Find Minimum in Rotated Sorted Array

The inflection point is the only place in the array where ascending order breaks. Comparing the midpoint against the rightmost element cleanly reveals which half contains that drop: if the middle is greater than the right end, the minimum must lie strictly to the right; otherwise, it lies at or to the left of the middle.

Full solution

Binary search against the right boundary: arr[mid] > arr[high] means the drop is to the right, otherwise mid or something left of it is the minimum. Comparing to arr[high] (not arr[low]) is what keeps unrotated input correct, and high = mid (not mid - 1) never discards the answer.

def find_min(arr: list[int]) -> int:
    low, high = 0, len(arr) - 1
    while low < high:
        mid = (low + high) // 2
        if arr[mid] > arr[high]:
            low = mid + 1  # drop is to the right of mid
        else:
            high = mid  # mid may itself be the minimum, keep it
    return arr[low]

function findMin(arr) {
  let low = 0;
  let high = arr.length - 1;
  while (low < high) {
    const mid = Math.floor((low + high) / 2);
    if (arr[mid] > arr[high]) {
      low = mid + 1; // drop is to the right of mid
    } else {
      high = mid; // mid may itself be the minimum, keep it
    }
  }
  return arr[low];
}

The theory behind it

Arrays — the ground this problem stands on. All Arrays problems

What Arrays is

An array is a row of fixed boxes laid side by side in computer memory, like numbered lockers in a hallway. Because each box occupies identical space and sits directly next to its neighbors, jumping to locker zero or locker ten thousand takes the exact same tiny fraction of time. Every box holds an item of the same type, addressed by an offset number called an index.

When to reach for it

Reach for an array when items arrive in a known sequence and need immediate retrieval by position number. Problems asking for running totals, prefix accumulations, cyclic rotations, or in-place rearrangements signal array mechanics. Whenever constraints require constant-time random lookups or contiguous cache scans across fixed collections, a flat sequence is the default container.

How the pattern works

Visualize a tape with zero-indexed slots stretching from start to end. Keep track of write and read cursors when modifying contents without allocating helper buffers. For running computations, maintain an invariant such as having processed all elements left of the current index while pending elements wait to the right. When modifying entries in place, consider scanning backwards from the end so unread data is not overwritten.