The Reduction Operations to Make the Array Elements Equal problem asks how many operations are needed to reduce all array elements to the minimum value. Each operation changes one element to the next smaller value in the array. This coding problem counts the total "reduction steps" for each element by determining how many distinct levels it must descend. The array and sorting interview pattern is demonstrated.
Microsoft asks this because sorting reveals the structure: each element needs to make as many "level drops" as there are distinct values below it. Counting passes through each distinct level gives the total operations.
Sort + level counting. Sort the array. For each new distinct value encountered (at position i), it has level distinct values above it (including itself). The cost to reduce this element is level. The total cost = sum of level for each distinct-value element × how many times it appears.
Actually: ops = 0. level = 0. For each element from smallest to largest: if it's greater than previous (new level), level++. ops += level.
arr=[5,1,3]. Sort: [1,3,5]. prev=1.
arr=[1,1,2,2,3]. Sort. [1,1,2,2,3]. ops: 0,0 (1s),1,1 (2s),2 (3). Total=4.
Reduction Operations shows that "how many reductions for each element" = number of distinct values strictly below it. Sorting makes this visible: increment a counter at each new distinct value. Each element's contribution is that counter value. Practice similar "count levels in sorted sequence" patterns — they appear in staircase counting and rank-assignment problems.
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