chore(CPlusPlus): add smallest-possible-sum (#555)

algorithms/CPlusPlus/Arrays/smallest-sum-possible.cpp

@@ -0,0 +1,61 @@
+/* 
+    Description
+    Given an array X of positive integers, its elements are to be transformed by running the following operation on them as many times as required:
+
+    if X[i] > X[j] then X[i] = X[i] - X[j]
+
+    When no more transformations are possible, return its sum ("smallest possible sum").
+
+    For instance, the successive transformation of the elements of input X = [6, 9, 21] is detailed below:
+
+    X_1 = [6, 9, 12] # -> X_1[2] = X[2] - X[1] = 21 - 9
+    X_2 = [6, 9, 6]  # -> X_2[2] = X_1[2] - X_1[0] = 12 - 6
+    X_3 = [6, 3, 6]  # -> X_3[1] = X_2[1] - X_2[0] = 9 - 6
+    X_4 = [6, 3, 3]  # -> X_4[2] = X_3[2] - X_3[1] = 6 - 3
+    X_5 = [3, 3, 3]  # -> X_5[1] = X_4[0] - X_4[1] = 6 - 3
+    The returning output is the sum of the final transformation (here 9).
+
+    Example
+    solution([6, 9, 21]) #-> 9
+*/
+
+/* 
+    ~~~~~~~ NOTE ~~~~~~~~~
+    There are performance tests consisted of very big numbers and arrays of size at least 30000. Please write an efficient algorithm to prevent timeout.
+    Your IDE may not show timeout, but timeout can occur in standard coding competetions.
+*/
+
+
+#include <vector>
+#include <algorithm>
+#include <iostream>
+#include <numeric>
+
+using namespace std;
+
+unsigned long long solution(const vector<unsigned long long>& arr){
+    unsigned long long prev_gcd = arr[0];
+    for (auto i : arr){
+        prev_gcd = gcd(i, prev_gcd);       // finding gcd of the array.
+    }
+    return arr.size()*prev_gcd;
+}
+
+int main() {
+    const vector<unsigned long long> vec = {9, 6, 12};
+    cout << solution(vec);
+}
+
+/*
+    Testcases : 
+    solution({1,21,55}) // --> 3
+    solution({3,13,23,7,83}) // --> 5
+    solution({4,16,24}) // --> 12
+    solution({30,12}) // --> 12
+    solution({60,12,96,48,60,24,72,36,72,72,48}) // --> 132 
+    solution({71,71,71,71,71,71,71,71,71,71,71,71,71}) // --> 923
+    solution({11,22}) // --> 22
+    solution({9}) // --> 9
+    solution({1}) // --> 1
+    solution({9, 9}) // --> 18
+*/

algorithms/CPlusPlus/README.md

@@ -20,10 +20,12 @@
 - [Segregate 0s and 1s](Arrays/segregate-0-and-1.cpp)
 - [Search insert position](Arrays/search-insert-position.cpp)
 - [Matrix Multiplication](Arrays/matrix-multiplication.cpp)
+- [Smallest Sum Possible](Arrays/smallest-sum-possible.cpp)
 - [Smallest Possible Sum](Arrays/smallest-possible-sum.cpp)
 - [Move Zeros to End of The Array](Arrays/move-zeros-to-end-of-array.cpp)
 - [Kadane's Algorithm](Arrays/Kadane's-Algorithm.cpp)
 
+
 ## Dynamic-Programming
 
 - [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)