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Problem solution · Python

CCC 1996 P5 - Max Distance

CCC 1996 P5 - Max Distance: a Python solution using binary search. Learn the idea, check the complexity, and read the full code, with credit to CCCSolutions.

Technique
Binary search
Source
CCCSolutions
Length
39 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Binary search

For CCC 1996 P5 - Max Distance, the implementation exploits a monotonic condition to discard half of the remaining search space after every check.

  1. Identify the ordered answer range or sorted search domain.
  2. Write a predicate whose truth changes only once.
  3. Move the appropriate boundary after each midpoint check and return the final feasible position.

Code notes

  • 39 lines of Python from the credited upstream file ccc96s5.py.
  • The implementation visibly relies on ordered lookup.
  • No explicit loop blocks detected.

Complexity

Multiply the logarithmic number of midpoint checks by the cost of one predicate evaluation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from CCCSolutions by CCCSolutions contributors · Milliken Mills High School and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCCC 1996 P5 - Max Distance · PythonPython
Use this to learn the idea, then write your own version.
# CCC 1996 Problem E: Maximum Distance## This algorithm is by Ahmed Sabie## Quite straight forward problem and solution.## The key problem is:# Given an x[i], find the last number in an array y, such that y[j] >= x[i],# (j is largest number possible)## Ahmed's approach is to use a binary search versus a linear search.## The binary search will put leave mid at the largest index such that# y[mid] >= x[i] file = open ("max.in", "r")testCases = int(file.readline())for k in range(testCases):    currentMax = 0    n = int(file.readline())    x = file.readline().split()    x = map(int, x)    y = file.readline().split()    y = map(int, y)     for i in range(n):        low = 0        high = n - 1        while low <= high:            mid = (low + high) / 2            if y[mid] >= x[i]:                low = mid + 1            else:                high = mid - 1         currentMax = max (currentMax, mid - i)     print currentMax

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