Checkout Assistant (Codeforces 19B)
Tags: DP, dp

Bob came to a cash & carry store, put n items into his trolley, and went to the checkout counter to pay. Each item is described by its price ci and time ti in seconds that a checkout assistant spends on this item. While the checkout assistant is occupied with some item, Bob can steal some other items from his trolley. To steal one item Bob needs exactly 1 second. What is the minimum amount of money that Bob will have to pay to the checkout assistant? Remember, please, that it is Bob, who determines the order of items for the checkout assistant.

Input: The first input line contains number n (1 ≤ n ≤ 2000). In each of the following n lines each item is described by a pair of numbers ti, ci (0 ≤ ti ≤ 2000, 1 ≤ ci ≤ 109). If ti is 0, Bob won't be able to steal anything, while the checkout assistant is occupied with item i.

Output: Output one number — answer to the problem: what is the minimum amount of money that Bob will have to pay.


Sample Inputs:
4
2 10
0 20
1 5
1 3

3
0 1
0 10
0 100

Sample Outputs:
8

111

Solution (Python):
n = int(input())
ar = [float('inf')] * (n + 1)
ar[0] = 0
for i in range(n):
    (t, c) = map(int, input().split())
    for j in range(n - 1, -1, -1):
        w = min(j + t + 1, n)
        ar[w] = min(ar[w], ar[j] + c)
print(ar[n])

Solution (Python):
import os, sys
from io import BytesIO, IOBase

def main():
    n = int(input())
    arr = [tuple(map(int, input().split())) for _ in range(n)]
    dp = [10 ** 15] * (n + 1)
    ''
    dp[n] = 0
    for i in arr:
        for j in range(1, n + 1):
            x = max(0, j - i[0] - 1)
            dp[x] = min(dp[x], dp[j] + i[1])
    print(dp[0])
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            (self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            (self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda : self.buffer.read().decode('ascii')
        self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')
if __name__ == '__main__':
    main()

Solution (Python):
nummy = int(input())
arsiri = [float('inf')] * (nummy + 1)
arsiri[0] = 0
for i in range(nummy):
    (t, c) = map(int, input().split())
    for j in range(nummy - 1, -1, -1):
        w = min(j + t + 1, nummy)
        arsiri[w] = min(arsiri[w], arsiri[j] + c)
print(arsiri[nummy])