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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. "Duel!" Betting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started. There are n cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly k consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these n cards face the same direction after one's move, the one who takes this move will win. Princess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won't make mistakes. Input The first line contains two integers n and k (1 โ‰ค k โ‰ค n โ‰ค 10^5). The second line contains a single string of length n that only consists of 0 and 1, representing the situation of these n cards, where the color side of the i-th card faces up if the i-th character is 1, or otherwise, it faces down and the i-th character is 0. Output Print "once again" (without quotes) if the total number of their moves can exceed 10^9, which is considered a draw. In other cases, print "tokitsukaze" (without quotes) if Tokitsukaze will win, or "quailty" (without quotes) if Quailty will win. Note that the output characters are case-sensitive, and any wrong spelling would be rejected. Examples Input 4 2 0101 Output quailty Input 6 1 010101 Output once again Input 6 5 010101 Output tokitsukaze Input 4 1 0011 Output once again Note In the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win. In the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw. In the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down. The fourth example can be explained in the same way as the second example does. Submitted Solution: ``` n = list(map(int, input().split())) st = input() i = 0 mas = [] while i < len(st): mas.insert(i, int(st[i])) i = i + 1 i = 0 cnt = 0 while i < n[0]: if(mas[i] == 1): cnt = cnt + 1 i = i + 1 i = 0 cnt2 = 0 while i < n[1]: if(mas[i] == 1): cnt2 = cnt2 + 1 i = i + 1 ans = 0 mn = cnt2 id = 0 izm = 0 if(cnt - cnt2 == n[0] - n[1]) or ((n[0] - cnt) - (n[1] - cnt2) == n[0] - n[1]): ans = 1 while i < n[0]: if(mas[i] == 1): cnt2 = cnt2 + 1 if(mas[i - n[1]] == 1): cnt2 = cnt2 - 1 if(cnt - cnt2 == n[0] - n[1]) or ((n[0] - cnt) - (n[1] - cnt2) == n[0] - n[1]): ans = 1 if(cnt2 <= mn): mn = cnt2 id = i - n[1] izm = 0 if(n[1] - cnt2 <= mn): mn = n[1] - cnt2 id = i - n[1] izm = 1 i = i + 1 if(ans == 1): print("tokitsukaze") exit(0) i = 0 zer = [1000000, -1] one = [1000000, -1] 10001 while i < n[0]: if(mas[i] == 1): one[0] = min(one[0], i) one[1] = max(one[1], i) if(mas[i] == 0): zer[0] = min(zer[0], i) zer[1] = max(zer[1], i) i = i + 1 if(one[1] - one[0] - 1 >= n[1]) or(zer[1] - zer[0] -1 >= n[1]): print("once again") exit(0) id2 = id while id < id2 + n[1]: mas[id] = izm id = id + 1 i = 0 cnt2 = 0 cnt = 0 while i < n[0]: if(mas[i] == 1): cnt = cnt + 1 i = i + 1 i = 0 while i < n[1]: if(mas[i] == 1): cnt2 = cnt2 + 1 i = i + 1 ans = 0 if(cnt - cnt2 == n[0] - n[1]) or ((n[0] - cnt) - (n[1] - cnt2) == n[0] - n[1]): ans = 1 while i < n[0]: if(mas[i] == 1): cnt2 = cnt2 + 1 if(mas[i - n[1]] == 1): cnt2 = cnt2 - 1 if(cnt - cnt2 == n[0] - n[1]) or ((n[0] - cnt) - (n[1] - cnt2) == n[0] - n[1]): ans = 1 i = i + 1 if(ans == 1): print("quailty") else: print("once again") ```
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48,918
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97,837
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. "Duel!" Betting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started. There are n cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly k consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these n cards face the same direction after one's move, the one who takes this move will win. Princess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won't make mistakes. Input The first line contains two integers n and k (1 โ‰ค k โ‰ค n โ‰ค 10^5). The second line contains a single string of length n that only consists of 0 and 1, representing the situation of these n cards, where the color side of the i-th card faces up if the i-th character is 1, or otherwise, it faces down and the i-th character is 0. Output Print "once again" (without quotes) if the total number of their moves can exceed 10^9, which is considered a draw. In other cases, print "tokitsukaze" (without quotes) if Tokitsukaze will win, or "quailty" (without quotes) if Quailty will win. Note that the output characters are case-sensitive, and any wrong spelling would be rejected. Examples Input 4 2 0101 Output quailty Input 6 1 010101 Output once again Input 6 5 010101 Output tokitsukaze Input 4 1 0011 Output once again Note In the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win. In the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw. In the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down. The fourth example can be explained in the same way as the second example does. Submitted Solution: ``` n, k = map(int, input().split()) s = input() p0 = s.rfind('0') - s.find('0') p1 = s.rfind('1') - s.find('1') if min(p0, p1) < k: print('tokitsukaze') elif p0 > k or p1 > k: print('once again') else: c0 = 0 c1 = 0 check = False for i in s: if i == 0: c1 = 0 c0 += 1 if c0 >= k: check = True break else: c0 = 0 c1 += 1 if c1 >= k: check = True break print('once again' if check else 'quailty') ```
instruction
0
48,919
19
97,838
No
output
1
48,919
19
97,839
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. "Duel!" Betting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started. There are n cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly k consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these n cards face the same direction after one's move, the one who takes this move will win. Princess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won't make mistakes. Input The first line contains two integers n and k (1 โ‰ค k โ‰ค n โ‰ค 10^5). The second line contains a single string of length n that only consists of 0 and 1, representing the situation of these n cards, where the color side of the i-th card faces up if the i-th character is 1, or otherwise, it faces down and the i-th character is 0. Output Print "once again" (without quotes) if the total number of their moves can exceed 10^9, which is considered a draw. In other cases, print "tokitsukaze" (without quotes) if Tokitsukaze will win, or "quailty" (without quotes) if Quailty will win. Note that the output characters are case-sensitive, and any wrong spelling would be rejected. Examples Input 4 2 0101 Output quailty Input 6 1 010101 Output once again Input 6 5 010101 Output tokitsukaze Input 4 1 0011 Output once again Note In the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win. In the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw. In the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down. The fourth example can be explained in the same way as the second example does. Submitted Solution: ``` n,k=(map(int,input().split())) cards=list(map(int,input().split())) #print(n,k,cards) if k==1 : print('once again') elif k==n or k==n-1: print('tokitsukaze') else: print('quailty') ''' if l.count(0) >1 or len(set(l))<n-1: print('cslnb') else: x=sum(l) if x%n !=0: print('cslnb') else: print('sjfnb') ''' ```
instruction
0
48,920
19
97,840
No
output
1
48,920
19
97,841
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. "Duel!" Betting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started. There are n cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly k consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these n cards face the same direction after one's move, the one who takes this move will win. Princess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won't make mistakes. Input The first line contains two integers n and k (1 โ‰ค k โ‰ค n โ‰ค 10^5). The second line contains a single string of length n that only consists of 0 and 1, representing the situation of these n cards, where the color side of the i-th card faces up if the i-th character is 1, or otherwise, it faces down and the i-th character is 0. Output Print "once again" (without quotes) if the total number of their moves can exceed 10^9, which is considered a draw. In other cases, print "tokitsukaze" (without quotes) if Tokitsukaze will win, or "quailty" (without quotes) if Quailty will win. Note that the output characters are case-sensitive, and any wrong spelling would be rejected. Examples Input 4 2 0101 Output quailty Input 6 1 010101 Output once again Input 6 5 010101 Output tokitsukaze Input 4 1 0011 Output once again Note In the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win. In the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw. In the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down. The fourth example can be explained in the same way as the second example does. Submitted Solution: ``` import sys def sum_range(l, r): if r < l: return 0 if l == 0: return sum[r] return sum[r] - sum[l - 1] n, k = map(int, input().split()) cards = input() sum = [0] * n for i in range(1, n): sum[i] += sum[i - 1] if cards[i] == '1': sum[i] += 1 min0 = min1 = n max0 = max1 = -1 for i in range(0, n): if cards[i] == '1': min1 = min(min1, i) max1 = i else: min0 = min(min0, i) max0 = i toki = False qual = True for i in range(0, n - k + 1): if sum_range(0, i - 1) + sum_range(i + k, n - 1) + k == n: toki = True if sum_range(0, i - 1) + sum_range(i + k, n - 1) + 0 == 0: toki = True if i - min0 > k or i - min1 > k or max0 - (i + k - 1) > k or max1 - (i + k - 1) > k: qual = False if toki == True: print('tokitsukaze') elif qual == True: print('quailty') else: print('once again') ```
instruction
0
48,921
19
97,842
No
output
1
48,921
19
97,843
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. "Duel!" Betting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started. There are n cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly k consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these n cards face the same direction after one's move, the one who takes this move will win. Princess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won't make mistakes. Input The first line contains two integers n and k (1 โ‰ค k โ‰ค n โ‰ค 10^5). The second line contains a single string of length n that only consists of 0 and 1, representing the situation of these n cards, where the color side of the i-th card faces up if the i-th character is 1, or otherwise, it faces down and the i-th character is 0. Output Print "once again" (without quotes) if the total number of their moves can exceed 10^9, which is considered a draw. In other cases, print "tokitsukaze" (without quotes) if Tokitsukaze will win, or "quailty" (without quotes) if Quailty will win. Note that the output characters are case-sensitive, and any wrong spelling would be rejected. Examples Input 4 2 0101 Output quailty Input 6 1 010101 Output once again Input 6 5 010101 Output tokitsukaze Input 4 1 0011 Output once again Note In the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win. In the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw. In the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down. The fourth example can be explained in the same way as the second example does. Submitted Solution: ``` import sys n, k = map(int, input().split()) cc = input() prefix = 1 i = 1 while cc[i] == cc[0]: prefix +=1 suffix = 1 i = len(cc) - 2 while cc[i] == cc[-1]: suffix +=1 if k + prefix >= n or k + suffix >= n or (cc[0] == cc[-1] and k+prefix+suffix >= n): print("tokitsukaze") sys.exit(0) if 2 * k > n: print("quailty") sys.exit(0) print("once again") ```
instruction
0
48,922
19
97,844
No
output
1
48,922
19
97,845
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,058
19
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Tags: data structures, greedy, math Correct Solution: ``` t = int(input()) for _ in range(t): n = int(input()) dec = list(map(int, input().split())) dic = {} for i in range(n): dic[dec[i]] = i covered_till = n new_dec = [] for i in range(n, 0, -1): if dic[i] < covered_till: # we found new max new_dec += dec[dic[i] : covered_till] covered_till = dic[i] print(*new_dec) ```
output
1
49,058
19
98,117
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,059
19
98,118
Tags: data structures, greedy, math Correct Solution: ``` #####segfunc##### def segfunc(x, y): return max(x,y) ################# #####ide_ele##### ide_ele =-10**18 ################# class SegTree: def __init__(self, init_val, segfunc, ide_ele): n = len(init_val) self.segfunc = segfunc self.ide_ele = ide_ele self.num = 1 << (n - 1).bit_length() self.tree = [ide_ele] * 2 * self.num for i in range(n): self.tree[self.num + i] = init_val[i] for i in range(self.num - 1, 0, -1): self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1]) def update(self, k, x): k += self.num self.tree[k] = x while k > 1: self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1]) k >>= 1 def query(self, l, r): res = self.ide_ele l += self.num r += self.num while l < r: if l & 1: res = self.segfunc(res, self.tree[l]) l += 1 if r & 1: res = self.segfunc(res, self.tree[r - 1]) l >>= 1 r >>= 1 return res import sys input = sys.stdin.readline import math import copy t = int(input()) for f in range(t): n = int(input()) p = list(map(int,input().split())) ans = [] a = copy.copy(p) a.reverse() last = n seg = SegTree(p,segfunc,ide_ele) flg = seg.query(0,last) for i in range(n): if a[i] == flg: for j in range(n-i-1,last): ans.append(p[j]) last = n-i-1 flg = seg.query(0,last) print(*ans) ```
output
1
49,059
19
98,119
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,060
19
98,120
Tags: data structures, greedy, math Correct Solution: ``` for _ in range(int(input())): n = int(input()) p = list(map(int,input().split())) l2 = [] a = p[0] s = [0] for i in range(1,n): if(p[i]>a): a = p[i] s.append(i) s = s[::-1] ind = n for j in s: l2.extend(p[j:ind]) ind = j print(*l2) ```
output
1
49,060
19
98,121
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,061
19
98,122
Tags: data structures, greedy, math Correct Solution: ``` t = int(input()) r = [] for _ in range(t): n = int(input()) nums = list(input().split()) pos = [0] * n for i in range(n): pos[int(nums[i])-1] = i index = 0 end = n-1 s = "" for i in range(n-1, -1, -1): if pos[i] > end: continue for j in nums[pos[i]:end+1]: print(j, end=" ") end = pos[i] -1 ```
output
1
49,061
19
98,123
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,062
19
98,124
Tags: data structures, greedy, math Correct Solution: ``` #########################################################################################################\ ######################################################################################################### ###################################The_Apurv_Rathore##################################################### ######################################################################################################### ######################################################################################################### import sys,os,io from sys import stdin from math import log, gcd, ceil from collections import defaultdict, deque, Counter from heapq import heappush, heappop from bisect import bisect_left , bisect_right import math alphabets = list('abcdefghijklmnopqrstuvwxyz') def isPrime(x): for i in range(2,x): if i*i>x: break if (x%i==0): return False return True def ncr(n, r, p): num = den = 1 for i in range(r): num = (num * (n - i)) % p den = (den * (i + 1)) % p return (num * pow(den, p - 2, p)) % p def primeFactors(n): l = [] while n % 2 == 0: l.append(2) n = n / 2 for i in range(3,int(math.sqrt(n))+1,2): while n % i== 0: l.append(int(i)) n = n / i if n > 2: l.append(n) return list(set(l)) def power(x, y, p) : res = 1 x = x % p if (x == 0) : return 0 while (y > 0) : if ((y & 1) == 1) : res = (res * x) % p y = y >> 1 # y = y/2 x = (x * x) % p return res def SieveOfEratosthenes(n): prime = [True for i in range(n+1)] p = 2 while (p * p <= n): if (prime[p] == True): for i in range(p * p, n+1, p): prime[i] = False p += 1 return prime def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def si(): return input() def prefix_sum(arr): r = [0] * (len(arr)+1) for i, el in enumerate(arr): r[i+1] = r[i] + el return r def divideCeil(n,x): if (n%x==0): return n//x return n//x+1 def ii(): return int(input()) def li(): return list(map(int,input().split())) def ws(s): sys.stdout.write(s + '\n') def wi(n): sys.stdout.write(str(n) + '\n') def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n') def power_set(L): """ L is a list. The function returns the power set, but as a list of lists. """ cardinality=len(L) n=2 ** cardinality powerset = [] for i in range(n): a=bin(i)[2:] subset=[] for j in range(len(a)): if a[-j-1]=='1': subset.append(L[j]) powerset.append(subset) #the function could stop here closing with #return powerset powerset_orderred=[] for k in range(cardinality+1): for w in powerset: if len(w)==k: powerset_orderred.append(w) return powerset_orderred def fastPlrintNextLines(a): # 12 # 3 # 1 #like this #a is list of strings print('\n'.join(map(str,a))) def sortByFirstAndSecond(A): A = sorted(A,key = lambda x:x[0]) A = sorted(A,key = lambda x:x[1]) return list(A) #__________________________TEMPLATE__________________OVER_______________________________________________________ if(os.path.exists('input.txt')): sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w") else: input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline t = 1 t = int(input()) for _ in range(t): n = ii() l = li() d = defaultdict(lambda:0) for i in range(n): d[l[i]]=i maxpre = [0]*n maxpre[0]=l[0] for i in range(1,n): maxpre[i]=max(maxpre[i-1],l[i]) # print(maxpre) ans = [] end = n i = maxpre[-1] while(1): # print(i) ans+=l[i:end] if i==0: break end = i i = d[maxpre[i-1]] print(*ans) ```
output
1
49,062
19
98,125
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,063
19
98,126
Tags: data structures, greedy, math Correct Solution: ``` # cook your dish here for _ in range(int(input())): n = int(input()) arr = list(map(int,input().split())) a = [0]*n t = [] for i in range(n): a[arr[i]-1] = i f = n+1 for i in range(len(a)-1,-1,-1): if(a[i]>f): continue t.append(arr[a[i]:f]) f = a[i] for i in range(len(t)): for j in range(len(t[i])): print(t[i][j],end = " ") print() ```
output
1
49,063
19
98,127
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
instruction
0
49,064
19
98,128
Tags: data structures, greedy, math Correct Solution: ``` import os import sys from io import BytesIO, IOBase import math from decimal import * getcontext().prec = 25 MOD = pow(10, 9) + 7 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") for _ in range(int(input())): n = int(input()) l = list(map(int, input().split(" "))) f = [0]*n for i in range(n): f[l[i]-1] = i r = [] z = n for i in range(n-1,-1,-1): if f[i] < z: r+= l[f[i]:z] z = f[i] print(*r) ```
output
1
49,064
19
98,129
Provide tags and a correct Python 3 solution for this coding contest problem. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166.
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49,065
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Tags: data structures, greedy, math Correct Solution: ``` for _ in range(int(input())): n=int(input()) li=list(map(int,input().split())) b={} li1=[] for i in range(n): b[li[i]]=i ck=n for i in range(n,0,-1): if b[i]<=ck: for j in range(b[i],ck): li1.append(li[j]) ck=b[i] print(*li1) ```
output
1
49,065
19
98,131
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` test = int(input()) for _ in range(test): nn = int(input()) l = list(map(int, input().split())) mark = [0]*(nn+1) i = nn-1 j = nn ans = [] while i >= 0 and j >= 1: k = i while l[k]!=j: k-=1 for index in range(k, i+1): ans.append(l[index]) mark[l[index]] = 1 i = k - 1 while mark[j] == 1: j-=1 for i in ans: print(i, end = ' ') print() ```
instruction
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49,066
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98,132
Yes
output
1
49,066
19
98,133
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` # DEFINING SOME GOOD STUFF from math import * import threading import sys from collections import * mod = 10 ** 9 inf = 10 ** 15 yes = 'YES' no = 'NO' # _______________________________________________________________# def npr(n, r): return factorial(n) // factorial(n - r) if n >= r else 0 def ncr(n, r): return factorial(n) // (factorial(r) * factorial(n - r)) if n >= r else 0 def lower_bound(li, num): answer = -1 start = 0 end = len(li) - 1 while (start <= end): middle = (end + start) // 2 if li[middle] >= num: answer = middle end = middle - 1 else: start = middle + 1 return answer # min index where x is not less than num def upper_bound(li, num): answer = -1 start = 0 end = len(li) - 1 while (start <= end): middle = (end + start) // 2 if li[middle] <= num: answer = middle start = middle + 1 else: end = middle - 1 return answer # max index where x is not greater than num def abs(x): return x if x >= 0 else -x def binary_search(li, val, lb, ub): # print(lb, ub, li) ans = -1 while (lb <= ub): mid = (lb + ub) // 2 # print('mid is',mid, li[mid]) if li[mid] > val: ub = mid - 1 elif val > li[mid]: lb = mid + 1 else: ans = mid # return index break return ans def kadane(x): # maximum sum contiguous subarray sum_so_far = 0 current_sum = 0 for i in x: current_sum += i if current_sum < 0: current_sum = 0 else: sum_so_far = max(sum_so_far, current_sum) return sum_so_far def pref(li): pref_sum = [0] for i in li: pref_sum.append(pref_sum[-1] + i) return pref_sum def SieveOfEratosthenes(n): prime = [True for i in range(n + 1)] p = 2 li = [] while (p * p <= n): if (prime[p] == True): for i in range(p * p, n + 1, p): prime[i] = False p += 1 for p in range(2, len(prime)): if prime[p]: li.append(p) return li def primefactors(n): factors = [] while (n % 2 == 0): factors.append(2) n //= 2 for i in range(3, int(sqrt(n)) + 1, 2): # only odd factors left while n % i == 0: factors.append(i) n //= i if n > 2: # incase of prime factors.append(n) return factors def prod(li): ans = 1 for i in li: ans *= i return ans def dist(a, b): d = abs(a[1] - b[1]) + abs(a[2] - b[2]) return d def power_of_n(x, n): cnt = 0 while (x % n == 0): cnt += 1 x //= n return cnt def ask(l, r): if l == r: return -1 print("?", l, r) sys.stdout.flush() return int(input()) # _______________________________________________________________# import itertools sys.setrecursionlimit(300000) # threading.stack_size(10**5) # remember it cause mle # def main(): # for _ in range(1): for _ in range(int(input()) if True else 1): n = int(input()) # p,a,b,c = map(int, input().split()) a = list(map(int, input().split())) # b = list(map(int, input().split())) # c = list(map(int, input().split())) # s = input() # c = list(map(int,input().split())) # adj = graph(n,m) # d = defaultdict(int) d = defaultdict() for i in range(n): d[a[i]] = i ind = [] last = n for i in range(n,0,-1): # print('>>',d[i], last) for j in range(d[i], last): print(a[j], end=' ') temp = d[i] last = temp print('') ''' t = threading.Thread(target=main) t.start() t.join() ''' ```
instruction
0
49,067
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98,134
Yes
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1
49,067
19
98,135
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` t=int(input()) def ceil(a,b): if a%b: return a//b+1 return a//b for _ in range(t): n=int(input()) l=list(map(int,input().split())) maxi=[0] for i in range(n): maxi.append(max(maxi[-1],l[i])) del(maxi[0]) j=n-1 ans=[] while j>=0: m=1 j-=1 while j>=0 and maxi[j]==maxi[j+1]: j-=1 m+=1 e=j+1 while m: ans.append(l[e]) e+=1 m-=1 print(*ans) ```
instruction
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49,068
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98,136
Yes
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1
49,068
19
98,137
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` # -*- coding: utf-8 -*- """ Created on Tue Feb 23 12:30:26 2021 @author: MI """ n=int(input()) for i in range(n): m=int(input()) a=list(map(int, input().split())) maxrest=[0 for i in range(m)] for j in range(1, m): if a[j]>a[maxrest[j-1]]: maxrest[j]=j else: maxrest[j]=maxrest[j-1] rest=m while rest!=0: newrest=maxrest[rest-1] for j in range(newrest, rest): print(a[j], end=' ') rest=newrest ```
instruction
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49,069
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98,138
Yes
output
1
49,069
19
98,139
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` t=int(input()) for _ in range(t): n=int(input()) arr = list(map(int,input().split())) out=[] b=sorted(arr) #print(b) ind = [] for i in range(n): ind.append(arr.index(b[i])) while(n>0): k=0 #print(ind) for i in range(ind[n-1],n): k+=1 print(arr[i],end=" ") n=n-(k) ```
instruction
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49,070
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98,140
No
output
1
49,070
19
98,141
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` def solution(n, plist): reslist = [] while plist: for i in range(len(plist)-1,-1,-1): if plist[i] == len(plist): reslist.extend(plist[i:]) plist = plist[:i] # print(plist) # print(reslist) for num in reslist: print(num, end=' ') print() return t = int(input()) for tt in range(t): n = int(input()) plist = list(map(int, input().split())) solution(n, plist) ```
instruction
0
49,071
19
98,142
No
output
1
49,071
19
98,143
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` t=int(input()) for _ in range(t): n=int(input()) a=list(map(int,input().split())) l=a[a.index(n):] k=len(a) a=a[:a.index(n):] a.reverse() while a: if len(a)>=k: for i in range(k): l.append(a[i]) else: l.extend(a) break a=a[k:] for i in l: print(i,end=' ') print() ```
instruction
0
49,072
19
98,144
No
output
1
49,072
19
98,145
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a deck of n cards, and you'd like to reorder it to a new one. Each card has a value between 1 and n equal to p_i. All p_i are pairwise distinct. Cards in a deck are numbered from bottom to top, i. e. p_1 stands for the bottom card, p_n is the top card. In each step you pick some integer k > 0, take the top k cards from the original deck and place them, in the order they are now, on top of the new deck. You perform this operation until the original deck is empty. (Refer to the notes section for the better understanding.) Let's define an order of a deck as โˆ‘_{i = 1}^{n}{n^{n - i} โ‹… p_i}. Given the original deck, output the deck with maximum possible order you can make using the operation above. Input The first line contains a single integer t (1 โ‰ค t โ‰ค 1000) โ€” the number of test cases. The first line of each test case contains the single integer n (1 โ‰ค n โ‰ค 10^5) โ€” the size of deck you have. The second line contains n integers p_1, p_2,..., p_n (1 โ‰ค p_i โ‰ค n; p_i โ‰  p_j if i โ‰  j) โ€” values of card in the deck from bottom to top. It's guaranteed that the sum of n over all test cases doesn't exceed 10^5. Output For each test case print the deck with maximum possible order. Print values of cards in the deck from bottom to top. If there are multiple answers, print any of them. Example Input 4 4 1 2 3 4 5 1 5 2 4 3 6 4 2 5 3 6 1 1 1 Output 4 3 2 1 5 2 4 3 1 6 1 5 3 4 2 1 Note In the first test case, one of the optimal strategies is the next one: 1. take 1 card from the top of p and move it to p': p becomes [1, 2, 3], p' becomes [4]; 2. take 1 card from the top of p: p becomes [1, 2], p' becomes [4, 3]; 3. take 1 card from the top of p: p becomes [1], p' becomes [4, 3, 2]; 4. take 1 card from the top of p: p becomes empty, p' becomes [4, 3, 2, 1]. In result, p' has order equal to 4^3 โ‹… 4 + 4^2 โ‹… 3 + 4^1 โ‹… 2 + 4^0 โ‹… 1 = 256 + 48 + 8 + 1 = 313. In the second test case, one of the optimal strategies is: 1. take 4 cards from the top of p and move it to p': p becomes [1], p' becomes [5, 2, 4, 3]; 2. take 1 card from the top of p and move it to p': p becomes empty, p' becomes [5, 2, 4, 3, 1]; In result, p' has order equal to 5^4 โ‹… 5 + 5^3 โ‹… 2 + 5^2 โ‹… 4 + 5^1 โ‹… 3 + 5^0 โ‹… 1 = 3125 + 250 + 100 + 15 + 1 = 3491. In the third test case, one of the optimal strategies is: 1. take 2 cards from the top of p and move it to p': p becomes [4, 2, 5, 3], p' becomes [6, 1]; 2. take 2 cards from the top of p and move it to p': p becomes [4, 2], p' becomes [6, 1, 5, 3]; 3. take 2 cards from the top of p and move it to p': p becomes empty, p' becomes [6, 1, 5, 3, 4, 2]. In result, p' has order equal to 6^5 โ‹… 6 + 6^4 โ‹… 1 + 6^3 โ‹… 5 + 6^2 โ‹… 3 + 6^1 โ‹… 4 + 6^0 โ‹… 2 = 46656 + 1296 + 1080 + 108 + 24 + 2 = 49166. Submitted Solution: ``` testcases = int(input()) for i in range(testcases): n = int(input()) deck = [int(i) for i in input().split(" ")] newdeck = [] highestindex = deck.index(n) deck, rest = deck[:highestindex], deck[highestindex:] while(len(deck) > 0): highestindex = deck.index(max(deck)) deck, rest = deck[:highestindex], deck[highestindex:] newdeck.append(rest) #for x in rest: # print(x, end=" ") newdeck = sum(newdeck, []) print(*newdeck) ```
instruction
0
49,073
19
98,146
No
output
1
49,073
19
98,147
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,429
19
98,858
"Correct Solution: ``` from bisect import * N=int(input()) A=list(map(int,input().split())) B=[0]*(N+1) for i in range(N): B[A[i]]+=1 C=[0]*(N+1) for i in range(N+1): C[B[i]]+=1 D=[0] E=[0] for i in range(N+1): D.append(D[i]+i*C[i]) E.append(E[i]+C[-i-1]) E=E[::-1] F=[] for i in range(1,N+1): F.append((D[i+1]//i)+E[i+1]) F=F[::-1] for i in range(N): print(N-bisect_left(F,i+1)) ```
output
1
49,429
19
98,859
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,430
19
98,860
"Correct Solution: ``` import sys from collections import Counter input = sys.stdin.readline N = int(input()) a = list(map(int, input().split())) c = Counter() for x in a: c[x] += 1 cv = Counter() for v in c.values(): cv[v] += 1 #print(cv) def check(x, K): t = 0 for k, v in cv.items(): t += min(k, x) * v return t >= K * x res = [N] * (N + 1) for K in range(1, N): ok = 0 ng = res[K] + 1 while ng - ok > 1: m = (ok + ng) // 2 if check(m, K + 1): ok = m else: ng = m res[K + 1] = ok for r in res[1: ]: print(r) ```
output
1
49,430
19
98,861
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,431
19
98,862
"Correct Solution: ``` #!/usr/bin/env python3 import sys from collections import Counter from itertools import accumulate from collections import defaultdict INF = float("inf") def solve(N: int, A: "List[int]"): c = Counter(A) d = Counter(c.values()) d = tuple(accumulate([d[i] for i in range(N, -1, -1)]))[::-1] S = [0]*(N+1) for i in range(1, N+1): S[i] = S[i-1] + d[i] def isOK(y): return S[y] < K*y def binary_search(x): ng = -1 ok = len(x)+1 while abs(ok - ng) > 1: mid = (ok + ng)//2 if isOK(mid): ok = mid else: ng = mid return ng, ok for K in range(1, N+1): ng, ok = binary_search(range(N)) print(ng) return def main(): def iterate_tokens(): for line in sys.stdin: for word in line.split(): yield word tokens = iterate_tokens() N = int(next(tokens)) # type: int A = [int(next(tokens)) for _ in range(N)] # type: "List[int]" solve(N, A) if __name__ == '__main__': main() ```
output
1
49,431
19
98,863
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,432
19
98,864
"Correct Solution: ``` from collections import defaultdict from bisect import bisect N = int(input()) A = list(map(int,input().split())) d = defaultdict(lambda:0) for i in range(N): d[A[i]] += 1 C = [0]*(N+1) for i in d: C[d[i]] += 1 C1 = [0]*(N+1) C2 = [0]*(N+1) for i in range(N): C1[i+1] = C1[i] + (i+1)*C[i+1] C2[i+1] = C2[i] + C[i+1] l = [0]*N for n in range(N): l[n] = C1[n+1]//(n+1)+C2[N]-C2[n+1] l[n] *= -1 for i in range(N): print(bisect(l,-(i+1))) ```
output
1
49,432
19
98,865
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,433
19
98,866
"Correct Solution: ``` from collections import Counter import bisect def main(): N = int(input()) A = list(map(int, input().split())) count_list = list(Counter(A).values()) count_list.sort() cumsum_count = [0] * len(count_list) cumsum_count[0] = count_list[0] for i in range(1, len(count_list)): cumsum_count[i] = cumsum_count[i - 1] + count_list[i] ans_list = [0] * N n_max = N for k in range(1, len(count_list) + 1): # ๆœ€ๅคงใงใ‚‚ N // k ๅ›žใพใงใ€‚ # ๅ„ใ‚ซใƒผใƒ‰ n_max ๆžšใพใงไฝฟใฃใฆ k * n_max ใฎ้•ทๆ–นๅฝข้ ˜ๅŸŸใ‚’ๅ…จ้ƒจๅŸ‹ใ‚ๅฐฝใใ›ใ‚‹ใ‹ใ‚’่ชฟในใ‚‹ใ€‚ # ๅŸ‹ใ‚ๅฐฝใใ›ใ‚‹ๆœ€ๅฐใฎ n_max ใŒ็ญ”ใˆใ€‚ n_max = min(n_max, N // k) s = 0 while True: # n_max ๆžšไปฅไธŠใ‚ใ‚‹ใ‚ซใƒผใƒ‰ใฏ n_max ๆžšๅ›บๅฎš index = bisect.bisect_left(count_list, n_max) s = n_max * (len(count_list) - index) # ใใ‚Œๆœชๆบ€ใฎใ‚ซใƒผใƒ‰ใฏใใฎใพใพๅ…จ้ƒจไฝฟใ† if index > 0: s += cumsum_count[index - 1] if s >= k * n_max or n_max == 0: break n_max -= 1 ans_list[k - 1] = n_max for ans in ans_list: print(ans) if __name__ == '__main__': main() ```
output
1
49,433
19
98,867
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,434
19
98,868
"Correct Solution: ``` import bisect N = int(input()) count = {} for x in map(int, input().split()): count[x] = count.get(x, 0) + 1 a = sorted(count.values()) sums = a[:] n = len(a) for i in range(1, n): sums[i] += sums[i-1] def check(k, x): pos = bisect.bisect_right(a, x) if pos == 0: return x * n >= k * x return sums[pos-1]+ x * (n - pos) >= k * x x = 0 res = [] for k in range(N, 0, -1): while check(k, x+1): x += 1 res.append(x) for x in res[::-1]: print(x) ```
output
1
49,434
19
98,869
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,435
19
98,870
"Correct Solution: ``` import bisect as b n = int(input()) d = [0]*n for el in map(int, input().split()): d[el-1] += 1 d.sort() s = [0]*(n+1) for i in range(n): s[i+1] = s[i] + d[i] for k in range(1, n+1): l = 0 r = n//k + 1 while(l+1 < r): c = (l+r)//2 i = b.bisect_left(d, c) total = s[i] + c * (n - i) if total >= k * c: l = c else: r = c print(l) ```
output
1
49,435
19
98,871
Provide a correct Python 3 solution for this coding contest problem. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0
instruction
0
49,436
19
98,872
"Correct Solution: ``` from collections import Counter from bisect import bisect_left from itertools import accumulate # https://betrue12.hateblo.jp/entry/2019/10/20/001106 N = int(input()) A = list(map(int, input().split())) a = list(Counter(A).values()) a.sort() b = list(accumulate(a)) length = len(a) for i in range(1, N + 1): if i == 1: print(b[-1]) elif len(a) < i: print(0) else: n = b[-1] // i for j in reversed(range(1, n + 1)): t = bisect_left(a, j) if j * i <= b[t - 1] + (length - t) * j: print(j) break ```
output
1
49,436
19
98,873
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` from collections import Counter as C N = int(input()) A = sorted(list(C([int(a) for a in input().split()]).values())) X = [0] * 303030 for a in A: X[a] += 1 s = 0 c = 0 B = [0] * 303030 for i in range(300030)[::-1]: s += c B[i] += s c += X[i] def chk(k, a): if N - B[a] >= k * a: return 1 return 0 for i in range(1, N+1): l, r = 0, N + 1 while r-l > 1: m = (l+r) // 2 if chk(i, m): l = m else: r = m print(l) ```
instruction
0
49,437
19
98,874
Yes
output
1
49,437
19
98,875
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` import sys input = sys.stdin.readline from collections import Counter from itertools import accumulate from math import floor from bisect import bisect_left def main(): n = int(input()) a = list(map(int, input().split())) c = Counter(a) c = list(c.values()) d = Counter(c) d_li = [0] * (n + 1) for k, v in d.items(): d_li[k] = v dk_acm = list(accumulate(d_li)) kdk_acm = [0] for k, e in enumerate(d_li[1:], 1): kdk_acm.append(kdk_acm[-1] + k * e) def f(x): kdk_sm = kdk_acm[x] dk_sm = dk_acm[n] - dk_acm[x] return floor((kdk_sm + x * dk_sm) / x) fs = [float("inf")] + [f(x) for x in range(1, n + 1)] fs = fs[::-1] for k in range(1, n + 1): print(n - bisect_left(fs, k)) if __name__ == "__main__": main() ```
instruction
0
49,438
19
98,876
Yes
output
1
49,438
19
98,877
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` from collections import defaultdict, deque, Counter from heapq import heappush, heappop, heapify import math from bisect import bisect_left, bisect_right import random from itertools import permutations, accumulate, combinations import sys import string INF = float('inf') def LI(): return list(map(int, sys.stdin.readline().split())) def I(): return int(sys.stdin.readline()) def LS(): return sys.stdin.readline().split() def S(): return sys.stdin.readline().strip() def IR(n): return [I() for i in range(n)] def LIR(n): return [LI() for i in range(n)] def SR(n): return [S() for i in range(n)] def LSR(n): return [LS() for i in range(n)] def SRL(n): return [list(S()) for i in range(n)] def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)] mod = 10 ** 9 + 7 n = I() L = [(0, 0)] + sorted([(k, v) for k, v in Counter(Counter(LI()).values()).items()]) m = len(L) acc = [0] * m ret = 0 for j in range(m): k, v = L[j] ret += k * v acc[j] = ret v_acc = [0] * m ret = 0 for l in range(m - 1, -1, -1): ret += L[l][1] v_acc[l] = ret v_acc += [0] for i in range(1, n + 1): ok = 0 ng = n // i + 1 while ng > ok + 1: mid = (ng + ok) // 2 lower_num = bisect_right(L, (mid, INF)) if acc[lower_num - 1] + v_acc[lower_num] * mid >= i * mid: ok = mid else: ng = mid print(ok) ```
instruction
0
49,439
19
98,878
Yes
output
1
49,439
19
98,879
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` import sys sys.setrecursionlimit(2147483647) INF=float("inf") MOD=10**9+7 input=lambda :sys.stdin.readline().rstrip() def resolve(): from collections import Counter n=int(input()) A=list(Counter(map(int,input().split())).values()) A.sort() m=len(A) S=[0]*(m+1) # cumulative distribution for i in range(m): S[i+1]=S[i]+A[i] # output from bisect import bisect_left p=n i=bisect_left(A,p) # pใซๅฟœใ˜ใฆiใŒๅฎšใพใ‚‹ for k in range(1,n+1): while(S[i]+p*(m-i)<k*p): # p>=0 and ใฏๆ›ธใ‹ใชใใฆใ‚‚ใ‚ˆใ„ p-=1 i=bisect_left(A,p) print(p) resolve() ```
instruction
0
49,440
19
98,880
Yes
output
1
49,440
19
98,881
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` #input N = int(input()) A = sorted(list(map(int, input().split()))) l = len(A) lx = len(list(set(A))) for k in range(1, N + 1): if k != 1 and lx != l: print(lx//k) else: print(l//k) ```
instruction
0
49,441
19
98,882
No
output
1
49,441
19
98,883
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` n = int(input()) li = [int(x) for x in input().split()] l2 = set(li) for k in range(1,n+1): if k==1: print(n) else: print(len(l2)//k) ```
instruction
0
49,442
19
98,884
No
output
1
49,442
19
98,885
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` N = int(input()) A = list(map(int,input().split())) A.sort() c = [] hoge = 1 for i in range(1,N): if A[i] == A[i-1]: hoge += 1 else: c.append(hoge) hoge = 1 c.sort(reverse = True) for i in range(N): print(N) if N > 0: N -= C[i] ```
instruction
0
49,443
19
98,886
No
output
1
49,443
19
98,887
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi has N cards. The i-th of these cards has an integer A_i written on it. Takahashi will choose an integer K, and then repeat the following operation some number of times: * Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.) For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation. Constraints * 1 \le N \le 3 \times 10^5 * 1 \le A_i \le N * All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 \ldots A_N Output Print N integers. The t-th (1 \le t \le N) of them should be the answer for the case K=t. Examples Input 3 2 1 2 Output 3 1 0 Input 5 1 2 3 4 5 Output 5 2 1 1 1 Input 4 1 3 3 3 Output 4 1 0 0 Submitted Solution: ``` import sys stdin = sys.stdin sys.setrecursionlimit(10 ** 7) def li(): return map(int, stdin.readline().split()) def li_(): return map(lambda x: int(x) - 1, stdin.readline().split()) def lf(): return map(float, stdin.readline().split()) def ls(): return stdin.readline().split() def ns(): return stdin.readline().rstrip() def lc(): return list(ns()) def ni(): return int(stdin.readline()) def nf(): return float(stdin.readline()) from collections import Counter def binsearch(n: int, k: int, nexs: list): left = 0 right = n // k + 1 while right - left > 1: mid = (left + right) // 2 if nexs[mid * k - 1] < k: right = mid else: left = mid return left n = ni() a = list(li()) # ไธฆใณๆ›ฟใˆ b = [] cnt = 0 numlist = Counter(a) while cnt < n: newnumlist = {} keys = sorted(list(numlist.keys())) for key in keys: val = numlist[key] b.append(key) cnt += 1 if val > 1: newnumlist[key] = val - 1 numlist = newnumlist # i็•ช็›ฎใฎๆ•ฐใซใคใ„ใฆใ€ๆฌกใซๅŒใ˜ใ‚‚ใฎใŒๅ‡บใ‚‹ใพใงใฎๆœ€ๅฐ่ท้›ข INF = float("inf") temp = [INF]*(n+1) nexs = [INF]*(2*n) for idx in range(n): if temp[b[idx]] != INF: nexs[idx] = idx - temp[b[idx]] temp[b[idx]] = idx for i in range(1,len(nexs)): nexs[i] = min(nexs[i-1], nexs[i]) # kใฎๅ€ๆ•ฐใ‹ใคๆฌกใซๅŒใ˜ใ‚‚ใฎใŒๅ‡บใ‚‹ใพใงใฎ่ท้›ขใŒkไปฅไธŠใงใ‚ใ‚‹ๆœ€ๅคงใฎๆ•ฐใ‚’ๆฑ‚ใ‚ใ‚‹ for k in range(1, n + 1): if k == 1: print(n) else: print(binsearch(n, k, nexs)) ```
instruction
0
49,444
19
98,888
No
output
1
49,444
19
98,889
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,445
19
98,890
"Correct Solution: ``` # -*- coding: utf-8 -*- """ Created on Sat Jun 1 20:46:31 2019 @author: Yamazaki Kenichi """ import time N, A, B, C = map(int,input().split()) mod = 10**9+7 tnow = time.time() def cmb(n, r, mod): if (r < 0 or r > n): return 0 r = min(r, n-r) return g1[n] * g2[r] * g2[n-r] % mod g1 = [1, 1] # ๅ…ƒใƒ†ใƒผใƒ–ใƒซ g2 = [1, 1] # ้€†ๅ…ƒใƒ†ใƒผใƒ–ใƒซ inv = [0, 1] # ้€†ๅ…ƒใƒ†ใƒผใƒ–ใƒซ่จˆ็ฎ—็”จใƒ†ใƒผใƒ–ใƒซ for i in range(2, 2*10**5+1): g1.append((g1[-1] * i) % mod) inv.append((-inv[mod % i] * (mod//i)) % mod) g2.append((g2[-1] * inv[-1]) % mod) #้€†ๅ…ƒๆฑ‚ใ‚ใ‚‹ #def g(a,mod): def g(a): b, u, v = mod, 1,0 while b: t = a//b a -= t * b u -= t * v a,b,u,v = b,a,v,u u %= mod return u if u > 0 else u + mod def modpow(a, n, mod): res = 1 while n > 0: if n & 1: res = res * a % mod a = a * a % mod n >>= 1 return res p1,p2 = A * g(A + B) % mod, B * g(A + B) % mod #p1,p2 = A * g(100) % mod, B * g(100) % mod p3 = (100 - C) * g(100) % mod #p1,p2ใฎในใไน—ใฎใƒชใ‚นใƒˆ P1, P2 = [1], [1] for i in range(N+1): P1.append(P1[-1] * p1 % mod) P2.append(P2[-1] * p2 % mod) ans = 0 for i in range(N): ans += (N+i) * cmb(N+i-1, i, mod) * P1[N] * P2[i] ans += (N+i) * cmb(N+i-1, i, mod) * P1[i] * P2[N] ans %= mod ans = ans * g(p3) % mod #ans = 0 #for i in range(N): # ans += (N+i)*cmb(N+i-1,i,mod)*((modpow(p1,N,mod) * modpow(p2,i,mod) # +(modpow(p2,i,mod) * modpow(p2,N,mod)))%mod) # ans %= mod #ans = ans * g(p3) % mod print(ans) #tnow = time.time() #pow(p1,100000) #tnow2 = time.time() #tnow3 = time.time() #print(tnow2 - tnow) #print(tnow3 - tnow2) ```
output
1
49,445
19
98,891
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,446
19
98,892
"Correct Solution: ``` N, A, B, C = map(int, input().split()) mod = 10 ** 9 + 7 W = [1] * (2 * N + 1) for w in range(2 * N): W[w + 1] = ((w + 1) * W[w]) % mod def rev(a): return pow(a, mod - 2, mod) def comb(a, b): return (W[a] * rev(W[b]) * rev(W[a - b])) % mod def f(a, b): res = 0 for i in range(N): res += ((i + N) * com[i] * pow(b, i, mod)) % mod res %= mod return (pow(a, N, mod) * res) % mod a = A * rev(A + B) b = B * rev(A + B) c = C * rev(100) com = [comb(i + N - 1, i) for i in range(N)] w_a = f(a, b) w_b = f(b, a) ans = ((w_a + w_b) * rev(1 - c)) % mod print(ans) ```
output
1
49,446
19
98,893
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,447
19
98,894
"Correct Solution: ``` from itertools import* import math from collections import* from heapq import* from bisect import bisect_left,bisect_right from copy import deepcopy inf = float("inf") mod = 10**9+7 from functools import reduce import sys sys.setrecursionlimit(10**7) k,A,B,C = map(int,input().split()) Max = max(2*k+10,101) #ไบŒ้ …ไฟ‚ๆ•ฐใจใใฎ้€†ๅ…ƒใƒ†ใƒผใƒ–ใƒซใ‚’ไฝœใ‚‹ๅ‰ๅ‡ฆ็† fac = [0]*(Max) finv = [0]*(Max) inv = [0]*(Max) fac[0]=fac[1]=1 finv[0]=finv[1]=1 inv[1]=1 for i in range(2,Max): fac[i] = fac[i-1] * i % mod inv[i] = mod - inv[mod%i]*(mod//i)%mod finv[i] = finv[i-1]*inv[i]%mod #O(1)ใงmod่จˆ็ฎ—ใ—ใŸ็ต„ๅˆใ›ๆ•ฐใ‚’่จˆ็ฎ— def Comb(n,r): if n < r: return 0 if n < 0 or r < 0 : return 0 return fac[n]*(finv[r]*finv[n-r]%mod)%mod def pow_mod(x,n): if n==0: return 1 if n%2:return x*pow_mod(x,n-1)%mod a = pow_mod(x,n//2) return a*a%mod M = A+B a = A*inv[M]%mod b = B*inv[M]%mod E = 0 for n in range(k,2*k): E += (((n)*pow_mod(a,k)%mod)*pow_mod(b,n-k)%mod)*Comb(n-1,k-1)%mod E += (((n)*pow_mod(b,k)%mod)*pow_mod(a,n-k)%mod)*Comb(n-1,k-1)%mod E %= mod E = E*100*inv[100-C]%mod print(E) ```
output
1
49,447
19
98,895
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,448
19
98,896
"Correct Solution: ``` def gcd(a,b): if b>a: a,b=b,a while b: a,b=b, a%b return a def inv(a): m=10**9+7 b=m (x, lastx) = (0, 1) (y, lasty) = (1, 0) while b != 0: q = a // b (a, b) = (b, a % b) (x, lastx) = (lastx - q * x, x) (y, lasty) = (lasty - q * y, y) return lastx % m def main(): MOD=10**9+7 n,a,b,c=map(int,input().split()) frac=[1] for i in range(1,2*n): frac.append(frac[-1]*i%MOD) fracinv=[inv(frac[i]) for i in range(2*n)] powa,powb,pow100=[1],[1],[1] for i in range(n): powa.append(powa[-1]*a%MOD) powb.append(powb[-1]*b%MOD) for i in range(2*n): pow100.append(pow100[-1]*(100-c)%MOD) ans=0 for m in range(n,2*n): tmpp=frac[m-1]*fracinv[n-1]*fracinv[m-n]%MOD*(powa[n]*powb[m-n]+powa[m-n]*powb[n])*m%MOD tmpq=pow100[m+1] ans=(ans+tmpp*inv(tmpq))%MOD print(ans*100%MOD) if __name__ == "__main__": main() ```
output
1
49,448
19
98,897
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,449
19
98,898
"Correct Solution: ``` import sys sys.setrecursionlimit(10**7) INF = 10 ** 18 MOD = 10 ** 9 + 7 def POW(x, y): return pow(x, y, MOD) def INV(x, m=MOD): return pow(x, m - 2, m) def DIV(x, y, m=MOD): return (x * INV(y, m)) % m def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def II(): return int(sys.stdin.readline()) def SI(): return input() # factorials _nfact = 2 * (10 ** 5) + 10 facts = [0] * _nfact facts[0] = 1 for i in range(1, _nfact): facts[i] = (facts[i - 1] * i) % MOD def binomial(m, n): return DIV(facts[m], facts[n] * facts[m - n]) def main(): N, A, B, C = LI() D = DIV(100, 100 - C) ans = 0 ap, bp, abp = [1], [1], [POW(A + B, N)] for _ in range(0, N + 1): ap.append(ap[-1] * A % MOD) bp.append(bp[-1] * B % MOD) abp.append(abp[-1] * (A + B) % MOD) for m in range(N, 2 * N): x = binomial(m - 1, N - 1) * DIV( ap[N] * bp[m - N] + ap[m - N] * bp[N], abp[m - N]) % MOD y = (m * D) % MOD ans = (ans + (x * y) % MOD) % MOD return ans print(main()) ```
output
1
49,449
19
98,899
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,450
19
98,900
"Correct Solution: ``` M=10**9+7 N,A,B,C=map(int,input().split()) f=[1] for i in range(1,2*N): f.append(f[-1]*i%M) t=pow(A+B,M-2,M) A*=t B*=t a=pow(A,N,M) b=pow(B,N,M) z=0 for i in range(N): z+=100*t*f[N+i]*pow(f[N-1]*f[i],M-2,M)*(a+b) z%=M a=a*B%M b=b*A%M print(z) ```
output
1
49,450
19
98,901
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,451
19
98,902
"Correct Solution: ``` class Combinatorics: def __init__(self, N, mod): ''' Preprocess for calculating binomial coefficients nCr (0 <= r <= n, 0 <= n <= N) over the finite field Z/(mod)Z. Input: N (int): maximum n mod (int): a prime number. The order of the field Z/(mod)Z over which nCr is calculated. ''' self.mod = mod self.fact = {i: None for i in range(N+1)} # n! self.inverse = {i: None for i in range(1, N+1)} # inverse of n in the field Z/(MOD)Z self.fact_inverse = {i: None for i in range(N+1)} # inverse of n! in the field Z/(MOD)Z # preprocess self.fact[0] = self.fact[1] = 1 self.fact_inverse[0] = self.fact_inverse[1] = 1 self.inverse[1] = 1 for i in range(2, N+1): self.fact[i] = i * self.fact[i-1] % self.mod q, r = divmod(self.mod, i) self.inverse[i] = (- (q % self.mod) * self.inverse[r]) % self.mod self.fact_inverse[i] = self.inverse[i] * self.fact_inverse[i-1] % self.mod def perm(self, n, r): ''' Calculate nPr = n! / (n-r)! % mod ''' if n < r or n < 0 or r < 0: return 0 else: return (self.fact[n] * self.fact_inverse[n-r]) % self.mod def binom(self, n, r): ''' Calculate nCr = n! /(r! (n-r)!) % mod ''' if n < r or n < 0 or r < 0: return 0 else: return self.fact[n] * (self.fact_inverse[r] * self.fact_inverse[n-r] % self.mod) % self.mod def hom(self, n, r): ''' Calculate nHr = {n+r-1}Cr % mod. Assign r objects to one of n classes. Arrangement of r circles and n-1 partitions: o o o | o o | | | o | | | o o | | o ''' if n == 0 and r > 0: return 0 if n >= 0 and r == 0: return 1 return self.binom(n + r - 1, r) def extended_euclid(a, b): x1, y1, m = 1, 0, a x2, y2, n = 0, 1, b while m % n != 0: q, r = divmod(m, n) x1, y1, m, x2, y2, n = x2, y2, n, x1 - q * x2, y1 - q * y2, r return (x2, y2, n) def modular_inverse(a, mod): x, _, g = extended_euclid(a, mod) if g != 1: return None # Modular inverse of a does not exist else: return x % mod N, A, B, C = map(int, input().split()) MOD = 10**9 + 7 com = Combinatorics(2*N, MOD) pa = A * modular_inverse(A+B, MOD); pb = B * modular_inverse(A+B, MOD); n_first_AB = (100 * modular_inverse(100 - C, MOD)) % MOD ans = 0 for m in range(N, 2*N): # E[X] = E_M[ E[X | M] ] Exp_X_given_M = (m * n_first_AB) % MOD prob_m = com.binom(m-1, N-1) * ((pow(pa, N, MOD) * pow(pb, m-N, MOD)) % MOD + (pow(pa, m-N, MOD) * pow(pb, N, MOD)) % MOD) % MOD ans = (ans + Exp_X_given_M * prob_m) % MOD print(ans) ```
output
1
49,451
19
98,903
Provide a correct Python 3 solution for this coding contest problem. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146
instruction
0
49,452
19
98,904
"Correct Solution: ``` def main(): mod = 10**9+7 fact = [1]*200001 for i in range(1, 200001): fact[i] = fact[i-1]*i % mod def inv_n(n, mod=10**9+7): return pow(n, mod-2, mod) def nCr(n, r, mod=10**9 + 7): return inv_n(fact[n-r]*fact[r] % mod, mod)*fact[n] % mod n, a, b, c = map(int, input().split()) pan = pow(a, n, mod) pbn = pow(b, n, mod) ivab = 100*inv_n(a+b) % mod ans = 0 for i in range(n, 2*n): ans = (ans + i*ivab*nCr(i-1, n-1)*(pan*pow(b, i-n, mod) + pow(a, i-n, mod)*pbn)*inv_n(pow(a+b, i, mod))) % mod print(ans) main() ```
output
1
49,452
19
98,905
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146 Submitted Solution: ``` N, A, B, C = map(int, input().split()) P = 10**9+7 fa = [1] al = A * pow(A + B, P-2, P) % P be = B * pow(A + B, P-2, P) % P ga = C * pow(100, P-2, P) % P for i in range(1, N*2+100): fa.append(fa[-1]*i%P) ans = 0 for i in range(N): ans = (ans + fa[N+i-1] * pow((fa[N-1]*fa[i]), P-2, P) * (pow(al, N, P) * pow(be, i, P) + pow(al, i, P) * pow(be, N, P)) * (i+N)) % P print(ans * pow(1-ga, P-2, P) % P) ```
instruction
0
49,453
19
98,906
Yes
output
1
49,453
19
98,907
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146 Submitted Solution: ``` def cmb(n, r): if ( r<0 or r>n ): return 0 r = min(r, n-r) return g1[n] * g2[r] * g2[n-r] % mod mod = 10**9+7 #ๅ‡บๅŠ›ใฎๅˆถ้™ N = 2*10**5+3 g1 = [1, 1] # ๅ…ƒใƒ†ใƒผใƒ–ใƒซ g2 = [1, 1] #้€†ๅ…ƒใƒ†ใƒผใƒ–ใƒซ inverse = [0, 1] #้€†ๅ…ƒใƒ†ใƒผใƒ–ใƒซ่จˆ็ฎ—็”จใƒ†ใƒผใƒ–ใƒซ for i in range( 2, N + 1 ): g1.append( ( g1[-1] * i ) % mod ) inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod ) g2.append( (g2[-1] * inverse[-1]) % mod ) n,a,b,c=map(int,input().split()) ans=0 for i in range(n):#A,B:nๅ‹,iๅ‹ ans=(ans+pow(a,n,mod)*pow(b,i,mod)*cmb(n-1+i,i)*(n+i)*pow(pow(a+b,mod-2,mod),n+i,mod))%mod for i in range(n): ans=(ans+pow(b,n,mod)*pow(a,i,mod)*cmb(n-1+i,i)*(n+i)*pow(pow(a+b,mod-2,mod),n+i,mod))%mod print(ans*100*pow(a+b,mod-2,mod)%mod) ```
instruction
0
49,454
19
98,908
Yes
output
1
49,454
19
98,909
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146 Submitted Solution: ``` import sys sys.setrecursionlimit(10**7) INF = 10 ** 18 MOD = 10 ** 9 + 7 def POW(x, y): return pow(x, y, MOD) def INV(x, m=MOD): return pow(x, m - 2, m) def DIV(x, y, m=MOD): return (x * INV(y, m)) % m def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def II(): return int(sys.stdin.readline()) def SI(): return input() # factorials _nfact = 2 * (10 ** 5) + 10 facts = [0] * _nfact t = facts[0] = 1 for i in range(1, _nfact): t = (t * i) % MOD facts[i] = t ifacts = [0] * _nfact t = ifacts[-1] = INV(facts[-1]) for i in range(_nfact - 1, 0, -1): t = (t * i) % MOD ifacts[i - 1] = t def binomial(m, n): return facts[m] * ifacts[n] * ifacts[m - n] def main(): N, A, B, C = LI() D = DIV(100, 100 - C) ans = 0 ap, bp, abp = [1], [1], [POW(A + B, N)] for _ in range(0, N + 1): ap.append(ap[-1] * A % MOD) bp.append(bp[-1] * B % MOD) abp.append(abp[-1] * (A + B) % MOD) for m in range(N, 2 * N): x = binomial(m - 1, N - 1) * DIV( ap[N] * bp[m - N] + ap[m - N] * bp[N], abp[m - N]) % MOD y = (m * D) % MOD ans = (ans + (x * y) % MOD) % MOD return ans print(main()) ```
instruction
0
49,455
19
98,910
Yes
output
1
49,455
19
98,911
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146 Submitted Solution: ``` import sys def solve(): file = sys.stdin.readline N, A, B, C = map(int, file().split()) mod = 7 + 10 ** 9 nfact = [1] * (2 * N) nrev = [1] * (2 * N) Apow, Bpow, Hpow = [A] * (2 * N), [B] * (2 * N), [A + B] * (2 * N) Apow[0] = 1 Bpow[0] = 1 Hpow[0] = 1 Crev = (pow(100 - C, mod - 2, mod) * 100) % mod for i in range(2, 2 * N): nfact[i] = (nfact[i-1] * i) % mod Apow[i] = (Apow[i-1] * A) % mod Bpow[i] = (Bpow[i-1] * B) % mod Hpow[i] = (Hpow[i-1] * (A + B)) % mod nrev[2 * N - 1] = pow(nfact[2 * N - 1], mod - 2, mod) Hpow[2 * N - 1] = pow(Hpow[2 * N - 1] , mod - 2, mod) for i in reversed(range(1, 2 * N - 1)): nrev[i] = (nrev[i + 1] * (i + 1)) % mod Hpow[i] = (Hpow[i + 1] * (A + B)) % mod ans = 0 for i in range(N, 2 * N): ans += (((nfact[i-1] * nrev[N-1] * nrev[i-N]) % mod) * ((Apow[N]*Bpow[i-N] + Apow[i-N]*Bpow[N]) % mod) * i * Hpow[i] * Crev) % mod ans %= mod print(ans) return if __name__ == "__main__": solve() ```
instruction
0
49,456
19
98,912
Yes
output
1
49,456
19
98,913
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total. When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows. We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.) Constraints * 1 \leq N \leq 100000 * 0 \leq A,B,C \leq 100 * 1 \leq A+B * A+B+C=100 * All values in input are integers. Input Input is given from Standard Input in the following format: N A B C Output Print the expected number of games that will be played, in the manner specified in the statement. Examples Input 1 25 25 50 Output 2 Input 4 50 50 0 Output 312500008 Input 1 100 0 0 Output 1 Input 100000 31 41 28 Output 104136146 Submitted Solution: ``` m = 10**9+7 def inv(x): m = 10**9+7 t = x y = 1 while True: if t == 1: break y *= m // t t = m % t y *= -1 y %= m return y import math def cc(x,y): return math.factorial(x) // math.factorial(y) // math.factorial(x-y) n,a,b,c = map(int,input().split()) d = 100 - c awin = a * inv(d) bwin = b * inv(d) asc = 0 bsc = 0 for i in range(n): p = cc(n-1,i) * awin**(n-1) * bwin**i asc += p asc %= m for i in range(n): p = cc(n-1,i) * awin**i * bwin**(n-1) bsc += p bsc %= m sc = asc * awin + bsc * bwin sc %= m scn = sc * 100 * inv(d) scn %= m print(scn) ```
instruction
0
49,457
19
98,914
No
output
1
49,457
19
98,915