C++ program to remove minimum elements from either side such that 2*min becomes more than max

The problem involves removing elements from any side of a list of integers in such a way that 2*min is greater than max.

vector<int> arr = {250, 10, 11, 12, 19, 200};
res = solve(arr);

We can use brute force approach. We can try all possible subarrays which satisfy and find the longest one in which 2*min > max condition holds. We can also use dynamic programming approach to try all possible subarray combinations that are overkill and not required.

Example  (Using Vector ADT)

Suppose we have an array such as "[250, 10, 11, 12, 19, 200]". To get the optimal solution, we need to remove elements [250, 200] to make the array [10, 11, 12, 19] where min is 10 and max is 19. So 2*10 > 19. We removed 2 elements from the array, so the output is printed as 2.

Following is a C++ program that depicts how to remove minimum number of elements from an array such that twice of minimum value is greater than the maximum value ?

<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 keyword">int</span> <span class="token function">solve</span><span class="token punctuation">(</span>vector<span class="token operator"><</span><span class="token keyword">int</span><span class="token operator">></span> arr<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">int</span> startIndex <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">,</span> endIndex <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
   <span class="token keyword">bool</span> foundAnAnswer <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
   <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> start<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> start<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> start<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">int</span> min <span class="token operator">=</span> INT32_MAX<span class="token punctuation">,</span> max <span class="token operator">=</span> INT32_MIN<span class="token punctuation">;</span>
      <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> end<span class="token operator">=</span>start<span class="token punctuation">;</span> end<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> end<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>arr<span class="token punctuation">[</span>end<span class="token punctuation">]</span> <span class="token operator"><</span> min<span class="token punctuation">)</span> min <span class="token operator">=</span> arr<span class="token punctuation">[</span>end<span class="token punctuation">]</span><span class="token punctuation">;</span>
         <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>end<span class="token punctuation">]</span> <span class="token operator">></span> max<span class="token punctuation">)</span> max <span class="token operator">=</span> arr<span class="token punctuation">[</span>end<span class="token punctuation">]</span><span class="token punctuation">;</span>
         <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>min <span class="token operator"><=</span> max<span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
         <span class="token keyword">if</span> <span class="token punctuation">(</span>end <span class="token operator">-</span> start <span class="token operator">></span> endIndex <span class="token operator">-</span> startIndex <span class="token operator">||</span> <span class="token operator">!</span>foundAnAnswer<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            startIndex <span class="token operator">=</span> start<span class="token punctuation">;</span>
            endIndex <span class="token operator">=</span> end<span class="token punctuation">;</span>
            foundAnAnswer <span class="token operator">=</span> <span class="token boolean">true</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">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>foundAnAnswer<span class="token punctuation">)</span> <span class="token keyword">return</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>
   <span class="token keyword">return</span> <span class="token punctuation">(</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 operator">-</span> <span class="token punctuation">(</span>endIndex <span class="token operator">-</span> startIndex <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">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">int</span><span class="token operator">></span> arr <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">250</span><span class="token punctuation">,</span> <span class="token number">10</span><span class="token punctuation">,</span> <span class="token number">11</span><span class="token punctuation">,</span> <span class="token number">12</span><span class="token punctuation">,</span> <span class="token number">19</span><span class="token punctuation">,</span> <span class="token number">200</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
   cout <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">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

2

Example (Without using Vector ADT)

Following is a C++ program that depicts how to remove minimum number of elements from an array such that twice of minimum value is greater than the maximum value, but without using the Vector ADT ?

<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 keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> <span class="token function">min</span><span class="token punctuation">(</span><span class="token keyword">int</span> a<span class="token punctuation">,</span> <span class="token keyword">int</span> b<span class="token punctuation">)</span> <span class="token punctuation">{</span><span class="token keyword">return</span> <span class="token punctuation">(</span>a <span class="token operator"><</span> b<span class="token punctuation">)</span><span class="token operator">?</span> a <span class="token operator">:</span> b<span class="token punctuation">;</span><span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">min</span><span class="token punctuation">(</span><span class="token keyword">int</span> arr<span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token keyword">int</span> low<span class="token punctuation">,</span> <span class="token keyword">int</span> high<span class="token punctuation">)</span>
   <span class="token punctuation">{</span>
      <span class="token keyword">int</span> minimum <span class="token operator">=</span> arr<span class="token punctuation">[</span>low<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>low<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator"><=</span>high<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>minimum <span class="token operator">></span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span>
         minimum <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 keyword">return</span> minimum<span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">max</span><span class="token punctuation">(</span><span class="token keyword">int</span> arr<span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token keyword">int</span> low<span class="token punctuation">,</span> <span class="token keyword">int</span> high<span class="token punctuation">)</span>
   <span class="token punctuation">{</span>
      <span class="token keyword">int</span> maximum <span class="token operator">=</span> arr<span class="token punctuation">[</span>low<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>low<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator"><=</span>high<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>maximum <span class="token operator"><</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span>
         maximum <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 keyword">return</span> maximum<span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">minimum_removals</span><span class="token punctuation">(</span><span class="token keyword">int</span> arr<span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token keyword">int</span> low<span class="token punctuation">,</span> <span class="token keyword">int</span> high<span class="token punctuation">)</span>
   <span class="token punctuation">{</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>low <span class="token operator">>=</span> high<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">int</span> m1 <span class="token operator">=</span> <span class="token function">min</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> low<span class="token punctuation">,</span> high<span class="token punctuation">)</span><span class="token punctuation">;</span>
      <span class="token keyword">int</span> m2 <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> low<span class="token punctuation">,</span> high<span class="token punctuation">)</span><span class="token punctuation">;</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>m1 <span class="token operator">></span> m2<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">return</span> <span class="token function">min</span><span class="token punctuation">(</span><span class="token function">minimum_removals</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> low<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span> high<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">minimum_removals</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> low<span class="token punctuation">,</span> high<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><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">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
   <span class="token punctuation">{</span>
      <span class="token keyword">int</span> arr<span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">12</span><span class="token punctuation">,</span> <span class="token number">45</span><span class="token punctuation">,</span> <span class="token number">32</span><span class="token punctuation">,</span> <span class="token number">88</span><span class="token punctuation">,</span> <span class="token number">100</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
      <span class="token keyword">int</span> n <span class="token operator">=</span> <span class="token keyword">sizeof</span><span class="token punctuation">(</span>arr<span class="token punctuation">)</span><span class="token operator">/</span><span class="token keyword">sizeof</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 punctuation">;</span>
      cout <span class="token operator"><<</span> <span class="token function">minimum_removals</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> n<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 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

3

Conclusion

Here we used the brute force approach to find the longest subarray. Other possible solutions might include checking every possible subarray by repeatedly popping elements from both sides and other approaches. Still, they are implementation heavy and less optimized. The time complexity here is O(n^2) as we have traversed all subarrays.