# Operations on Binomial Heap – Decrease key

**Decrease key** refers to **reducing** the key value of any node.If we want to decrease a key in Binomial heap,we will replace the key with reduced value and will repeatedly **exchange** the reduced key with the parent in order to restore **min-heap** property.The** running time** to perform this operation is **O(log n)**.

**Example**

Say we want to decrease **50 to 4** in binomial heap given in Fig 1.The steps further followed are given in Fig 2,3,4,5 respectively.

4 and 21 are swapped in Fig 3 and 4 and 8 are swapped in Fig 4** **in order to retain min-heap property.

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