# 25.07.2023 [852. Peak Index in a Mountain Array]

Mountain pattern `index` in the array in log time

25.07.2023

852. Peak Index in a Mountain Array medium
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Problem TLDR

Mountain pattern index in the array in log time

Intuition

Do the Binary Search of the biggest growing index

Approach

For more robust Binary Search code:

• use inclusive lo and hi

• do the last check lo == hi

• always write the result ind = mid if conditions are met

• always move the borders lo = mid - 1, hi = mid + 1

Complexity

• Time complexity:
  O(log(n))

• Space complexity:
  O(1)

Code

    fun peakIndexInMountainArray(arr: IntArray): Int {
        var lo = 1
        var hi = arr.lastIndex
        var ind = -1
        while (lo <= hi) {
          val mid = lo + (hi - lo) / 2
          if (arr[mid] > arr[mid - 1]) {
            ind = mid
            lo = mid + 1
          } else hi = mid - 1
        }
        return ind
    }

Magical Rundown

🌄 "Look at that crimson blush, Alpha!" A radiant sunrise anoints the 
towering Everest, its snow-capped peaks aglow with the day's first 
light. An ethereal landscape, a symphony of shadows and silhouettes, 
lays the stage for an impending adventure. 🏔️

Team Alpha 🥾 chuckles, their voices swallowed by the wind, "Today's 
the day we've been dreaming of, Charlie!" Team Charlie 🦅, encased 
in their mountain gear, share their excitement. Their eyes, reflecting 
the sunlit peaks, are fixated on the summit – their celestial goal.

Base Camps (BC):   
0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
Everest Heights:  
1K  2K  3K  4K  5K  6K  7K  8K  9K 10K 11K 12K 13K 14K 15K 16K 15K 14K 13K 12K 11K
    🥾(Team Alpha)                  🏔️(Mysterious Mid Point)                    🦅(Team Charlie)

🧭 "We're off to conquer the Everest!" Alpha's voice reverberates 
with a hopeful intensity. Their strategy, an intricate dance with 
numbers and ambition – Binary Search. The mountain, its snow-capped 
peaks reaching for the skies, hums ancient tales to their eager ears.

BC:        0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
Heights:  1K  2K  3K  4K  5K  6K  7K  8K  9K 10K 11K 12K 13K 14K 15K 16K 15K 14K 13K 12K 11K
                                                 🥾🏁(Team Alpha's Milestone)            🦅(Team Charlie)

"10K! Feels like we've captured a bit of heaven," Team Alpha shares 
their awe, their voices a mere whisper against the grandeur of the 
landscape. 

🏞️ But the mountain, a grand enigma, hides her secrets well...

With a sudden, heart-stopping rumble, the mountain shivers, the 
seemingly innocuous snow beneath Team Charlie's feet giving way. A 
fierce avalanche sweeps down the slopes, sending Charlie scrambling 
for cover.

BC:        0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
Heights:  1K  2K  3K  4K  5K  6K  7K  8K  9K 10K 11K 12K 13K 14K 15K 16K 15K 14K 13K 12K 11K
                                                 🥾🏁(Team Alpha's Resolve)              ❄️🦅(Team Charlie's Setback)

"Avalanche!" Charlie's voice, choked with frosty fear, crackles over 
the radio. Yet, Team Alpha, undeterred by the wrath of the mountain, 
pushes forward. "Hold tight, Charlie! We're stardust-bound!" They 
continue their daring ascent, breaching the cloudline to a dizzying 
16K.

🚩 "Charlie, we're among the stars!" Alpha's voice, filled with 
joyous triumph, echoes through the radio. The peak is conquered.

BC:   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
Heights:  1K  2K  3K  4K  5K  6K  7K  8K  9K 10K 11K 12K 13K 14K 15K 16K 15K 14K 13K 12K 11K
                                                                🚩🎉(Victorious Summit at BC 15!)

As the sun bathes the snowy peaks in a golden hue, Team Alpha plants 
their triumphant flag at the top. They stand there, at the roof of 
the world, their hearts swelling with joy and pride. It's the journey, 
the shared aspirations, the dream of reaching for the stars, that truly 
defines their adventure. 🌠