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    <p>Create a <a href="http://en.wikipedia.org/wiki/Heap_structure" rel="nofollow">heap structure</a> (for the second bullet) and put each of its nodes in a map (for the first bullet).</p> <p><strong>EDIT:</strong> An implementation of min heap I had done some time in the past</p> <pre><code>#ifndef MINHEAP_H #define MINHEAP_H //////////////////////// MinHeap with Map for Data //////////////////////// template &lt;class T, class M = int&gt; class MinHeap { T* array; unsigned const int arr_max; unsigned int elements; M map; void percolate_down(unsigned int i=0) { unsigned int n = elements-1, min; do { unsigned int l = 2*i + 1, r = 2*i + 2; if (l &lt;= n &amp;&amp; array[i] &gt; array[l]) min = l; else min = i; if (r &lt;= n &amp;&amp; array[i] &gt; array[r] &amp;&amp; array[l] &gt; array[r]) min = r; if (i != min) { T temp = array[i]; array[i] = array[min]; array[min] = temp; map.update(array[i], i); map.update(array[min], min); i = min; } else break; } while (i &lt; n); } void percolate_up(unsigned int i) { while (i &amp;&amp; array[(i-1)/2] &gt; array[i]) { T temp = array[i]; array[i] = array[(i-1)/2]; array[(i-1)/2] = temp; map.update(array[i], i); map.update(array[(i-1)/2], (i-1)/2); i = (i-1)/2; } } public: MinHeap(const int max) : array(new T[max]), arr_max(max), elements(0), map(max) {} ~MinHeap(void) { delete[] array; } bool empty(void) const { return elements == 0; } unsigned int capacity(void) const { return arr_max; } unsigned int size(void) const { return elements; } const M&amp; heapmap(void) const { return map; } const T&amp; peek(unsigned int i=0) const { return array[i]; } bool insert(T&amp; element) { if (arr_max == elements) return false; unsigned int k = elements++; map.update(element, k); array[k] = element; percolate_up(k); return true; } unsigned int mass_insert(T copy[], unsigned int n) { unsigned int i = 0; for( ; i &lt; n ; i++) if (!insert(copy[i])) break; return i; } bool delete_min(void) { if (elements == 0) return false; map.update(array[0], arr_max+1); array[0] = array[--elements]; map.update(array[0], 0); percolate_down(); return true; } bool delete_element(unsigned int i) { if (i &gt; elements) return false; map.update(array[i], arr_max+1); T temp = array[i]; array[i] = array[--elements]; map.update(array[i], i); if (array[i] &gt; temp) percolate_down(i); else if (temp &gt; array[i]) percolate_up(i); return true; } bool update(unsigned int i, T&amp; element) { if (i &gt; elements) return false; map.update(array[i], arr_max+1); T temp = array[i]; array[i] = element; map.update(array[i], i); if (array[i] &gt; temp) percolate_down(i); else if (temp &gt; array[i]) percolate_up(i); return true; } // void print() { using namespace std; for (unsigned int i=0 ; i &lt; elements ; i++) cout &lt;&lt; array[i] &lt;&lt; " | "; cout &lt;&lt; endl; } // Iterators /* friend class Const_Iterator; class Const_Iterator { MinHeap&lt;T&gt;* heap; unsigned int index; Const_Iterator(MinHeap&lt;T&gt;* h, unsigned int i) : heap(h), index(i) {} public: Const_Iterator(const Const_Iterator&amp; clone) : heap(clone.heap), index(clone.index) {} friend Const_Iterator MinHeap&lt;T&gt;::begin(void); }; Const_Iterator begin(void) { return Const_Iterator(this, 0); } */ }; ////////////////////////////////////////////////////////////////////////////// //////////////////////// MinHeap without Map for Data //////////////////////// template &lt;class T&gt; class MinHeap &lt;T, int&gt; { T* array; unsigned const int arr_max; unsigned int elements; void percolate_down(unsigned int i=0) { unsigned int n = elements-1, min; do { unsigned int l = 2*i + 1, r = 2*i + 2; if (l &lt;= n &amp;&amp; array[i] &gt; array[l]) min = l; else min = i; if (r &lt;= n &amp;&amp; array[i] &gt; array[r] &amp;&amp; array[l] &gt; array[r]) min = r; if (i != min) { T temp = array[i]; array[i] = array[min]; array[min] = temp; i = min; } else break; } while (i &lt; n); } void percolate_up(unsigned int i) { while (i &amp;&amp; array[(i-1)/2] &gt; array[i]) { T temp = array[i]; array[i] = array[(i-1)/2]; array[(i-1)/2] = temp; i = (i-1)/2; } } public: MinHeap(const int max) : array(new T[max]), arr_max(max), elements(0) {} ~MinHeap(void) { delete[] array; } bool empty(void) const { return elements == 0; } unsigned int capacity(void) const { return arr_max; } unsigned int size(void) const { return elements; } const T&amp; peek(unsigned int i=0) const { return array[i]; } bool insert(T&amp; element) { if (arr_max == elements) return false; unsigned int k = elements++; array[k] = element; percolate_up(k); return true; } unsigned int mass_insert(T copy[], unsigned int n) { unsigned int i = 0; for( ; i &lt; n ; i++) if (!insert(copy[i])) break; return i; } bool delete_min(void) { if (elements == 0) return false; array[0] = array[--elements]; percolate_down(); return true; } bool delete_element(unsigned int i) { if (i &gt; elements) return false; T temp = array[i]; array[i] = array[--elements]; if (array[i] &gt; temp) percolate_down(i); else if (temp &gt; array[i]) percolate_up(i); return true; } bool update(unsigned int i, T&amp; element) { if (i &gt; elements) return false; T temp = array[i]; array[i] = element; if (array[i] &gt; temp) percolate_down(i); else if (temp &gt; array[i]) percolate_up(i); return true; } // void print() { using namespace std; for (unsigned int i=0 ; i &lt; elements ; i++) cout &lt;&lt; array[i] &lt;&lt; " | "; cout &lt;&lt; endl; } }; ////////////////////////////////////////////////////////////////////////////// #endif // MINHEAP_H </code></pre>
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    1. USGeorge Kastrinis
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    1. COYou could also use `std::priority_queue`.
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    2. CO@Toolbox A heap structure is a way to implement a priority_queue :)
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    3. COI know -- what I meant was that there's no need to re-implement what's already part of standard C++.
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