Removing a Number from Array to make It Geometric Progression using C++

We are given an array of elements. We need to find whether the elements in the array are in Geometric Progression (GP) or not after removing any 1 element from the array. We can run out the possibilities and with observations to figure out that the first element is fake, or the second element is fake, or these 2 elements will give the common ratio of the array.

After the common ratio is found, we can iterate on the array to see if all elements follow that rule. 2 base conditions would be to check if the first and second elements are fake or not.

Let us look at some input/output scenarios to get a better understanding of the method ?

Assume the input given to the problem is already in geometric progression, so there is not a necessity to remove any element from the array ?

Input: {1, 2, 4, 8, 16}
Result: Already in GP

Assume the input given to the problem is not in geometric progression, the output can be obtained in two ways; if removal of any element will not give us a geometric progression then the output is printed as "not possible" ?

Input: {1, 2, 3, 4, 5, 6}
Result: Not Possible

Assume the input given to the problem is not in geometric progression, the output can be obtained in two ways; if removing one element will give us a geometric progression then the element to be removed is printed as the output ?

Input: {1, 4, 5, 16, 64, 256}
Result: Remove 5

Example

Suppose we have an array such as [1,3,6,9,27,81], and the array would be in GP if we remove element 6 from it.

Following is a program to show the implementation of the same method in C++ ?

<div class="execute"></div><div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span> <span class="token string"><iostream></span></span>
<span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span> <span class="token string"><vector></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">define</span> <span class="token macro-name">DOUBLE_COMPARE_LIMIT</span> <span class="token expression"><span class="token number">1e-6</span></span></span>
<span class="token keyword">bool</span> <span class="token function">isEqual</span><span class="token punctuation">(</span><span class="token keyword">double</span> a<span class="token punctuation">,</span> <span class="token keyword">double</span> b<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">return</span> <span class="token punctuation">(</span><span class="token function">abs</span><span class="token punctuation">(</span>a <span class="token operator">-</span> b<span class="token punctuation">)</span> <span class="token operator"><</span> DOUBLE_COMPARE_LIMIT<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">bool</span> <span class="token function">isGP</span><span class="token punctuation">(</span>vector<span class="token operator"><</span><span class="token keyword">double</span><span class="token operator">></span> arr<span class="token punctuation">,</span> <span class="token keyword">int</span> index<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">double</span> previous <span class="token operator">=</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token keyword">double</span> ratio <span class="token operator">=</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator"><</span> arr<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>i <span class="token operator">!=</span> index<span class="token punctuation">)</span> <span class="token punctuation">{</span>
         <span class="token keyword">if</span> <span class="token punctuation">(</span>previous <span class="token operator">!=</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token keyword">if</span> <span class="token punctuation">(</span>ratio <span class="token operator">==</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
               ratio <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">/</span> previous<span class="token punctuation">;</span>
            <span class="token punctuation">}</span>
            <span class="token keyword">else</span> <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span><span class="token function">isEqual</span><span class="token punctuation">(</span>ratio<span class="token punctuation">,</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">/</span> previous<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
               <span class="token keyword">return</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
            <span class="token punctuation">}</span>
         <span class="token punctuation">}</span>
         previous <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">return</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">solve</span><span class="token punctuation">(</span>vector<span class="token operator"><</span><span class="token keyword">double</span><span class="token operator">></span> arr<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token function">isGP</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> <span class="token operator">-</span><span class="token number">2</span><span class="token punctuation">;</span>

   <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token function">isGP</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
   
   <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token function">isGP</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> <span class="token number">1</span><span class="token punctuation">;</span>
   <span class="token keyword">double</span> ratio <span class="token operator">=</span> arr<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">/</span>arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
   <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">2</span><span class="token punctuation">;</span> i <span class="token operator"><</span> arr<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span><span class="token function">isEqual</span><span class="token punctuation">(</span>ratio<span class="token punctuation">,</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">/</span>arr<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
         <span class="token keyword">return</span> <span class="token punctuation">(</span><span class="token function">isGP</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token operator">?</span> i <span class="token operator">:</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
      <span class="token punctuation">}</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">return</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
   vector<span class="token operator"><</span><span class="token keyword">double</span><span class="token operator">></span> arr <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">6</span><span class="token punctuation">,</span><span class="token number">9</span><span class="token punctuation">,</span><span class="token number">27</span><span class="token punctuation">,</span><span class="token number">81</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
   <span class="token keyword">int</span> index <span class="token operator">=</span> <span class="token function">solve</span><span class="token punctuation">(</span>arr<span class="token punctuation">)</span><span class="token punctuation">;</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>index <span class="token operator">==</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      cout <span class="token operator"><<</span> <span class="token string">"Not possible"</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">else</span> <span class="token keyword">if</span><span class="token punctuation">(</span>index <span class="token operator">==</span> <span class="token operator">-</span><span class="token number">2</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      cout <span class="token operator"><<</span> <span class="token string">"Already in GP"</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">else</span> <span class="token punctuation">{</span>
      cout <span class="token operator"><<</span> <span class="token string">"Remove "</span> <span class="token operator"><<</span> arr<span class="token punctuation">[</span>index<span class="token punctuation">]</span><span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</div><div class="output-wrapper"><div class="console-close"></div><div class="code-output"></div></div>

Output

Remove 6

The common ratio of the elements in the array becomes 3, and the starting element is 1. So the array becomes [1 3,9,27,81]

Conclusion

The above algorithm runs perfectly. This was a pure brute force and implementation problem. We used a function to compare float values because of overflow. We used floats because the common ratio can be in fractions. DOUBLE_COMPARE_LIMIT will compare the float values to a certain decimal place because we might have a long result or never ending decimal. Code it yourself once to better understand the problem.