二分法

二分法的几个位置

比如

有时候想要寻找小于3的最大数字

有时候想要寻找第一个满足>=3的数字，

有时候想要寻找最后一个满足>=3的数字，

有时候想要寻找小于4的最大数字

nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9]
n = len(nums)

left = 0
right = n - 1
result = -1
target = 5
while left <= right:
    mid = (left + right) // 2

    if nums[mid] < target:
        result = mid
        left = mid + 1
    else:
        right = mid - 1

print(result, nums[result])

left = 0
right = n - 1
result = -1
target = 5
while left <= right:
    mid = (left + right) // 2

    if nums[mid] > target:
        result = mid
        right = mid - 1
    else:
        left = mid + 1

print(result, nums[result])

left = 0
right = n - 1
result = -1
target = 5
while left <= right:
    mid = (left + right) // 2

    if nums[mid] == target:
        result = mid
        right = mid - 1
    elif nums[mid] > target:
        right = mid - 1
    else:
        left = mid + 1

print(result, nums[result])

left = 0
right = n - 1
result = -1
target = 5
while left <= right:
    mid = (left + right) // 2

    if nums[mid] == target:
        result = mid
        left = mid + 1
    elif nums[mid] > target:
        right = mid - 1
    else:
        left = mid + 1

print(result, nums[result])