Merge pull request #25 from Aqdas-7/main

#24 smallest multiple

challenge/smallest_multiple/smallestMultiple.cpp

@@ -0,0 +1,91 @@
+
+// Factor all the integers from 1 to 20 into their prime factorizations. For example, factor 18 as 18 = 3^2 * 2. 
+//Now, for each prime number p that appears in the prime factorization of some integer in the range 1 to 20, 
+//find the maximum exponent that it has among all those prime factorizations. 
+//For example, the prime 3 will have exponent 2 because it appears in the factorization of 18 as 3^2 and if it appeared in any prime factorization with an exponent of 3 (i.e., 3^3),
+//that number would have to be at least as large as 3^3 = 27 which it outside of the range 1 to 20. 
+//Now collect all of these primes with their corresponding exponent and you have the answer.
+
+
+// So, as example, let's find the smallest number evenly divisible by all the numbers from 1 to 4.
+
+// 2 = 2^1
+// 3 = 3^1
+// 4 = 2^2
+// The primes that appear are 2 and 3. We note that the maximum exponent of 2 is 2 and the maximum exponent of 3 
+// is 1. Thus, the smallest number that is evenly divisible by all the numbers from 1 to 4 is 2^2 * 3 = 12.
+
+// Here's a relatively straightforward implementation.
+
+#include <iostream>
+#include <vector>
+
+
+
+    std::vector<int> GetPrimes(int max) {
+    bool *isPrime = new bool[max + 1];
+    for(int i = 0; i <= max; i++) {
+        isPrime[i] = true;
+    }
+    isPrime[0] = isPrime[1] = false;
+    int p = 2;
+    while(p <= max) {
+        if(isPrime[p]) {
+            for(int j = 2; p * j <= max; j++) {
+                isPrime[p * j] = false;
+            }
+        }
+        p++;
+    }
+
+    std::vector<int> primes;
+
+    for(int i = 0; i <= max; i++) {
+        if(isPrime[i]) primes.push_back(i);
+    }
+
+    delete []isPrime;
+    return primes;
+}
+
+std::vector<int> Factor(int n, const std::vector<int> &primes) {
+    std::vector<int> exponents(primes.size(), 0);
+    while(n > 1) {
+        for(int i = 0; i < primes.size(); i++) {
+        if(n % primes[i] == 0) { 
+        exponents[i]++;
+            n /= primes[i];
+        break;
+        }
+            }
+    }
+    return exponents;
+}
+
+
+int main() {
+    int n;
+    std::cout << "Enter an integer: ";
+    std::cin >> n;
+    std::vector<int> primes = GetPrimes(n);
+    std::vector<int> exponents(primes.size(), 0);
+
+    for(int i = 2; i <= n; i++) {
+        std::vector<int> factors = Factor(i, primes);
+        for(int i = 0; i < exponents.size(); i++) {
+            if(factors[i] > exponents[i]) exponents[i] = factors[i];
+        }
+    }
+
+    int p = 1;
+    for(int i = 0; i < primes.size(); i++) {
+            for(int j = 0; j < exponents[i]; j++) {
+            p *= primes[i];
+        }
+    }
+
+    std::cout << "Answer: " << p << std::endl;
+
+
+}
+