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question:You have n stacks of coins, each containing only two types of coins: gold and silver. Each stack is initially arranged such that gold coins are on top of silver coins. In one move, you can swap the top gold coin with the bottom silver coin in any stack. Your objective is to maximize the total number of visible gold coins (i.e., the top coin of each stack). Write a program to determine the maximum number of visible gold coins that can be obtained after performing any number of swaps. Input The first line of input contains an integer n (1 ≤ n ≤ 100,000) — the number of stacks. The following n lines each contain two integers g and s (0 ≤ g, s ≤ 109) — the number of gold coins and silver coins in the stack, respectively. Output Print a single integer — the maximum number of visible gold coins that can be obtained. Examples Input 3 2 1 1 2 3 0 Output 3 Input 4 1 1 2 2 0 3 3 3 Output 3 Note In the first sample, all stacks already have gold coins visible on top. No swaps are needed, and the answer is 3. In the second sample, the first, second, and fourth stacks initially have gold coins visible, but the third stack does not. By swapping the bottom silver coin with one of the top gold coins in the fourth stack, you can have gold coins on top of all stacks except the third one. Thus, the answer is 3.
answer:def max_visible_gold_coins(n, stacks): visible_gold = 0 for g, s in stacks: if g > 0: visible_gold += 1 return visible_gold
question:# Problem Statement You are tasked with organizing a grand parade in your city. The parade consists of `N` floats, each represented by an integer. The floats must be arranged such that the sum of every contiguous subarray of floats is unique, i.e., no two different contiguous subarrays of floats should have the same sum. Given the number of floats `N`, your task is to determine a sequence of integers such that the sum of every contiguous subarray is unique. # Constraints The input satisfies the following conditions: - 1 leq N leq 100 # Input The input consists of a single integer `N`. # Output Output `N` integers, representing the sequence of float numbers such that the sum of every contiguous subarray is unique. If multiple sequences satisfy the condition, any valid sequence will be accepted. # Example Input ``` 3 ``` Output ``` 1 2 4 ``` Explanation - For subarray `[1]`, sum = 1 - For subarray `[2]`, sum = 2 - For subarray `[4]`, sum = 4 - For subarray `[1, 2]`, sum = 3 - For subarray `[2, 4]`, sum = 6 - For subarray `[1, 2, 4]`, sum = 7 All contiguous subarray sums are unique. # Note In this problem, multiple sequences may satisfy the conditions. The proposed solution is one of the possible sequences. Ensure the output sequence adheres to the constraints specified.
answer:def arrange_floats(N): Returns a sequence of N integers such that sums of all contiguous subarrays are unique. A simple sequence that ensures unique sums is to use consecutive powers of 2. result = [] current_power = 1 for _ in range(N): result.append(current_power) current_power *= 2 return result
question:A company has a series of meeting rooms in a building. Each meeting room can be reserved for meetings that do not overlap. You are given a list of meeting intervals, where each interval is represented by its start time and end time in the format [start, end]. Your task is to determine if a person could attend all meetings without any overlaps. Write a function `canAttendMeetings` that receives a list of meeting intervals and returns a boolean value indicating whether the person can attend all meetings without any overlaps. Input - An integer T denoting the number of test cases. - Each test case begins with an integer N, the number of meeting intervals. - The next N lines each contain two integers start and end, the start time and end time of a meeting. Output - For each test case, output "YES" if the person can attend all meetings without any overlaps and "NO" otherwise. Constraints - 1 ≤ T ≤ 100 - 1 ≤ N ≤ 100 - 0 ≤ start < end ≤ 10^5 Example Input: 3 2 0 30 5 10 3 7 10 2 4 5 9 2 3 8 10 15 Output: NO NO YES Explanation Example case 1. The meetings [0, 30] and [5, 10] overlap, so the person cannot attend both. Example case 2. The meetings [2, 4] and [5, 9] do not overlap, but [7, 10] overlaps with [5, 9], so the person cannot attend all meetings. Example case 3. The meetings [3, 8] and [10, 15] do not overlap, so the person can attend all meetings.
answer:def canAttendMeetings(intervals): Determines if a person can attend all meetings without any overlaps. :param intervals: List of tuples [(start, end), (start, end), ...] :return: Boolean - True if the person can attend all meetings, otherwise False # First, sort the intervals by their start times intervals.sort(key=lambda x: x[0]) # Compare each meeting time with the next one to check for overlaps for i in range(len(intervals) - 1): if intervals[i][1] > intervals[i + 1][0]: return False return True def process_input(T, test_cases): results = [] for intervals in test_cases: if canAttendMeetings(intervals): results.append("YES") else: results.append("NO") return results
question:You are given a list of integers and your task is to determine whether it is possible to rearrange the list such that no two consecutive numbers are the same. Input The first line contains a single integer T denoting the number of test cases. Each of the next T lines begins with an integer N, which describes the length of the list followed by N space-separated integers which constitute the list. Output For each test case, print "Possible" if the list can be rearranged such that no two consecutive numbers are the same. Otherwise, print "Not Possible". Constraints 1 ≤ T ≤ 100 1 ≤ N ≤ 10^5 1 ≤ list[i] ≤ 10^9 Example Input: 3 5 1 1 1 2 3 4 2 2 2 3 3 7 7 7 Output: Possible Not Possible Not Possible Explanation Example case 1. The list [1, 1, 1, 2, 3] can be rearranged to [1, 2, 1, 3, 1] such that no two consecutive numbers are the same. Example case 2. The list [2, 2, 2, 3] cannot be rearranged to avoid two consecutive same numbers. Example case 3. The list [7, 7, 7] only contains identical numbers and thus cannot be rearranged to avoid two consecutive same numbers.
answer:def is_possible_rearrangement(arr): Determines if it is possible to rearrange the list such that no two consecutive numbers are the same. Parameters: arr (list): A list of integers Returns: str: 'Possible' if the list can be rearranged, 'Not Possible' otherwise from collections import Counter count = Counter(arr) most_common = count.most_common(1)[0][1] # if the most common element exceeds the acceptable limit if most_common > (len(arr) + 1) // 2: return 'Not Possible' else: return 'Possible' def solve(test_cases): results = [] for case in test_cases: N, arr = case[0], case[1:] results.append(is_possible_rearrangement(arr)) return results