(b) return vdef complexNumberMultiply(v): # If size==1 means we reached at result while (len(v) != 1): # Extract the first two elements v1 = findnum(v[0]) v2 = findnum(v[1]) # Remove them del v[0] del v[0] # Calculate and store the real part r = (v1[0] * v2[0] - v1[1] * v2[1]) # Calculate and store the imaginary part img = v1[0] * v2[1] + v1[1] * v2[0] res = "" # Append the real part res += str(r) res += '+' # Append the imaginary part res += str(img) + 'i' # Insert into vector v.insert(0, res) return v[0]# Driver codeif __name__ == '__main__': n = 3 v = [ "3+1i", "2+1i", "-5+-7i" ] print(complexNumberMultiply(v))# This code is contributed by mohit kumar 29 |
C#
// C# Program to multiply// N complex Numbersusing System;using System.Linq;using System.Collections.Generic;class GFG{ // Function which returns the // string in digit format static List<int> findnum(string s1) { List<int> v = new List<int>(); // a : real // b : imaginary int a = 0, b = 0; int sa = 0, sb = 0, i = 0; // sa : sign of a // sb : sign of b if (s1[0] == '-') { sa = 1; i = 1; } // Extract the real number while (Char.IsDigit(s1[i])) { a = a * 10 + (s1[i] - '0'); i++; } if (s1[i] == '+') { sb = 0; i += 1; } if (s1[i] == '-') { sb = 1; i += 1; } // Extract the imaginary part while (i < s1.Length && Char.IsDigit(s1[i])) { b = b * 10 + (s1[i] - '0'); i++; } if (sa != 0) a *= -1; if (sb != 0) b *= -1; v.Add(a); v.Add(b); return v; } static string complexNumberMultiply(List<string> v) { // if size==1 means we reached at result while (v.Count != 1) { // Extract the first two elements List<int> v1 = findnum(v[0]); List<int> v2 = findnum(v[1]); // Remove them v.RemoveAt(0); v.RemoveAt(0); // Calculate and store the real part int r = (v1[0] * v2[0] - v1[1] * v2[1]); // Calculate and store the imaginary part int img = v1[0] * v2[1] + v1[1] * v2[0]; string res = ""; // Append the real part res += Convert.ToString(r); res += '+'; // Append the imaginary part res += Convert.ToString(img) + 'i'; // Insert into List v.Insert(0, res); } return v[0]; } // Driver Function public static void Main(string[] args) { int n = 3; List<string> v = new List<string>(); v.Add("3+1i"); v.Add("2+1i"); v.Add("-5+-7i"); Console.WriteLine(complexNumberMultiply(v)); }}// This code is contributed by phasing17 |
Javascript
<script>// JavaScript Program to multiply// N complex Numbers// Function which returns the// string in digit formatfunction findnum(s1){ let v = []; // a : real // b : imaginary let a = 0, b = 0; let sa = 0, sb = 0, i = 0; // sa : sign of a // sb : sign of b if (s1[0] == '-') { sa = 1; i = 1; } // Extract the real number while (s1.charCodeAt(i)>='0'.charCodeAt(0) && s1.charCodeAt(i)<='9'.charCodeAt(0)) { a = a * 10 + (s1.charCodeAt(i) - 48); i++; } if (s1[i] == '+') { sb = 0; i += 1; } if (s1[i] == '-') { sb = 1; i += 1; } // Extract the imaginary part while (i < s1.length && s1.charCodeAt(i)>='0'.charCodeAt(0) && s1.charCodeAt(i)<='9'.charCodeAt(0)) { b = b * 10 + (s1.charCodeAt(i) - 48); i++; } if (sa) a *= -1; if (sb) b *= -1; v.push(a); v.push(b); return v;}function complexNumberMultiply(v){ // if size==1 means we reached at result while (v.length != 1) { // Extract the first two elements let v1 = findnum(v[0]); let v2 = findnum(v[1]); // Remove them v.shift(); v.shift(); // Calculate and store the real part let r = (v1[0] * v2[0] - v1[1] * v2[1]); // Calculate and store the imaginary part let img = v1[0] * v2[1] + v1[1] * v2[0]; let res = ""; // Append the real part res += r.toString(); res += '+'; // Append the imaginary part res += img.toString() + 'i'; // Insert into vector v.unshift(res); } return v[0];}// Driver Functionlet n = 3;let v = [ "3+1i", "2+1i", "-5+-7i" ];document.write(complexNumberMultiply(v),"</br>")// This code is contributed by Shinjanpatra</script> |
Output
10+-60i
Time Complexity: O(N)
Auxiliary Space: O(N)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
