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railroad_renovations.py
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railroad_renovations.py
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# Copyright (c) 2020 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2020 Round 3 - Problem B. Railroad Renovations
# https://www.facebook.com/codingcompetitions/hacker-cup/2020/round-3/problems/B
#
# Time: O(N^3)
# Space: O(N * K)
#
from bisect import bisect_left
def railroad_renovations():
N, K = map(int, raw_input().strip().split())
observations = []
for i in xrange(N):
Pi, Ri = map(int, raw_input().strip().split())
observations.append((Pi, i, Ri))
observations.sort()
dp = [[float("inf")]*(K+1) for _ in xrange(N+1)] # dp[i][j]: min renovations after first i observations with j rearrangements
dp[0][0] = 0
for i in xrange(N):
if i-1 >= 0 and observations[i][0] == observations[i-1][0]:
continue
count = [0]*2
ordered_set = []
for j in xrange(i, N):
ordered_set.insert(bisect_left(ordered_set, observations[j][1:]), observations[j][1:])
count[observations[j][2]] += 1
if j+1 < N and observations[j][0] == observations[j+1][0]:
continue
min_cost = min(count) # find min cost to make all 0s before all 1s
curr_count = [0]*2
for _, r in ordered_set: # Time: O(N)
curr_count[r] += 1
min_cost = min(min_cost, curr_count[1]+(count[0]-curr_count[0])) # check each 0-1 splitting point
for k in xrange(min_cost, K+1):
dp[j+1][k] = min(dp[j+1][k], dp[i][k-min_cost]+int(count[1] > 0))
result = min(dp[N])
return result if result != float("inf") else -1
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, railroad_renovations())