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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One day Sasha visited the farmer 2D and his famous magnetic farm. On this farm, the crop grows due to the influence of a special magnetic field. Maintaining of the magnetic field is provided by n machines, and the power of the i-th machine is a_i. This year 2D decided to cultivate a new culture, but what exactly he didn't say. For the successful growth of the new culture, it is necessary to slightly change the powers of the machines. 2D can at most once choose an arbitrary integer x, then choose one machine and reduce the power of its machine by x times, and at the same time increase the power of one another machine by x times (powers of all the machines must stay positive integers). Note that he may not do that if he wants. More formally, 2D can choose two such indices i and j, and one integer x such that x is a divisor of a_i, and change powers as following: a_i = (a_i)/(x), a_j = a_j ⋅ x Sasha is very curious, that's why he wants to calculate the minimum total power the farmer can reach. There are too many machines, and Sasha can't cope with computations, help him! Input The first line contains one integer n (2 ≤ n ≤ 5 ⋅ 10^4) — the number of machines. The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 100) — the powers of the machines. Output Print one integer — minimum total power. Examples Input 5 1 2 3 4 5 Output 14 Input 4 4 2 4 4 Output 14 Input 5 2 4 2 3 7 Output 18 Note In the first example, the farmer can reduce the power of the 4-th machine by 2 times, and increase the power of the 1-st machine by 2 times, then the powers will be: [2, 2, 3, 2, 5]. In the second example, the farmer can reduce the power of the 3-rd machine by 2 times, and increase the power of the 2-nd machine by 2 times. At the same time, the farmer can leave is be as it is and the total power won't change. In the third example, it is optimal to leave it be as it is. Submitted Solution: ``` from math import ceil n=int(input()) a=list(map(int,input().split())) a.sort() ans=[0]*101 for i in range(n): ans[a[i]]+=1 x=0 y=100 #print(ans) res=0 flag=0 t=0 while(x<=100 and y>0): flag=0 if(x>=y): break if(ans[x]<=0): x+=1 continue if(ans[y]<=0): y-=1 continue q=int(ceil(((y/x)**0.5))) #print(q) t=0 for i in range(q,1,-1): if(y%i==0): #res+=y//i #res+=x*i if(x+y<=x*i+y//i): break ans[y]-=1 ans[x]-=1 ans[y//i]+=1 ans[x*i]+=1 flag=1 break if(flag==0): y-=1 if(flag==1): break #print(y) ''' if(flag==0): ans[y]-=1 #res+=x res+=y #print(res) ''' #print(ans) for i in range(101): res+=i*ans[i] print(res) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One day Sasha visited the farmer 2D and his famous magnetic farm. On this farm, the crop grows due to the influence of a special magnetic field. Maintaining of the magnetic field is provided by n machines, and the power of the i-th machine is a_i. This year 2D decided to cultivate a new culture, but what exactly he didn't say. For the successful growth of the new culture, it is necessary to slightly change the powers of the machines. 2D can at most once choose an arbitrary integer x, then choose one machine and reduce the power of its machine by x times, and at the same time increase the power of one another machine by x times (powers of all the machines must stay positive integers). Note that he may not do that if he wants. More formally, 2D can choose two such indices i and j, and one integer x such that x is a divisor of a_i, and change powers as following: a_i = (a_i)/(x), a_j = a_j ⋅ x Sasha is very curious, that's why he wants to calculate the minimum total power the farmer can reach. There are too many machines, and Sasha can't cope with computations, help him! Input The first line contains one integer n (2 ≤ n ≤ 5 ⋅ 10^4) — the number of machines. The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 100) — the powers of the machines. Output Print one integer — minimum total power. Examples Input 5 1 2 3 4 5 Output 14 Input 4 4 2 4 4 Output 14 Input 5 2 4 2 3 7 Output 18 Note In the first example, the farmer can reduce the power of the 4-th machine by 2 times, and increase the power of the 1-st machine by 2 times, then the powers will be: [2, 2, 3, 2, 5]. In the second example, the farmer can reduce the power of the 3-rd machine by 2 times, and increase the power of the 2-nd machine by 2 times. At the same time, the farmer can leave is be as it is and the total power won't change. In the third example, it is optimal to leave it be as it is. Submitted Solution: ``` cnt=lambda s,i:s.count(i) ii=lambda:int(input()) si=lambda:input() f=lambda:map(int,input().split()) lf=lambda:list(map(int,input().split())) n=ii() l=sorted(lf()) lst=set() for i in l: for j in (2,101): if i%j==0: lst.add(j) lst=sorted(list(lst)) for i in range(n-1,0,-1): for j in range(len(lst)-1,-1,-1): if l[i]%lst[j]==0: l[i]//=lst[j] l[0]*=lst[j] exit(print(sum(l))) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Greg the Dwarf has been really busy recently with excavations by the Neverland Mountain. However for the well-known reasons (as you probably remember he is a very unusual dwarf and he cannot stand sunlight) Greg can only excavate at night. And in the morning he should be in his crypt before the first sun ray strikes. That's why he wants to find the shortest route from the excavation point to his crypt. Greg has recollected how the Codeforces participants successfully solved the problem of transporting his coffin to a crypt. So, in some miraculous way Greg appeared in your bedroom and asks you to help him in a highly persuasive manner. As usual, you didn't feel like turning him down. After some thought, you formalized the task as follows: as the Neverland mountain has a regular shape and ends with a rather sharp peak, it can be represented as a cone whose base radius equals r and whose height equals h. The graveyard where Greg is busy excavating and his crypt can be represented by two points on the cone's surface. All you've got to do is find the distance between points on the cone's surface. The task is complicated by the fact that the mountain's base on the ground level and even everything below the mountain has been dug through by gnome (one may wonder whether they've been looking for the same stuff as Greg...). So, one can consider the shortest way to pass not only along the side surface, but also along the cone's base (and in a specific case both points can lie on the cone's base — see the first sample test) Greg will be satisfied with the problem solution represented as the length of the shortest path between two points — he can find his way pretty well on his own. He gave you two hours to solve the problem and the time is ticking! Input The first input line contains space-separated integers r and h (1 ≤ r, h ≤ 1000) — the base radius and the cone height correspondingly. The second and third lines contain coordinates of two points on the cone surface, groups of three space-separated real numbers. The coordinates of the points are given in the systems of coordinates where the origin of coordinates is located in the centre of the cone's base and its rotation axis matches the OZ axis. In this coordinate system the vertex of the cone is located at the point (0, 0, h), the base of the cone is a circle whose center is at the point (0, 0, 0), lying on the XOY plane, and all points on the cone surface have a non-negative coordinate z. It is guaranteed that the distances from the points to the cone surface do not exceed 10 - 12. All real numbers in the input have no more than 16 digits after decimal point. Output Print the length of the shortest path between the points given in the input, with absolute or relative error not exceeding 10 - 6. Examples Input 2 2 1.0 0.0 0.0 -1.0 0.0 0.0 Output 2.000000000 Input 2 2 1.0 0.0 0.0 1.0 0.0 1.0 Output 2.414213562 Input 2 2 1.0 0.0 1.0 -1.0 0.0 1.0 Output 2.534324263 Input 2 2 1.0 0.0 0.0 0.0 1.0 1.0 Output 3.254470198 Submitted Solution: ``` import math mas = list(map(int, input().split())) r = mas[0] h = mas[1] l = (r ** 2 + h ** 2) ** 0.5#2 * math.pi * r mas = list(map(float, input().split())) x1 = mas[0] y1 = mas[1] z1 = mas[2] mas = list(map(float, input().split())) x2 = mas[0] y2 = mas[1] z2 = mas[2] s = 0 if ((z1 == 0) and (z2 == 0)): s = ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 elif ((z1 != 0) and (z2 != 0)): alf = math.acos((x1 * x2 + y1 * y2) / math.sqrt((x1 ** 2 + y1 ** 2) * (x2 ** 2 + y2 ** 2))) l1 = l * (1 - z1 / h) l2 = l * (1 - z2 / h) xx1 = l1; yy1 = 0; xx1_ = l1 * math.cos(2 * math.pi * r / l); yy1_ = l1 * math.sin(2 * math.pi * r / l); phi = alf * r / l xx2 = l2 * math.cos(phi); yy2 = l2 * math.sin(phi) # расстояние только по боковой поверхности sbok = min(((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2) ** 0.5, ((xx1_ - xx2) ** 2 + (yy1_ - yy2) ** 2) ** 0.5) #print(sbok) # расстояние через основание step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 sbok1min = 0 sbok2min = 0 sosnmin = 0 alf1min = 0 alf2min = 0 phi1min = 0 phi2min = 0 i1min = 0 i2min = 0 for j in range(20): k = 100 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 phi2 = alf2 * r / l xxx2 = l * math.cos(phi2) yyy2 = l * math.sin(phi2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 sbok2 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 sosn = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 ss = sbok1 + sbok2 + sosn if (ss < smin): smin = ss alf1min = alf1 start1min = alf1min - step1 / k i1min = i1 alf2min = alf2 start2min = alf2min - step2 / k i2min = i2 sbok1min = sbok1 sbok2min = sbok2 sosnmin = sosn phi1min = phi1 phi2min = phi2 step1 = step1 / k * 2 start1 = start1min if (start1 < 0): start1 = 0 step2 = step2 / k * 2 start2 = start2min if (start2 < 0): start2 = 0 #print(smin, alf1min, alf2min, phi1min, phi2min, phi) #print(sbok1min, sbok2min, sosnmin) s = min(sbok, smin) else: if (z1 == 0): xtemp = x2 ytemp = y2 ztemp = z2 x2 = x1 y2 = y1 z2 = z1 x1 = xtemp y1 = ytemp z1 = ztemp if ((x1 ** 2 + y1 ** 2 == 0) and (x2 ** 2 + y2 ** 2 == 0)): alf = 0 else: alf = math.acos((x1 * x2 + y1 * y2) / math.sqrt((x1 ** 2 + y1 ** 2) * (x2 ** 2 + y2 ** 2))) l1 = l * (1 - z1 / h) xx1 = l1; yy1 = 0; xx1_ = l1 * math.cos(2 * math.pi * r / l); yy1_ = l1 * math.sin(2 * math.pi * r / l); step1 = 2 * math.pi start1 = 0 smin = 1000000000000000 sbok1min = 0 alf1min = 0 phi1min = 0 i1min = 0 for j in range(20): k = 100 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 rosn = (x2 ** 2 + y2 ** 2) ** 0.5 xosn = rosn * math.cos(alf) yosn = rosn * math.sin(alf) sosn = ((xxx1_ - xosn) ** 2 + (yyy1_ - yosn) ** 2) ** 0.5 ss = sbok1 + sosn if (ss < smin): smin = ss alf1min = alf1 start1min = alf1min - step1 / k i1min = i1 sbok1min = sbok1 sosnmin = sosn phi1min = phi1 step1 = step1 / k * 2 start1 = start1min if (start1 < 0): start1 = 0 s = smin print(s) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Greg the Dwarf has been really busy recently with excavations by the Neverland Mountain. However for the well-known reasons (as you probably remember he is a very unusual dwarf and he cannot stand sunlight) Greg can only excavate at night. And in the morning he should be in his crypt before the first sun ray strikes. That's why he wants to find the shortest route from the excavation point to his crypt. Greg has recollected how the Codeforces participants successfully solved the problem of transporting his coffin to a crypt. So, in some miraculous way Greg appeared in your bedroom and asks you to help him in a highly persuasive manner. As usual, you didn't feel like turning him down. After some thought, you formalized the task as follows: as the Neverland mountain has a regular shape and ends with a rather sharp peak, it can be represented as a cone whose base radius equals r and whose height equals h. The graveyard where Greg is busy excavating and his crypt can be represented by two points on the cone's surface. All you've got to do is find the distance between points on the cone's surface. The task is complicated by the fact that the mountain's base on the ground level and even everything below the mountain has been dug through by gnome (one may wonder whether they've been looking for the same stuff as Greg...). So, one can consider the shortest way to pass not only along the side surface, but also along the cone's base (and in a specific case both points can lie on the cone's base — see the first sample test) Greg will be satisfied with the problem solution represented as the length of the shortest path between two points — he can find his way pretty well on his own. He gave you two hours to solve the problem and the time is ticking! Input The first input line contains space-separated integers r and h (1 ≤ r, h ≤ 1000) — the base radius and the cone height correspondingly. The second and third lines contain coordinates of two points on the cone surface, groups of three space-separated real numbers. The coordinates of the points are given in the systems of coordinates where the origin of coordinates is located in the centre of the cone's base and its rotation axis matches the OZ axis. In this coordinate system the vertex of the cone is located at the point (0, 0, h), the base of the cone is a circle whose center is at the point (0, 0, 0), lying on the XOY plane, and all points on the cone surface have a non-negative coordinate z. It is guaranteed that the distances from the points to the cone surface do not exceed 10 - 12. All real numbers in the input have no more than 16 digits after decimal point. Output Print the length of the shortest path between the points given in the input, with absolute or relative error not exceeding 10 - 6. Examples Input 2 2 1.0 0.0 0.0 -1.0 0.0 0.0 Output 2.000000000 Input 2 2 1.0 0.0 0.0 1.0 0.0 1.0 Output 2.414213562 Input 2 2 1.0 0.0 1.0 -1.0 0.0 1.0 Output 2.534324263 Input 2 2 1.0 0.0 0.0 0.0 1.0 1.0 Output 3.254470198 Submitted Solution: ``` import math mas = list(map(int, input().split())) r = mas[0] h = mas[1] l = (r ** 2 + h ** 2) ** 0.5#2 * math.pi * r mas = list(map(float, input().split())) x1 = mas[0] y1 = mas[1] z1 = mas[2] mas = list(map(float, input().split())) x2 = mas[0] y2 = mas[1] z2 = mas[2] s = 0 if ((z1 == 0) and (z2 == 0)): s = ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 elif ((z1 != 0) and (z2 != 0)): alf = math.acos((x1 * x2 + y1 * y2) / math.sqrt((x1 ** 2 + y1 ** 2) * (x2 ** 2 + y2 ** 2))) l1 = l * (1 - z1 / h) l2 = l * (1 - z2 / h) xx1 = l1; yy1 = 0; xx1_ = l1 * math.cos(2 * math.pi * r / l); yy1_ = l1 * math.sin(2 * math.pi * r / l); phi = alf * r / l xx2 = l2 * math.cos(phi); yy2 = l2 * math.sin(phi) # расстояние только по боковой поверхности sbok = min(((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2) ** 0.5, ((xx1_ - xx2) ** 2 + (yy1_ - yy2) ** 2) ** 0.5) #print(sbok) # расстояние через основание ''' step1 = 0.1 step2 = 0.1 alf1_ = 0 alf2_ = 2 * math.pi#phi smin = 10000000000000 for j in range(1000): for i1 in range(-1, 2, 1): for i2 in range(-1, 2, 1): alf1 = alf1_ + i1 * step1 alf2 = alf2_ + i2 * step2 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) phi2 = alf2 * r / l xxx2 = l * math.cos(phi2) yyy2 = l * math.sin(phi2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 sbok2 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 sosn = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 ss = sbok1 + sbok2 + sosn if (ss < smin): smin = ss alf1min = alf1 alf2min = alf2 print(smin) ''' step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 sbok1min = 0 sbok2min = 0 sosnmin = 0 alf1min = 0 alf2min = 0 phi1min = 0 phi2min = 0 i1min = 0 i2min = 0 for j in range(50): k = 10 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 phi2 = alf2 * r / l xxx2 = l * math.cos(phi2) yyy2 = l * math.sin(phi2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 sbok2 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 sosn = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 ss = sbok1 + sbok2 + sosn if (ss < smin): smin = ss alf1min = alf1 i1min = i1 alf2min = alf2 i2min = i2 sbok1min = sbok1 sbok2min = sbok2 sosnmin = sosn phi1min = phi1 phi2min = phi2 step1 = step1 / k start1 = alf1min - step1 if (start1 < 0): start1 = 0 step2 = step2 / k if (start2 < 0): start2 = 0 start2 = alf2min - step2 #print(smin, alf1min, alf2min, phi1min, phi2min, phi) #print(sbok1min, sbok2min, sosnmin) s = min(sbok, smin) ''' # путь по боковой поверхности конуса if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): betta2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) betta2 = alf2 * r / l if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = (x2 ** 2 + y2 ** 2 + (h - z2) ** 2) ** 0.5 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) xx2 = rad2 * math.cos(betta2) yy2 = rad2 * math.sin(betta2) xx2_ = rad2 * math.cos(betta2 - 2 * math.pi * r / l) yy2_ = rad2 * math.sin(betta2 - 2 * math.pi * r / l) s = min((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2, (xx1 - xx2_) ** 2 + (yy1 - yy2_) ** 2) ** 0.5 # путь боковая + основание + боковая step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 alf1min = 0 alf2min = 0 i1min = 0 i2min = 0 for j in range(3): k = 150 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 betta1 = alf1 * r / l xxx1 = l * math.cos(betta1) yyy1 = l * math.sin(betta1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 betta2 = alf2 * r / l xxx2 = l * math.cos(betta2) yyy2 = l * math.sin(betta2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) s1 = ((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2) ** 0.5 s2 = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 s3 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 s_ = s1 + s2 + s3 if (s_ < smin): smin = s_ alf1min = alf1 i1min = i1 alf2min = alf2 i2min = i2 step1 = step1 / k * 4 start1 = alf1min - step1 step2 = step2 / k * 4 start2 = alf2min - step2 #print(smin) s = min(s, smin) ''' else: if (z1 == 0): xtemp = x2 ytemp = y2 ztemp = z2 x2 = x1 y2 = y1 z2 = z1 x1 = xtemp y1 = ytemp z1 = ztemp if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): alf2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = r2 #print(rad2, alf2) smin = 1000000000 start = 0 step = 2 * math.pi for j in range(3): k = 1000 for i in range(k + 1): alf = start + i / k * step #s1 xx2 = rad2 * math.cos(alf2) yy2 = rad2 * math.sin(alf2) xx = r * math.cos(alf) yy = r * math.sin(alf) s1 = ((xx - xx2) ** 2 + (yy - yy2) ** 2) ** 0.5 #if (i == 0): # print(xx2, yy2, xx, yy, s1) #s2 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) betta = alf * r / l xx = l * math.cos(betta) yy = l * math.sin(betta) xx_ = l * math.cos(betta - 2 * math.pi * r / l) yy_ = l * math.sin(betta - 2 * math.pi * r / l) xx_ = xx yy_ = yy s2 = min((xx1 - xx) ** 2 + (yy1 - yy) ** 2, (xx1 - xx_) ** 2 + (yy1 - yy_) ** 2) ** 0.5 s_ = s1 + s2 #if (i == 0): # print(xx1, yy1, xx, yy, xx_, yy_, s2) # print(s) if (s_ < smin): smin = s_ alfmin = alf imin = i step = step / k * 2 start = alfmin - step / 2 s = smin print(s) ```
instruction
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No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Greg the Dwarf has been really busy recently with excavations by the Neverland Mountain. However for the well-known reasons (as you probably remember he is a very unusual dwarf and he cannot stand sunlight) Greg can only excavate at night. And in the morning he should be in his crypt before the first sun ray strikes. That's why he wants to find the shortest route from the excavation point to his crypt. Greg has recollected how the Codeforces participants successfully solved the problem of transporting his coffin to a crypt. So, in some miraculous way Greg appeared in your bedroom and asks you to help him in a highly persuasive manner. As usual, you didn't feel like turning him down. After some thought, you formalized the task as follows: as the Neverland mountain has a regular shape and ends with a rather sharp peak, it can be represented as a cone whose base radius equals r and whose height equals h. The graveyard where Greg is busy excavating and his crypt can be represented by two points on the cone's surface. All you've got to do is find the distance between points on the cone's surface. The task is complicated by the fact that the mountain's base on the ground level and even everything below the mountain has been dug through by gnome (one may wonder whether they've been looking for the same stuff as Greg...). So, one can consider the shortest way to pass not only along the side surface, but also along the cone's base (and in a specific case both points can lie on the cone's base — see the first sample test) Greg will be satisfied with the problem solution represented as the length of the shortest path between two points — he can find his way pretty well on his own. He gave you two hours to solve the problem and the time is ticking! Input The first input line contains space-separated integers r and h (1 ≤ r, h ≤ 1000) — the base radius and the cone height correspondingly. The second and third lines contain coordinates of two points on the cone surface, groups of three space-separated real numbers. The coordinates of the points are given in the systems of coordinates where the origin of coordinates is located in the centre of the cone's base and its rotation axis matches the OZ axis. In this coordinate system the vertex of the cone is located at the point (0, 0, h), the base of the cone is a circle whose center is at the point (0, 0, 0), lying on the XOY plane, and all points on the cone surface have a non-negative coordinate z. It is guaranteed that the distances from the points to the cone surface do not exceed 10 - 12. All real numbers in the input have no more than 16 digits after decimal point. Output Print the length of the shortest path between the points given in the input, with absolute or relative error not exceeding 10 - 6. Examples Input 2 2 1.0 0.0 0.0 -1.0 0.0 0.0 Output 2.000000000 Input 2 2 1.0 0.0 0.0 1.0 0.0 1.0 Output 2.414213562 Input 2 2 1.0 0.0 1.0 -1.0 0.0 1.0 Output 2.534324263 Input 2 2 1.0 0.0 0.0 0.0 1.0 1.0 Output 3.254470198 Submitted Solution: ``` import math mas = list(map(int, input().split())) r = mas[0] h = mas[1] l = (r ** 2 + h ** 2) ** 0.5#2 * math.pi * r mas = list(map(float, input().split())) x1 = mas[0] y1 = mas[1] z1 = mas[2] mas = list(map(float, input().split())) x2 = mas[0] y2 = mas[1] z2 = mas[2] s = 0 if ((z1 == 0) and (z2 == 0)): s = ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 elif ((z1 != 0) and (z2 != 0)): alf = math.acos((x1 * x2 + y1 * y2) / math.sqrt((x1 ** 2 + y1 ** 2) * (x2 ** 2 + y2 ** 2))) l1 = l * (1 - z1 / h) l2 = l * (1 - z2 / h) xx1 = l1; yy1 = 0; xx1_ = l1 * math.cos(2 * math.pi * r / l); yy1_ = l1 * math.sin(2 * math.pi * r / l); phi = alf * r / l xx2 = l2 * math.cos(phi); yy2 = l2 * math.sin(phi) # расстояние только по боковой поверхности sbok = min(((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2) ** 0.5, ((xx1_ - xx2) ** 2 + (yy1_ - yy2) ** 2) ** 0.5) #print(sbok) # расстояние через основание ''' step1 = 0.1 step2 = 0.1 alf1_ = 0 alf2_ = 2 * math.pi#phi smin = 10000000000000 for j in range(1000): for i1 in range(-1, 2, 1): for i2 in range(-1, 2, 1): alf1 = alf1_ + i1 * step1 alf2 = alf2_ + i2 * step2 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) phi2 = alf2 * r / l xxx2 = l * math.cos(phi2) yyy2 = l * math.sin(phi2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 sbok2 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 sosn = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 ss = sbok1 + sbok2 + sosn if (ss < smin): smin = ss alf1min = alf1 alf2min = alf2 print(smin) ''' step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 sbok1min = 0 sbok2min = 0 sosnmin = 0 alf1min = 0 alf2min = 0 phi1min = 0 phi2min = 0 i1min = 0 i2min = 0 for j in range(20): k = 100 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 phi1 = alf1 * r / l xxx1 = l * math.cos(phi1) yyy1 = l * math.sin(phi1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 phi2 = alf2 * r / l xxx2 = l * math.cos(phi2) yyy2 = l * math.sin(phi2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) sbok1 = (min((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2, (xx1_ - xxx1) ** 2 + (yy1_ - yyy1) ** 2)) ** 0.5 sbok2 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 sosn = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 ss = sbok1 + sbok2 + sosn if (ss < smin): smin = ss alf1min = alf1 start1min = alf1min - step1 / k i1min = i1 alf2min = alf2 start2min = alf2min - step2 / k i2min = i2 sbok1min = sbok1 sbok2min = sbok2 sosnmin = sosn phi1min = phi1 phi2min = phi2 step1 = step1 / k * 2 start1 = start1min if (start1 < 0): start1 = 0 step2 = step2 / k * 2 start2 = start2min if (start2 < 0): start2 = 0 #print(smin, alf1min, alf2min, phi1min, phi2min, phi) #print(sbok1min, sbok2min, sosnmin) s = min(sbok, smin) ''' # путь по боковой поверхности конуса if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): betta2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) betta2 = alf2 * r / l if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = (x2 ** 2 + y2 ** 2 + (h - z2) ** 2) ** 0.5 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) xx2 = rad2 * math.cos(betta2) yy2 = rad2 * math.sin(betta2) xx2_ = rad2 * math.cos(betta2 - 2 * math.pi * r / l) yy2_ = rad2 * math.sin(betta2 - 2 * math.pi * r / l) s = min((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2, (xx1 - xx2_) ** 2 + (yy1 - yy2_) ** 2) ** 0.5 # путь боковая + основание + боковая step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 alf1min = 0 alf2min = 0 i1min = 0 i2min = 0 for j in range(3): k = 150 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 betta1 = alf1 * r / l xxx1 = l * math.cos(betta1) yyy1 = l * math.sin(betta1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 betta2 = alf2 * r / l xxx2 = l * math.cos(betta2) yyy2 = l * math.sin(betta2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) s1 = ((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2) ** 0.5 s2 = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 s3 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 s_ = s1 + s2 + s3 if (s_ < smin): smin = s_ alf1min = alf1 i1min = i1 alf2min = alf2 i2min = i2 step1 = step1 / k * 4 start1 = alf1min - step1 step2 = step2 / k * 4 start2 = alf2min - step2 #print(smin) s = min(s, smin) ''' else: if (z1 == 0): xtemp = x2 ytemp = y2 ztemp = z2 x2 = x1 y2 = y1 z2 = z1 x1 = xtemp y1 = ytemp z1 = ztemp if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): alf2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = r2 #print(rad2, alf2) smin = 1000000000 start = 0 step = 2 * math.pi for j in range(3): k = 1000 for i in range(k + 1): alf = start + i / k * step #s1 xx2 = rad2 * math.cos(alf2) yy2 = rad2 * math.sin(alf2) xx = r * math.cos(alf) yy = r * math.sin(alf) s1 = ((xx - xx2) ** 2 + (yy - yy2) ** 2) ** 0.5 #if (i == 0): # print(xx2, yy2, xx, yy, s1) #s2 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) betta = alf * r / l xx = l * math.cos(betta) yy = l * math.sin(betta) xx_ = l * math.cos(betta - 2 * math.pi * r / l) yy_ = l * math.sin(betta - 2 * math.pi * r / l) xx_ = xx yy_ = yy s2 = min((xx1 - xx) ** 2 + (yy1 - yy) ** 2, (xx1 - xx_) ** 2 + (yy1 - yy_) ** 2) ** 0.5 s_ = s1 + s2 #if (i == 0): # print(xx1, yy1, xx, yy, xx_, yy_, s2) # print(s) if (s_ < smin): smin = s_ alfmin = alf imin = i step = step / k * 2 start = alfmin - step / 2 s = smin print(s) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Greg the Dwarf has been really busy recently with excavations by the Neverland Mountain. However for the well-known reasons (as you probably remember he is a very unusual dwarf and he cannot stand sunlight) Greg can only excavate at night. And in the morning he should be in his crypt before the first sun ray strikes. That's why he wants to find the shortest route from the excavation point to his crypt. Greg has recollected how the Codeforces participants successfully solved the problem of transporting his coffin to a crypt. So, in some miraculous way Greg appeared in your bedroom and asks you to help him in a highly persuasive manner. As usual, you didn't feel like turning him down. After some thought, you formalized the task as follows: as the Neverland mountain has a regular shape and ends with a rather sharp peak, it can be represented as a cone whose base radius equals r and whose height equals h. The graveyard where Greg is busy excavating and his crypt can be represented by two points on the cone's surface. All you've got to do is find the distance between points on the cone's surface. The task is complicated by the fact that the mountain's base on the ground level and even everything below the mountain has been dug through by gnome (one may wonder whether they've been looking for the same stuff as Greg...). So, one can consider the shortest way to pass not only along the side surface, but also along the cone's base (and in a specific case both points can lie on the cone's base — see the first sample test) Greg will be satisfied with the problem solution represented as the length of the shortest path between two points — he can find his way pretty well on his own. He gave you two hours to solve the problem and the time is ticking! Input The first input line contains space-separated integers r and h (1 ≤ r, h ≤ 1000) — the base radius and the cone height correspondingly. The second and third lines contain coordinates of two points on the cone surface, groups of three space-separated real numbers. The coordinates of the points are given in the systems of coordinates where the origin of coordinates is located in the centre of the cone's base and its rotation axis matches the OZ axis. In this coordinate system the vertex of the cone is located at the point (0, 0, h), the base of the cone is a circle whose center is at the point (0, 0, 0), lying on the XOY plane, and all points on the cone surface have a non-negative coordinate z. It is guaranteed that the distances from the points to the cone surface do not exceed 10 - 12. All real numbers in the input have no more than 16 digits after decimal point. Output Print the length of the shortest path between the points given in the input, with absolute or relative error not exceeding 10 - 6. Examples Input 2 2 1.0 0.0 0.0 -1.0 0.0 0.0 Output 2.000000000 Input 2 2 1.0 0.0 0.0 1.0 0.0 1.0 Output 2.414213562 Input 2 2 1.0 0.0 1.0 -1.0 0.0 1.0 Output 2.534324263 Input 2 2 1.0 0.0 0.0 0.0 1.0 1.0 Output 3.254470198 Submitted Solution: ``` import math mas = list(map(int, input().split())) r = mas[0] h = mas[1] l = (r ** 2 + h ** 2) ** 0.5#2 * math.pi * r mas = list(map(float, input().split())) x1 = mas[0] y1 = mas[1] z1 = mas[2] mas = list(map(float, input().split())) x2 = mas[0] y2 = mas[1] z2 = mas[2] s = 0 if ((z1 == 0) and (z2 == 0)): s = ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 elif ((z1 != 0) and (z2 != 0)): # путь по боковой поверхности конуса if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): betta2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) betta2 = alf2 * r / l if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = (x2 ** 2 + y2 ** 2 + (h - z2) ** 2) ** 0.5 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) xx2 = rad2 * math.cos(betta2) yy2 = rad2 * math.sin(betta2) xx2_ = rad2 * math.cos(betta2 - 2 * math.pi * r / l) yy2_ = rad2 * math.sin(betta2 - 2 * math.pi * r / l) s = min((xx1 - xx2) ** 2 + (yy1 - yy2) ** 2, (xx1 - xx2_) ** 2 + (yy1 - yy2_) ** 2) ** 0.5 # путь боковая + основание + боковая step1 = 2 * math.pi step2 = 2 * math.pi start1 = 0 start2 = 0 smin = 1000000000000000 alf1min = 0 alf2min = 0 i1min = 0 i2min = 0 for j in range(3): k = 100 i1 = 0 for i1 in range(k + 1): alf1 = start1 + i1 / k * step1 betta1 = alf1 * r / l xxx1 = l * math.cos(betta1) yyy1 = l * math.sin(betta1) xxx1_ = r * math.cos(alf1) yyy1_ = r * math.sin(alf1) i2 = 0 for i2 in range(k + 1): alf2 = start2 + i2 / k * step2 betta2 = alf2 * r / l xxx2 = l * math.cos(betta2) yyy2 = l * math.sin(betta2) xxx2_ = r * math.cos(alf2) yyy2_ = r * math.sin(alf2) s1 = ((xx1 - xxx1) ** 2 + (yy1 - yyy1) ** 2) ** 0.5 s2 = ((xxx1_ - xxx2_) ** 2 + (yyy1_ - yyy2_) ** 2) ** 0.5 s3 = ((xx2 - xxx2) ** 2 + (yy2 - yyy2) ** 2) ** 0.5 s_ = s1 + s2 + s3 if (s_ < smin): smin = s_ alf1min = alf1 i1min = i1 alf2min = alf2 i2min = i2 step1 = step1 / k * 4 start1 = alf1min - step1 step2 = step2 / k * 4 start2 = alf2min - step2 print(smin) s = min(s, smin) else: if (z1 == 0): xtemp = x2 ytemp = y2 ztemp = z2 x2 = x1 y2 = y1 z2 = z1 x1 = xtemp y1 = ytemp z1 = ztemp if ((x1 == 0) and (y1 == 0)): betta1 = 0 rad1 = 0 else: r1 = (x1 ** 2 + y1 ** 2) ** 0.5 alf1 = math.acos(x1 / r1) if (y1 < 0): alf1 = 2 * math.pi - alf1 betta1 = alf1 * r / l rad1 = (x1 ** 2 + y1 ** 2 + (h - z1) ** 2) ** 0.5 if ((x2 == 0) and (y2 == 0)): alf2 = 0 rad2 = 0 else: r2 = (x2 ** 2 + y2 ** 2) ** 0.5 alf2 = math.acos(x2 / r2) if (y2 < 0): alf2 = 2 * math.pi - alf2 rad2 = r2 #print(rad2, alf2) smin = 1000000000 start = 0 step = 2 * math.pi for j in range(3): k = 1000 for i in range(k + 1): alf = start + i / k * step #s1 xx2 = rad2 * math.cos(alf2) yy2 = rad2 * math.sin(alf2) xx = r * math.cos(alf) yy = r * math.sin(alf) s1 = ((xx - xx2) ** 2 + (yy - yy2) ** 2) ** 0.5 #if (i == 0): # print(xx2, yy2, xx, yy, s1) #s2 xx1 = rad1 * math.cos(betta1) yy1 = rad1 * math.sin(betta1) betta = alf * r / l xx = l * math.cos(betta) yy = l * math.sin(betta) xx_ = l * math.cos(betta - 2 * math.pi * r / l) yy_ = l * math.sin(betta - 2 * math.pi * r / l) xx_ = xx yy_ = yy s2 = min((xx1 - xx) ** 2 + (yy1 - yy) ** 2, (xx1 - xx_) ** 2 + (yy1 - yy_) ** 2) ** 0.5 s_ = s1 + s2 #if (i == 0): # print(xx1, yy1, xx, yy, xx_, yy_, s2) # print(s) if (s_ < smin): smin = s_ alfmin = alf imin = i step = step / k * 2 start = alfmin - step / 2 s = smin print(s) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr loves Chemistry, and specially doing experiments. He is preparing for a new interesting experiment. Amr has n different types of chemicals. Each chemical i has an initial volume of ai liters. For this experiment, Amr has to mix all the chemicals together, but all the chemicals volumes must be equal first. So his task is to make all the chemicals volumes equal. To do this, Amr can do two different kind of operations. * Choose some chemical i and double its current volume so the new volume will be 2ai * Choose some chemical i and divide its volume by two (integer division) so the new volume will be <image> Suppose that each chemical is contained in a vessel of infinite volume. Now Amr wonders what is the minimum number of operations required to make all the chemicals volumes equal? Input The first line contains one number n (1 ≤ n ≤ 105), the number of chemicals. The second line contains n space separated integers ai (1 ≤ ai ≤ 105), representing the initial volume of the i-th chemical in liters. Output Output one integer the minimum number of operations required to make all the chemicals volumes equal. Examples Input 3 4 8 2 Output 2 Input 3 3 5 6 Output 5 Note In the first sample test, the optimal solution is to divide the second chemical volume by two, and multiply the third chemical volume by two to make all the volumes equal 4. In the second sample test, the optimal solution is to divide the first chemical volume by two, and divide the second and the third chemical volumes by two twice to make all the volumes equal 1. Submitted Solution: ``` #TL def f(a, b): k = 0 while a != b: if a > b: a //= 2 else: b //= 2 k += 1 return k x = int(input()) y = list(map(int, input().split(' '))) ans = 10000000000000 for i in y: ek = 0 for j in y: ek += f(i, j) ans = min(ans, ek) print(ans) ```
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No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` n,m = map(int,input().split()) h = list(map(int,input().split())) ans = [1]*n for i in range(m): a,b = map(int,input().split()) if h[a-1] <= h[b-1]: ans[a-1] = 0 if h[b-1] <= h[a-1]: ans[b-1] = 0 print(sum(ans)) ```
instruction
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75,030
Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` N, M = list(map(int,input().split())) H= list(map(int,input().split())) t=[0]*N for i in range(M): A,B= list(map(int,input().split())) t[A-1]=max(t[A-1],H[B-1]) t[B-1]=max(t[B-1],H[A-1]) ans=0 for i in range(N): if t[i]<H[i]: ans+=1 print(ans) ```
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Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` N,M=map(int,input().split()) H=list(map(int,input().split())) ab=[0]*N for i in range(M): a,b=map(int,input().split()) ab[a-1]=max(ab[a-1],H[b-1]) ab[b-1]=max(ab[b-1],H[a-1]) ans=0 for i in range(N): if ab[i]<H[i]: ans+=1 print(ans) ```
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Yes
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1
37,517
3
75,035
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` N, M = map(int, input().split()) H = list(map(int, input().split())) x = [1] * N for i in range(M): A, B = map(int, input().split()) if H[A-1] <= H[B-1]: x[A-1] = 0 if H[A-1] >= H[B-1]: x[B-1] = 0 print(x.count(1)) ```
instruction
0
37,518
3
75,036
Yes
output
1
37,518
3
75,037
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` import sys from math import factorial from collections import Counter from fractions import Fraction import heapq, bisect, fractions import math import itertools sys.setrecursionlimit(10 ** 5 + 10) INF = 10**15 +5 def input(): return sys.stdin.readline().strip() def INT(): return int(input()) def MAP(): return map(int, input().split()) def LIST(): return list(map(int, input().split())) MOD = 10**9 + 7 n, m = MAP() H = LIST() low = [0]*m for i in range(m): a, b= MAP() if H[a-1] == H[b-1]: low.append(a-1) low.append(b-1) elif H[a-1] < H[b-1]: low.append(a-1) else: low.append(b-1) print(n-len(set(low))) ```
instruction
0
37,519
3
75,038
No
output
1
37,519
3
75,039
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` N, M = map(int, input().split()) Hi = list(map(int,input().split(" "))) path = [list() for _ in range(M+1)] for i in range(M): a, b = map(int, input().split()) a -= 1 b -= 1 path[a].append(b) path[b].append(a) goodT = 0 T = range(M) for i, p in zip(T, path): good = 1 if p == []: goodT += good else: for t in p: if Hi[i] <= Hi[t]: good = 0 goodT +=good print (goodT) ```
instruction
0
37,520
3
75,040
No
output
1
37,520
3
75,041
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i. There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j. Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road. Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road. How many good observatories are there? Constraints * 2 \leq N \leq 10^5 * 1 \leq M \leq 10^5 * 1 \leq H_i \leq 10^9 * 1 \leq A_i,B_i \leq N * A_i \neq B_i * Multiple roads may connect the same pair of observatories. * All values in input are integers. Input Input is given from Standard Input in the following format: N M H_1 H_2 ... H_N A_1 B_1 A_2 B_2 : A_M B_M Output Print the number of good observatories. Examples Input 4 3 1 2 3 4 1 3 2 3 2 4 Output 2 Input 6 5 8 6 9 1 2 1 1 3 4 2 4 3 4 6 4 6 Output 3 Submitted Solution: ``` def solve(n, m, h, a, b): for j in range(m): a[j] -= 1 b[j] -= 1 parents = [i for i in range(n)] def root(x): return x if parents[x] == x else root(parents[x]) for a_j, b_j in zip(a, b): if root(a_j) != root(b_j): if a_j > b_j: a_j, b_j = b_j, a_j parents[root(b_j)] = root(a_j) D = {} for j, pj in enumerate(parents): if not pj in D: D[pj] = [] D[pj].append(h[j]) ans = 0 for k, v in D.items(): if len(v) == 1: ans += 1 else: v = sorted(v) ans += int(v[-1] > v[-2]) return ans n, m = map(int, input().split()) h = list(map(int, input().split())) a = [0] * m b = [0] * m for j in range(m): a[j], b[j] = map(int, input().split()) print(solve(n,m, h, a, b)) ```
instruction
0
37,521
3
75,042
No
output
1
37,521
3
75,043
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` def main(): while True: N = int(input()) if N == 0: return m = [1, 2, 3, 4, 5, 6] ans = 1 for i in range(N): o = input()[0] if o == 'N': m = [m[1], m[5], m[2], m[3], m[0], m[4]] elif o == 'S': m = [m[4], m[0], m[2], m[3], m[5], m[1]] elif o == 'W': m = [m[2], m[1], m[5], m[0], m[4], m[3]] elif o == 'E': m = [m[3], m[1], m[0], m[5], m[4], m[2]] elif o == 'R': m = [m[0], m[2], m[4], m[1], m[3], m[5]] elif o == 'L': m = [m[0], m[3], m[1], m[4], m[2], m[5]] ans += m[0] print(ans) if __name__ == '__main__': main() ```
instruction
0
37,683
3
75,366
Yes
output
1
37,683
3
75,367
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` while 1: n=int(input()) if n==0:break a=1;s='123456' for _ in[0]*n: s=[s[int(e)]for e in{'N':"152304",'E':"310542",'W':"215043",'S':"402351",'R':"024135",'L':"031425"}[input()[0]]] a+=int(s[0]) print(a) ```
instruction
0
37,684
3
75,368
Yes
output
1
37,684
3
75,369
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` c={'N':"152304",'E':"310542",'W':"215043",'S':"402351",'R':"024135",'L':"031425"} while 1: n=int(input()) if n==0:break a=1;s='123456' for _ in[0]*n: s=[s[int(e)]for e in c[input()[0]]] a+=int(s[0]) print(a) ```
instruction
0
37,685
3
75,370
Yes
output
1
37,685
3
75,371
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` def North(d): d[0], d[1], d[3], d[5] = d[1], d[5], d[0], d[3] return int(d[0]) def West(d): d[0], d[2], d[4], d[5] = d[2], d[5], d[0], d[4] return int(d[0]) def East(d): d[0], d[2], d[4], d[5] = d[4], d[0], d[5], d[2] return int(d[0]) def South(d): d[0], d[1], d[3], d[5] = d[3], d[0], d[5], d[1] return int(d[0]) def Right(d): d[1], d[2], d[3], d[4] = d[2], d[3], d[4], d[1] return int(d[0]) def Left(d): d[1], d[2], d[3], d[4] = d[4], d[1], d[2], d[3] return int(d[0]) while True: n = int(input()) if n == 0: break dice = ['1','2','3','5','4','6'] total = 1 for i in range(n): ss = str(input().split()[0]) if ss == "North": total += North(dice) elif ss == "West": total += West(dice) elif ss == "East": total += East(dice) elif ss == "South": total += South(dice) elif ss == "Right": total += Right(dice) elif ss == "Left": total += Left(dice) print(total) ```
instruction
0
37,686
3
75,372
Yes
output
1
37,686
3
75,373
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` # coding: utf-8 # Here your code ! Dice = [1,2,3] # top,front,right def North(d): d = [d[1]] + [7 -d[0]] + [d[2]] return d def East(d): d = [7-d[2]] + [d[1]] + [d[0]] return d def South(d): d = [7-d[1]] + [d[0]] + [d[2]] return d def West(d): d = [d[2]] + [d[1]] + [7-d[0]] return d def Right(d): d = [d[0]] + [d[2]] + [7-d[1]] return d def Left(d): d = [d[0]] + [7-d[2]] + [d[1]] return d while True: n = int(input()) if n == 0: break dice = [1,2,3] result = 1 for _ in range(n): direction = input() dice = eval(direction+"(dice)") #print(dice) result += dice[0] print(result) ```
instruction
0
37,687
3
75,374
No
output
1
37,687
3
75,375
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` import sys def main(): for line in sys.stdin: n = int(line) if n == 0: break else: act = [] for _ in range(n): act.append(input()) total = 1 dice = [0, 1, 2, 3, 4, 5, 6] #Top, South, East, West, North, Bottom for x in range(n): hoge = act[x] if hoge == "North": tmp = dice[6] dice[6] = dice[5] dice[5] = dice[1] dice[1] = dice[2] dice[2] = tmp elif hoge == "East": tmp = dice[6] dice[6] = dice[3] dice[3] = dice[1] dice[1] = dice[4] dice[4] = tmp elif hoge == "West": tmp = dice[6] dice[6] = dice[4] dice[4] = dice[1] dice[1] = dice[3] dice[3] = tmp elif hoge == "South": tmp = dice[6] dice[6] = dice[2] dice[2] = dice[1] dice[1] = dice[5] dice[5] = tmp elif hoge == "Right": tmp = dice[5] dice[5] = dice[4] dice[4] = dice[2] dice[2] = dice[3] dice[3] = tmp elif hoge == "Left": tmp = dice[5] dice[5] = dice[3] dice[3] = dice[2] dice[2] = dice[4] dice[4] = tmp total += dice[1] print(total) if __name__ == "__main__": main() ```
instruction
0
37,688
3
75,376
No
output
1
37,688
3
75,377
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. The dice are placed in the orientation shown in the figure below. <image> As shown in this figure, the dice used here have 1 on the upper side and 2 on the south side, and 3 on the east side. Since the sum of the facing faces of the dice is always 7, the invisible faces are 5 on the north side, 4 on the west side, and 6 on the bottom side, respectively. From this initial arrangement, move the dice according to the instructions. However, the instruction is to perform the following six operations several times. <image> | <image> | <image> | <image> --- | --- | --- | --- <image> | <image> | | The North, East, South, and West operations rotate the dice 90 degrees in the indicated direction. The two operations, Right and Left, rotate 90 degrees horizontally while keeping the upper and lower surfaces unchanged. (Be careful of the direction of rotation.) The initial value is the number of eyes 1 that appears on the upper surface in the initial arrangement, and after each operation, the number of eyes that appear on the upper surface is added, and all operations are completed according to the instructions. Create a program that outputs the total value of the above. The first line of the input file contains the total number of instructions n, and each of the following n lines contains one of the "North, East, South, West, Right, Left" instructions. Let. However, n ≤ 10000. Input example 1 | Input example 2 --- | --- 5 | 8 North | West North | North East | Left South | South West | Right | North | Left | East Output example 1 | Output example 2 21 | 34 input The input consists of multiple datasets. Input ends when n is 0. The number of datasets does not exceed 5. output The total value is output to one line for each data set. Example Input 5 North North East South West 8 West North Left South Right North Left East 0 Output 21 34 Submitted Solution: ``` orders = { 'North': (2, 6, 3, 4, 1, 5), 'East': (4, 2, 1, 6, 5, 3), 'West': (3, 2, 6, 1, 5, 4), 'South': (5, 1, 3, 4, 6, 2), 'Right': (1, 3, 5, 2, 4, 6), 'Left': (1, 4, 2, 5, 3, 6), } while True: n = int(input()) if not n: break dice = list(range(1, 7)) top = 1 while n: new_dice = [dice[s - 1] for s in orders[input()]] dice = new_dice top += dice[0] n -= 1 print(top) ```
instruction
0
37,689
3
75,378
No
output
1
37,689
3
75,379
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a chain consisting of multiple circles on a plane. The first (last) circle of the chain only intersects with the next (previous) circle, and each intermediate circle intersects only with the two neighboring circles. Your task is to find the shortest path that satisfies the following conditions. * The path connects the centers of the first circle and the last circle. * The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles. Figure E-1 shows an example of such a chain and the corresponding shortest path. <image> Figure E-1: An example chain and the corresponding shortest path Input The input consists of multiple datasets. Each dataset represents the shape of a chain in the following format. > n > x1 y1 r1 > x2 y2 r2 > ... > xn yn rn > The first line of a dataset contains an integer n (3 ≤ n ≤ 100) representing the number of the circles. Each of the following n lines contains three integers separated by a single space. (xi, yi) and ri represent the center position and the radius of the i-th circle Ci. You can assume that 0 ≤ xi ≤ 1000, 0 ≤ yi ≤ 1000, and 1 ≤ ri ≤ 25. You can assume that Ci and Ci+1 (1 ≤ i ≤ n−1) intersect at two separate points. When j ≥ i+2, Ci and Cj are apart and either of them does not contain the other. In addition, you can assume that any circle does not contain the center of any other circle. The end of the input is indicated by a line containing a zero. Figure E-1 corresponds to the first dataset of Sample Input below. Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input. <image> Figure E-2: Example chains and the corresponding shortest paths Output For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle. The value should not have an error greater than 0.001. No extra characters should appear in the output. Sample Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output for the Sample Input 58.953437 11.414214 16.0 61.874812 63.195179 Example Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output 58.953437 11.414214 16.0 61.874812 63.195179 Submitted Solution: ``` import math class Vec: def __init__(self, x, y): self.x = x self.y = y def __mul__(self, other): return Vec(self.x * other, self.y * other) def length(self): return math.sqrt(self.x * self.x + self.y * self.y) def __str__(self): return "({},{})".format(self.x, self.y) def __sub__(self, other): return Vec(self.x - other.x, self.y - other.y) def __add__(self, other): return Vec(self.x + other.x, self.y + other.y) def __truediv__(self, other): return Vec(self.x / other, self.y / other) def turn90(self): return Vec(-self.y, self.x) def normalized(self): return self / self.length() def is_clock(self, other): return self.x * other.y - self.y * other.x < 0 class Circle: def __init__(self, x, y, r): self.r = r self.center = Vec(x, y) def intersection(self, other): d = (self.center - other.center).length() r1 = self.r r2 = other.r d1 = (d * d + r1 * r1 - r2 * r2) / 2 / d x = math.sqrt(r1 * r1 - d1 * d1) e1 = (other.center - self.center).normalized() e2 = e1.turn90() p1 = self.center + e1 * d1 + e2 * x p2 = self.center + e1 * d1 - e2 * x return p1, p2 def __str__(self): return "({},{})".format(self.center, self.r) def solve(ps: [Circle]): intersects = [] for i in range(len(ps) - 1): ci = ps[i] ci_next = ps[i + 1] intersection1, intersection2 = ci.intersection(ci_next) intersects.append((intersection1, intersection2)) res = [[ps[0].center, -1, 0]] # 候補座標とその深度と左右(0,1) dists = [[2 ** 32, 2 ** 32] for _ in range(len(intersects))] # 各交点の距離バッファ min_path_length = 2 ** 32 while len(res) != 0: res = sorted(res, key=lambda a: a[1], reverse=True) c, depth, lr = res.pop() current_path_length = dists[depth][lr] if depth != -1 else 0 if depth == len(intersects) - 1: last_path = ps[-1].center - c min_path_length = min(min_path_length, current_path_length + last_path.length()) continue l_limit_min, r_limit_min = [a - c for a in intersects[depth + 1]] # 左右の限界 l_limit, r_limit = l_limit_min, r_limit_min # 到達可能限界 l_limit_d, r_limit_d = depth + 1, depth + 1 for i in range(depth + 2, len(intersects)): l_limit2, r_limit2 = [a - c for a in intersects[i]] if l_limit_min.is_clock(l_limit2): # 限界更新 l_limit_min = l_limit2 if l_limit2.is_clock(r_limit_min): # 到達可能なら、こっちも更新 l_limit = l_limit2 l_limit_d = i if r_limit2.is_clock(r_limit_min): # 限界更新 r_limit_min = r_limit2 if l_limit_min.is_clock(r_limit2): # 到達可能なら、こっちも更新 r_limit = r_limit2 r_limit_d = i last_path = ps[-1].center - c if l_limit_min.is_clock(last_path) and last_path.is_clock(r_limit_min): # この点からゴールまで行ける min_path_length = min(min_path_length, current_path_length + last_path.length()) continue if dists[l_limit_d][0] > l_limit.length() + current_path_length: dists[l_limit_d][0] = l_limit.length() + current_path_length res.append([l_limit + c, l_limit_d, 0]) if dists[r_limit_d][1] > r_limit.length() + current_path_length: dists[r_limit_d][1] = r_limit.length() + current_path_length res.append([r_limit + c, r_limit_d, 1]) return min_path_length def main(): while True: n = int(input()) if n == 0: break ps = [Circle(*[int(a) for a in input().split()]) for _ in range(n)] print(solve(ps)) if __name__ == '__main__': main() ```
instruction
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37,700
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75,400
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1
37,700
3
75,401
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a chain consisting of multiple circles on a plane. The first (last) circle of the chain only intersects with the next (previous) circle, and each intermediate circle intersects only with the two neighboring circles. Your task is to find the shortest path that satisfies the following conditions. * The path connects the centers of the first circle and the last circle. * The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles. Figure E-1 shows an example of such a chain and the corresponding shortest path. <image> Figure E-1: An example chain and the corresponding shortest path Input The input consists of multiple datasets. Each dataset represents the shape of a chain in the following format. > n > x1 y1 r1 > x2 y2 r2 > ... > xn yn rn > The first line of a dataset contains an integer n (3 ≤ n ≤ 100) representing the number of the circles. Each of the following n lines contains three integers separated by a single space. (xi, yi) and ri represent the center position and the radius of the i-th circle Ci. You can assume that 0 ≤ xi ≤ 1000, 0 ≤ yi ≤ 1000, and 1 ≤ ri ≤ 25. You can assume that Ci and Ci+1 (1 ≤ i ≤ n−1) intersect at two separate points. When j ≥ i+2, Ci and Cj are apart and either of them does not contain the other. In addition, you can assume that any circle does not contain the center of any other circle. The end of the input is indicated by a line containing a zero. Figure E-1 corresponds to the first dataset of Sample Input below. Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input. <image> Figure E-2: Example chains and the corresponding shortest paths Output For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle. The value should not have an error greater than 0.001. No extra characters should appear in the output. Sample Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output for the Sample Input 58.953437 11.414214 16.0 61.874812 63.195179 Example Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output 58.953437 11.414214 16.0 61.874812 63.195179 Submitted Solution: ``` import math class Vec: def __init__(self, x, y): self.x = x self.y = y def __mul__(self, other): return Vec(self.x * other, self.y * other) def length(self): return math.sqrt(self.x * self.x + self.y * self.y) def __str__(self): return "({},{})".format(self.x, self.y) def __sub__(self, other): return Vec(self.x - other.x, self.y - other.y) def __add__(self, other): return Vec(self.x + other.x, self.y + other.y) def __truediv__(self, other): return Vec(self.x / other, self.y / other) def turn90(self): return Vec(-self.y, self.x) def normalized(self): return self / self.length() def is_clock(self, other): return self.x * other.y - self.y * other.x < 0 class Circle: def __init__(self, x, y, r): self.r = r self.center = Vec(x, y) def intersection(self, other): d = (self.center - other.center).length() r1 = self.r r2 = other.r d1 = (d * d + r1 * r1 - r2 * r2) / 2 / d x = math.sqrt(r1 * r1 - d1 * d1) e1 = (other.center - self.center).normalized() e2 = e1.turn90() p1 = self.center + e1 * d1 + e2 * x p2 = self.center + e1 * d1 - e2 * x return p1, p2 def __str__(self): return "({},{})".format(self.center, self.r) def solve(ps: [Circle]): intersects = [] for i in range(len(ps) - 1): ci = ps[i] ci_next = ps[i + 1] intersection1, intersection2 = ci.intersection(ci_next) intersects.append((intersection1, intersection2)) res = [[ps[0].center, -1, 0]] # 候補座標とその深度と左右(0,1) dists = [[2 ** 32, 2 ** 32] for _ in range(len(intersects))] # 各交点の距離バッファ min_path_length = 2 ** 32 while len(res) != 0: res = sorted(res, key=lambda a: a[1], reverse=True) c, depth, lr = res.pop() current_path_length = dists[depth][lr] if depth != -1 else 0 if depth == len(intersects) - 1: last_path = ps[-1].center - c min_path_length = min(min_path_length, current_path_length + last_path.length()) continue l_limit_min, r_limit_min = [a - c for a in intersects[depth + 1]] # 左右の限界 l_limit, r_limit = l_limit_min, r_limit_min # 到達可能限界 l_limit_d, r_limit_d = depth + 1, depth + 1 for i in range(depth + 2, len(intersects)): l_limit2, r_limit2 = [a - c for a in intersects[i]] if l_limit_min.is_clock(l_limit2): # 限界更新 l_limit_min = l_limit2 if l_limit2.is_clock(r_limit_min): # 到達可能なら、こっちも更新 l_limit = l_limit2 l_limit_d = i if r_limit2.is_clock(r_limit_min): # 限界更新 r_limit_min = r_limit2 if l_limit_min.is_clock(r_limit2): # 到達可能なら、こっちも更新 r_limit = r_limit2 r_limit_d = i # if l_limit.is_clock(l_limit2) and l_limit2.is_clock(r_limit): # l_limit = l_limit2 # l_limit_d = i # if l_limit.is_clock(r_limit2) and r_limit2.is_clock(r_limit): # r_limit = r_limit2 # r_limit_d = i last_path = ps[-1].center - c if l_limit.is_clock(last_path) and last_path.is_clock(r_limit): # この点からゴールまで行ける min_path_length = min(min_path_length, current_path_length + last_path.length()) continue if dists[l_limit_d][0] > l_limit.length() + current_path_length: dists[l_limit_d][0] = l_limit.length() + current_path_length res.append([l_limit + c, l_limit_d, 0]) if dists[r_limit_d][1] > r_limit.length() + current_path_length: dists[r_limit_d][1] = r_limit.length() + current_path_length res.append([r_limit + c, r_limit_d, 1]) return min_path_length def main(): while True: n = int(input()) if n == 0: break ps = [Circle(*[int(a) for a in input().split()]) for _ in range(n)] print(solve(ps)) if __name__ == '__main__': main() ```
instruction
0
37,701
3
75,402
No
output
1
37,701
3
75,403
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a chain consisting of multiple circles on a plane. The first (last) circle of the chain only intersects with the next (previous) circle, and each intermediate circle intersects only with the two neighboring circles. Your task is to find the shortest path that satisfies the following conditions. * The path connects the centers of the first circle and the last circle. * The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles. Figure E-1 shows an example of such a chain and the corresponding shortest path. <image> Figure E-1: An example chain and the corresponding shortest path Input The input consists of multiple datasets. Each dataset represents the shape of a chain in the following format. > n > x1 y1 r1 > x2 y2 r2 > ... > xn yn rn > The first line of a dataset contains an integer n (3 ≤ n ≤ 100) representing the number of the circles. Each of the following n lines contains three integers separated by a single space. (xi, yi) and ri represent the center position and the radius of the i-th circle Ci. You can assume that 0 ≤ xi ≤ 1000, 0 ≤ yi ≤ 1000, and 1 ≤ ri ≤ 25. You can assume that Ci and Ci+1 (1 ≤ i ≤ n−1) intersect at two separate points. When j ≥ i+2, Ci and Cj are apart and either of them does not contain the other. In addition, you can assume that any circle does not contain the center of any other circle. The end of the input is indicated by a line containing a zero. Figure E-1 corresponds to the first dataset of Sample Input below. Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input. <image> Figure E-2: Example chains and the corresponding shortest paths Output For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle. The value should not have an error greater than 0.001. No extra characters should appear in the output. Sample Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output for the Sample Input 58.953437 11.414214 16.0 61.874812 63.195179 Example Input 10 802 0 10 814 0 4 820 1 4 826 1 4 832 3 5 838 5 5 845 7 3 849 10 3 853 14 4 857 18 3 3 0 0 5 8 0 5 8 8 5 3 0 0 5 7 3 6 16 0 5 9 0 3 5 8 0 8 19 2 8 23 14 6 23 21 6 23 28 6 19 40 8 8 42 8 0 39 5 11 0 0 5 8 0 5 18 8 10 8 16 5 0 16 5 0 24 5 3 32 5 10 32 5 17 28 8 27 25 3 30 18 5 0 Output 58.953437 11.414214 16.0 61.874812 63.195179 Submitted Solution: ``` def solve(): from math import acos from cmath import phase, rect, pi from sys import stdin file_input = stdin while True: n = int(file_input.readline()) if n == 0: break C = (map(int, file_input.readline().split()) for i in range(n)) P = [] x, y, r1 = next(C) c1 = x + y * 1j P.append(c1) # calculation of cross points of circles for x, y, r2 in C: c2 = x + y * 1j base = c2 - c1 d = abs(base) a = acos((r1 ** 2 + d ** 2 - r2 ** 2) / (2 * r1 * d)) t = phase(base) cp1 = c1 + rect(r1, t + a) cp2 = c1 + rect(r1, t - a) P.append(cp1) P.append(cp2) c1, r1 = c2, r2 # search path and calculation of its cost lim = 5000 dist = [lim] * (2 * n) dist[0] = 0 goal = c1 g_idx = 2 * n - 1 indices = ((i + (i % 2) + 1, i + (i % 2) + 2) for i in range(g_idx)) for tpl_idx, cp, d in zip(indices, P, dist): j, k = tpl_idx if j != g_idx: s1 = P[j] - cp s2 = P[k] - cp else: s1 = goal - cp s2 = goal - cp p_s1 = None p_s2 = None for l, cp1, cp2 in zip(range(j, g_idx, 2), P[j::2], P[k::2]): t_s1 = cp1 - cp t_s2 = cp2 - cp if phase(s1 / t_s1) >= 0: s1 = t_s1 if phase(s2 / t_s2) <= 0: s2 = t_s2 if phase(s1 / s2) < 0: break if p_s1 != s1: dist[l] = min(dist[l], d + abs(s1)) p_s1 = s1 if p_s2 != s2: dist[l+1] = min(dist[l+1], d + abs(s2)) p_s2 = s2 else: gs = goal - cp if phase(s1 / gs) >= 0 and phase(s2 / gs) <= 0: dist[g_idx] = min(dist[g_idx], d + abs(gs)) print(dist[g_idx]) solve() ```
instruction
0
37,702
3
75,404
No
output
1
37,702
3
75,405
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,823
3
75,646
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` x0, y0, ax, ay, bx, by = map(int, input().split()) sx, sy, t = map(int, input().split()) x = [] y = [] x.append(x0) y.append(y0) for i in range(147): x.append(x[-1] * ax + bx) y.append(y[-1] * ay + by) ans = 0 for i in range(len(x)): for zliva in range(0, i + 1): for sprava in range(i, len(x)): c = abs(sx - x[i]) + abs(sy - y[i]) if c <= t: ans = max(ans, 1) d = abs(x[i] - x[zliva]) + abs(y[i] - y[zliva]) if c + d <= t: ans = max(ans, i - zliva + 1) e = abs(x[zliva] - x[sprava]) + abs(y[zliva] - y[sprava]) if c + d + e <= t: ans = max(ans, sprava - zliva + 1) d = abs(x[i] - x[sprava]) + abs(y[i] - y[sprava]) if c + d <= t: ans = max(ans, sprava - i + 1) e = abs(x[zliva] - x[sprava]) + abs(y[zliva] - y[sprava]) if c + d + e <= t: ans = max(ans, sprava - zliva + 1) print(ans) ```
output
1
37,823
3
75,647
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,824
3
75,648
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` xo,yo,ax,ay,bx,by=map(int,input().split()) orx,ory=xo,yo xs,ys,t=map(int,input().split()) cur=abs(xo-xs)+abs(yo-ys) sort=[cur] while True: x,y=xo,yo xo,yo=ax*xo+bx,ay*yo+by cur=abs(xo-xs)+abs(yo-ys) if cur>sort[-1]: break else: sort.append(cur) dpoint=0 copyx,copyy=x,y mina=abs(x-xs)+abs(y-ys) if mina<=t: dpoint+=1 time=0 copy=time while time<t and (x,y)!=(orx,ory): a,b=x,y x,y=(x-bx)//ax,(y-by)//ay time+=abs(x-a)+abs(y-b) if (time+min(mina,abs(x-xs)+abs(y-ys)))<=t: dpoint+=1 if time+min(mina,(abs(x-xs)+abs(y-ys)))<t: mina=abs(x-xs)+abs(y-ys) while time<t: a,b=ax*copyx+bx,ay*copyy+by time+=abs(a-copyx)+abs(b-copyy) copyx,copyy=a,b x,y=a,b if (time+min(mina,(abs(a-xs)+(b-ys))))<=t: dpoint+=1 print(dpoint) ```
output
1
37,824
3
75,649
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,825
3
75,650
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` x0, y0, ax, ay, bx, by = map(int, input().split()) xs, ys, t = map(int, input().split()) ans = [(x0, y0)] for i in range(100): tmpx, tmpy = ans[-1] ans.append((ax * tmpx + bx, ay * tmpy + by)) res = 0 for i in range(100): posx, posy = xs, ys next_i = i time = 0 cnt = 0 while True: if not (0 <= next_i < 100): break nextx, nexty = ans[next_i] time += abs(nextx - posx) + abs(nexty - posy) if time > t: break cnt += 1 next_i += 1 posy = nexty posx = nextx res = max(res, cnt) for i in range(100): posx, posy = xs, ys next_i = i time = 0 cnt = 0 while True: if not (0 <= next_i < 100): break nextx, nexty = ans[next_i] time += abs(nextx - posx) + abs(nexty - posy) if time > t: break cnt += 1 next_i -= 1 posy = nexty posx = nextx res = max(res, cnt) print(res) ```
output
1
37,825
3
75,651
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,826
3
75,652
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` def dist(x,y): return abs(x[0]-y[0])+abs(x[1]-y[1]) x,y,ax,ay,bx,by = list(map(int,input().split())) xs,ys,coins = list(map(int,input().split())) arr = [(x,y)] for i in range(60): x = ax*x+bx y = ay*y+by arr.append((x,y)) cur = (xs,ys) ans = 0 for i in range(60): for j in range(60): # current node to ith node (1 imp node) and then ith node to jth node (abs(j-i)+1 imp nodes ) t = dist(cur,arr[i])+dist(arr[i],arr[j]) if t<=coins: ans = max(ans,abs(i-j)+1) print(ans) ```
output
1
37,826
3
75,653
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,827
3
75,654
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` import sys # sys.setrecursionlimit(10**6) from sys import stdin, stdout import bisect #c++ upperbound import math import heapq def modinv(n,p): return pow(n,p-2,p) def cin(): return map(int,sin().split()) def ain(): #takes array as input return list(map(int,sin().split())) def sin(): return input() def inin(): return int(input()) import math def Divisors(n) : l = [] for i in range(1, int(math.sqrt(n) + 1)) : if (n % i == 0) : if (n // i == i) : l.append(i) else : l.append(i) l.append(n//i) return l """*******************************************************""" def main(): x,y,ax,ay,bx,by=cin() s=[(x,y)] for i in range(100): if(math.log10(ax)+math.log10(x)>18 or math.log10(ay)+math.log10(y)>18): break xx=ax*x+bx yy=ay*y+by x=xx y=yy s.append((x,y)) x,y,t=cin() n=len(s) p=0 if (x,y) in s: p=1 s.remove((x,y)) # print(s) n=len(s) an=p for i in range(n): f=0 ans=p xx=x yy=y for j in range(i,n): f+=abs(s[j][0]-xx)+abs(s[j][1]-yy) xx=s[j][0] yy=s[j][1] if(f>t): break ans+=1 an=max(an,ans) # print(ans) s=s[::-1] for i in range(n): f=0 ans=p xx=x yy=y for j in range(i,n): f+=abs(s[j][0]-xx)+abs(s[j][1]-yy) xx=s[j][0] yy=s[j][1] if(f>t): break ans+=1 an=max(an,ans) print(an) ######## Python 2 and 3 footer by Pajenegod and c1729 # Note because cf runs old PyPy3 version which doesn't have the sped up # unicode strings, PyPy3 strings will many times be slower than pypy2. # There is a way to get around this by using binary strings in PyPy3 # but its syntax is different which makes it kind of a mess to use. # So on cf, use PyPy2 for best string performance. py2 = round(0.5) if py2: from future_builtins import ascii, filter, hex, map, oct, zip range = xrange import os, sys from io import IOBase, BytesIO BUFSIZE = 8192 class FastIO(BytesIO): newlines = 0 def __init__(self, file): self._file = file self._fd = file.fileno() self.writable = "x" in file.mode or "w" in file.mode self.write = super(FastIO, self).write if self.writable else None def _fill(self): s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.seek((self.tell(), self.seek(0,2), super(FastIO, self).write(s))[0]) return s def read(self): while self._fill(): pass return super(FastIO,self).read() def readline(self): while self.newlines == 0: s = self._fill(); self.newlines = s.count(b"\n") + (not s) self.newlines -= 1 return super(FastIO, self).readline() def flush(self): if self.writable: os.write(self._fd, self.getvalue()) self.truncate(0), self.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable if py2: self.write = self.buffer.write self.read = self.buffer.read self.readline = self.buffer.readline else: 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') # Cout implemented in Python import sys class ostream: def __lshift__(self,a): sys.stdout.write(str(a)) return self cout = ostream() endl = '\n' # Read all remaining integers in stdin, type is given by optional argument, this is fast def readnumbers(zero = 0): conv = ord if py2 else lambda x:x A = []; numb = zero; sign = 1; i = 0; s = sys.stdin.buffer.read() try: while True: if s[i] >= b'0' [0]: numb = 10 * numb + conv(s[i]) - 48 elif s[i] == b'-' [0]: sign = -1 elif s[i] != b'\r' [0]: A.append(sign*numb) numb = zero; sign = 1 i += 1 except:pass if s and s[-1] >= b'0' [0]: A.append(sign*numb) return A if __name__== "__main__": main() ```
output
1
37,827
3
75,655
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,828
3
75,656
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` from sys import stdin, stdout import sys #brutal search if __name__ == '__main__': fa = list(map(int, stdin.readline().split())) x0 = fa[0] y0 = fa[1] ax = fa[2] ay = fa[3] bx = fa[4] by = fa[5] sa = list(map(int, stdin.readline().split())) xs = sa[0] ys = sa[1] t = sa[2] dis = [] cx = x0 cy = y0 px = x0 py = y0 disSum = 0 for i in range(60): disSum += abs(cx-px) + abs(cy-py) la = [cx, cy, disSum] dis.append(la) nx = ax * cx + bx ny = ay * cy + by px = cx py = cy cx = nx cy = ny res = 0 #brutal #print(dis) for i in range(60): for j in range(i, 60): for k in range(i, j+1): #op1 2*(i,k) + k,j #print(i) #print(j) #print(k) op1 = 2*(dis[k][2] - dis[i][2]) + (dis[j][2] - dis[k][2]) #op2 i,k + 2*(k,j) op2 = (dis[k][2] - dis[i][2]) + 2*(dis[j][2] - dis[k][2]) ttldis = abs(xs-dis[k][0]) + abs(ys-dis[k][1]) + min(op1, op2) if t >= ttldis: res = max(res, j-i+1) print(str(res)) ```
output
1
37,828
3
75,657
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,829
3
75,658
Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` dist = [] def get_dist(x1, y1, x2, y2): return abs(x1-x2) + abs(y1-y2) def bs(ind, t): if t < 0: return ind+1 if t == 0: return ind l = 0 r = ind+1 while r-l > 1: o = (r+l)//2 if dist[ind]-dist[o] < t: r = o else: l = o if dist[ind]-dist[l] <= t: return l else: return r x0, y0, ax, ay, bx, by = map(int, input().split()) xs, ys, t = map(int, input().split()) x = ax*x0+bx y = ay*y0+by prevx = 0 prevy = 0 cords = [[x0, y0]] while get_dist(x, y, xs, ys) > t: prevx = x prevy = y x = ax*x+bx y = ay*y+by if x < prevx or y < prevy: break if get_dist(x, y, xs, ys) > get_dist(x0, y0, xs, ys): break if x > prevx and y > prevy: prevx = x prevy = y while x >= prevx and y >= prevy and get_dist(x, y, xs, ys) <= t: cords.append([x, y]) x = ax*x+bx y = ay*y+by dist = [0] * len(cords) dist[0] = 0 for i in range(1, len(cords)): dist[i] = dist[i-1] + get_dist(cords[i][0], cords[i][1], cords[i-1][0], cords[i-1][1]) ma = 0 tmp = get_dist(x0, y0, xs, ys) for i in range(len(dist)): if t - tmp - dist[i] >= 0: ma = max(ma, i+1) ma = max(ma, 1 + i - bs(i, t - get_dist(cords[i][0], cords[i][1], xs, ys))) print(ma) ```
output
1
37,829
3
75,659
Provide tags and a correct Python 3 solution for this coding contest problem. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
instruction
0
37,830
3
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Tags: brute force, constructive algorithms, geometry, greedy, implementation Correct Solution: ``` x0, y0, ax, ay, bx, by = map(int, input().split()) xs, ys, t = map(int, input().split()) LIM = 60 arr_xs = [x0] for i in range(LIM * 2): arr_xs.append(arr_xs[i] * ax + bx) arr_ys = [y0] for i in range(LIM * 2): arr_ys.append(arr_ys[i] * ay + by) # print(arr_xs[:5]) def dst(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) ans = 0 for start in range(len(arr_ys)): cur_d = dst(arr_xs[start], arr_ys[start], xs, ys) pt = start if (cur_d > t): continue cnt = 1 while(pt < len(arr_xs)): cur_d += dst(arr_xs[pt], arr_ys[pt], arr_xs[pt + 1], arr_ys[pt + 1]) if (cur_d > t) : break cnt += 1 pt += 1 ans = max(ans, cnt) for start in range(len(arr_xs)): cur_d = dst(arr_xs[start], arr_ys[start], xs, ys) pt = start if (cur_d > t): continue cnt = 1 while(pt > 0): cur_d += dst(arr_xs[pt], arr_ys[pt], arr_xs[pt - 1], arr_ys[pt - 1]) if (cur_d > t) : break cnt += 1 pt -= 1 ans = max(ans, cnt) print(ans) ```
output
1
37,830
3
75,661
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` from math import * def d(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) x0, y0, ax, ay, bx, by = list(map(int, input().split())) xs, ys, t = list(map(int, input().split())) v = [] v.append([x0, y0]) for i in range(64): x1, y1 = ax * x0 + bx, ay * y0 + by v.append([x1, y1]) x0, y0 = x1, y1 n = len(v) v.sort() ans = 0 for i in range(n): for j in range(i, n): v1, v2 = 0, 0 px, py = xs, ys for p in range(i, j + 1): v2 += d(px, py, v[p][0], v[p][1]) px, py = v[p][0], v[p][1] px, py = xs, ys p = j while p >= i: v1 += d(px, py, v[p][0], v[p][1]) px, py = v[p][0], v[p][1] p -= 1 if min(v1, v2) <= t: ans = max(ans, j - i + 1) print(ans) ```
instruction
0
37,831
3
75,662
Yes
output
1
37,831
3
75,663
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` #!/usr/bin/env python3 # coding: utf-8 # Last Modified: 19/Jan/20 11:14:20 PM import sys def main(): x0, y0, ax, ay, bx, by = get_ints() points = [] points.append((x0, y0)) xs, ys, t = get_ints() # cin >> xs >> ys >> t; x = x0 y = y0 def manhattan(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) for i in range(1, 100): x = ax * x + bx y = ay * y + by points.append((x, y)) ans, curr = 0, 0 for i in range(len(points)): T = t XS = xs YS = ys curr = 0 f = 1 for j in range(i, len(points)): x = points[j][0] y = points[j][1] dist = manhattan(XS, YS, x, y) T -= dist XS = x YS = y curr += 1 if T < 0: ans = max(ans, curr - 1) f = 0 break if f: ans = max(ans, curr) points.reverse() for i in range(len(points)): T = t XS = xs YS = ys curr = 0 f = 1 for j in range(i, len(points)): x = points[j][0] y = points[j][1] dist = manhattan(XS, YS, x, y) T -= dist curr += 1 XS = x YS = y if T < 0: ans = max(ans, curr - 1) f = 0 break if f: ans = max(ans, curr) print(ans) get_array = lambda: list(map(int, sys.stdin.readline().split())) get_ints = lambda: map(int, sys.stdin.readline().split()) input = lambda: sys.stdin.readline().strip() if __name__ == "__main__": main() ```
instruction
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Yes
output
1
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75,665
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x0, y0, ax, ay, bx, by = map(int, input().split()) xs, ys, t = map(int, input().split()) x = [x0] y = [y0] dx = [0] dy = [0] for i in range(59): x.append(x[-1] * ax + bx) y.append(y[-1] * ay + by) n = len(x) ans = 0 for i in range(n): for j in range(i, n): curt = min(abs(x[i] - xs) + abs(y[i] - ys), abs(x[j] - xs) + abs(y[j] - ys)) + (abs(x[i] - x[j]) + abs(y[i] - y[j])) if curt <= t: ans = max(ans, j - i + 1) print(ans) ```
instruction
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37,833
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Yes
output
1
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75,667
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x0,y0,ax,ay,bx,by=map(int,input().split()) xs,ys,t=map(int,input().split()) imp=[[x0,y0]] for i in range(64): imp.append([imp[-1][0]*ax+bx,imp[-1][1]*ay+by]) l=len(imp) pro=0 for i in range(l): for j in range(l): if abs(xs-imp[i][0])+abs(ys-imp[i][1])+abs(imp[j][0]-imp[i][0])+abs(imp[j][1]-imp[i][1])<=t: pro=max(pro,abs(i-j)+1) print(pro) ```
instruction
0
37,834
3
75,668
Yes
output
1
37,834
3
75,669
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x0, y0, ax, ay, bx, by = list(map(int, input().split())) xs, ys, t = list(map(int, input().split())) all_numbers = [(x0, y0)] for i in range(55): x, y = all_numbers[-1] all_numbers.append((ax * x + bx, ay * y + by)) for i in range(0, len(all_numbers)): if xs < all_numbers[i][0]: break # print(all_numbers[13:17]) ind = i - 1 maximum = 0 if ind >= 0: total = 0 t1 = t x1, y1 = xs, ys flag = 1 for i in range(ind, -1, -1): diff = abs(x1 - all_numbers[i][0]) + abs(y1 - all_numbers[i][1]) if diff <= t1: t1 -= diff total += 1 else: flag = 0 break x1, y1 = all_numbers[i] # print(t1) if flag == 1: t1 = t1 - (t - t1) # print(t1) if t1 > 0: x1, y1 = xs, ys for i in range(ind + 1, len(all_numbers)): diff = abs(x1 - all_numbers[i][0]) + abs(y1 - all_numbers[i][1]) if diff <= t1: t1 -= diff total += 1 x1, y1 = all_numbers[i] maximum = max(total, maximum) if abs(xs - all_numbers[ind + 1][0]) + abs(ys - all_numbers[ind + 1][1]) <= t: t =t-( abs(xs - all_numbers[ind + 1][0]) + abs(ys - all_numbers[ind + 1][1])) xs, ys = all_numbers[ind + 1] # print("asdsa") total = 1 flag = 1 t1 = t x1, y1 = xs, ys flag = 1 for i in range(ind, -1, -1): diff = abs(x1 - all_numbers[i][0]) + abs(y1 - all_numbers[i][1]) if diff <= t1: t1 -= diff total += 1 else: flag = 0 break x1, y1 = all_numbers[i] # print(t1) if flag == 1: t1 = t1 - (t - t1) # print(t1) if t1 > 0: x1, y1 = xs, ys for i in range(ind + 1, len(all_numbers)): diff = abs(x1 - all_numbers[i][0]) + abs(y1 - all_numbers[i][1]) if diff <= t1: t1 -= diff total += 1 x1, y1 = all_numbers[i] maximum = max(total, maximum) print(maximum) else: total=0 for i in range(0,len(all_numbers)): diff = abs(xs - all_numbers[i][0]) + abs(ys - all_numbers[i][1]) if diff<=t: total+=1 t-=diff else: break xs,ys=all_numbers[i] print(maximum) ```
instruction
0
37,835
3
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No
output
1
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3
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x0, y0, ax, ay, bx, by = list(map(int, input().split())) xs, ys, t = list(map(int, input().split())) r = [] for i in range(50): r.append((x0, y0)) x0 = ax * x0 + bx y0 = ay * y0 + by ans = 0 def distance(l, r): return abs(l[0] - r[0]) + abs(l[1] - r[1]) init = (xs, ys) for i in range(len(r)): d = distance(r[i], init) if d <= t: ans = max(ans, 1) cd = d add = 0 now = 1 for left in range(i - 1, -1, -1): cd += distance(r[left], r[left + 1]) add += distance(r[left], r[left + 1]) now += 1 if cd <= t: ans = max(ans, now) maybe_cd = cd + add maybe_now = now for right in range(i + 1, len(r)): maybe_cd += distance(r[right], r[right - 1]) maybe_now += 1 if maybe_cd <= t: ans = max(ans, maybe_now) else: break else: break cd = d add = 0 now = 1 for right in range(i + 1, len(r)): cd += distance(r[right], r[right - 1]) add += distance(r[right], r[right - 1]) now += 1 if cd <= t: ans = max(ans, now) maybe_cd = cd + add maybe_now = now for left in range(i - 1, -1, -1): maybe_cd += distance(r[left], r[left + 1]) maybe_now += 1 if maybe_cd <= t: ans = max(ans, maybe_now) else: break else: break print(ans) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x,y,ax,ay,bx,by=map(int,input().split(" ")) xs,ys,t=map(int,input().split(" ")) ans=0 points=[] tx,ty=x,y while(tx<=10**20 and ty<=10**20): points.append((tx,ty)) tx=(tx*ax)+bx ty=(ty*ay)+by ind=-1 mini=10**20 for i in range(len(points)): z=((points[i][0]-xs)**2)+((points[i][1]-ys)**2) if(z<mini): mini=z ind=i #print(ind) #print(points) #print(ind) start=ind+1 lol=0 cx=xs cy=ys #print(t,lol,"ppp") while ((lol+abs(cx-points[ind][0])+abs(cy-points[ind][1]))<=t and ind>=0): #print("lol") #print(cx,cy,"curr") lol+=abs(cx-points[ind][0])+abs(cy-points[ind][1]) cx=points[ind][0] cy=points[ind][1] ans+=1 ind-=1 #print(lol) #print(cx,cy,"popop",start) while(start<len(points) and (lol+abs(cx-points[start][0])+abs(cy-points[start][1]))<=t): lol+=abs(cx-points[start][0])+abs(cy-points[start][1]) ans+=1 start+=1 #print(ans) ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. [THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu) [KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives) With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows: * The coordinates of the 0-th node is (x_0, y_0) * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? Input The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes. The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available. Output Print a single integer — the maximum number of data nodes Aroma can collect within t seconds. Examples Input 1 1 2 3 1 0 2 4 20 Output 3 Input 1 1 2 3 1 0 15 27 26 Output 2 Input 1 1 2 3 1 0 2 2 1 Output 0 Note In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0). In the first example, the optimal route to collect 3 nodes is as follows: * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. In the second example, the optimal route to collect 2 nodes is as follows: * Collect the 3-rd node. This requires no seconds. * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. Submitted Solution: ``` x0,y0,ax,ay,bx,by = list(map(int,input().split())) x,y,hadtime = list(map(int,input().split())) a = [] num = 0 a.append([x0,y0]) for i in range(1,100): a.append([a[i-1][0]*ax+bx,a[i-1][1]*ay+by]) for i in range(100): if abs(a[i][0]-x)+abs(a[i][1]-y)<=hadtime: num+=1 print(num) ```
instruction
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37,838
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No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` import sys input = sys.stdin.buffer.readline strInp = lambda : input().strip().split() intInp = lambda : list(map(int,strInp())) for t in range(int(input())): n = int(input()) arr = intInp() arr.sort(reverse=True) m = 0 myMax = arr.pop() groupLen = 1 while len(arr) >= 0: if groupLen == myMax: m += 1 groupLen = 1 if len(arr) == 0: break myMax = arr.pop() continue if len(arr) == 0: break nex = arr.pop() myMax = max(myMax, nex) groupLen += 1 print(m) ```
instruction
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Yes
output
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3
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` from sys import stdin from sys import stdout def main(): t = int(stdin.readline()) for _ in range(t): n = int(stdin.readline()) e = sorted(map(int, stdin.readline().split())) i = 0 res = 0 while i < n: max_ = e[i] cnt = 1 i += 1 while i < n and max_ > cnt: max_ = e[i] cnt += 1 i += 1 if max_ <= cnt: res += 1 stdout.write(str(res) + "\n") main() ```
instruction
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3
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Yes
output
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` for i in range(int(input())): n=int(input()) q=sorted(list(map(int,input().split()))) if n==1 and q[0]==1: print("1") elif n==1 and q[0]!=1: print("0") else: p=0 cnt=0 for i in q: cnt+=1 if cnt==i: cnt=0 p+=1 print(p) ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` from sys import stdin, stdout import math,sys from itertools import permutations, combinations from collections import defaultdict,deque,OrderedDict import bisect as bi import heapq #------------------PYPY FAst I/o--------------------------------# def I():return (int(stdin.readline())) def In():return(map(int,stdin.readline().split())) ''' #------------------Sublime--------------------------------------# #sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w'); def I():return (int(input())) def In():return(map(int,input().split())) def L():return(list(In())) ''' def main(): try: n=I() l=list(In()) if n==1 and l[0]==1: print(1) else: l.sort() ans=0 temp=0 ma=-1 for i in range(n): temp1=l[i] ma=max(temp1,ma) temp+=1 if temp==ma: ans+=1 temp=0 ma=-1 #print(ans) print(ans) except: pass M = 998244353 P = 1000000007 if __name__ == '__main__': for _ in range(I()): main() ```
instruction
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Yes
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3
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Evaluate the correctness of the submitted Python 2 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict from itertools import permutations, combinations raw_input = stdin.readline pr = stdout.write mod=10**9+7 def ni(): return int(raw_input()) def li(): return map(int,raw_input().split()) def pn(n): stdout.write(str(n)+'\n') def pa(arr): pr(' '.join(map(str,arr))+'\n') # fast read function for total integer input def inp(): # this function returns whole input of # space/line seperated integers # Use Ctrl+D to flush stdin. return map(int,stdin.read().split()) range = xrange # not for python 3.0+ for t in range(ni()): n=ni() l=li() d=Counter(l) temp=0 ans=0 for i in sorted(d): ans+=(temp+d[i])/i temp=(temp+d[i])%i pn(ans) ```
instruction
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37,872
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75,744
Yes
output
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3
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` from collections import defaultdict a=int(input()) for i in range(a): r=int(input()) z=list(map(int,input().split())) from collections import defaultdict al=defaultdict(int) for i in range(len(z)): al[z[i]]+=1 z.sort() fill=0 count=0 z=list(set(z)) for i in range(len(z)): count+=al[z[i]]//z[i] rem=al[z[i]]%z[i] count+=rem//z[i] fill=rem%z[i] print(count) ```
instruction
0
37,873
3
75,746
No
output
1
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3
75,747
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` import os,sys;from io import BytesIO, IOBase 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) try:sys.stdin,sys.stdout=open('in.txt','r'),open('out.txt','w') except:pass ii1=lambda:int(sys.stdin.readline().strip()) # for interger is1=lambda:sys.stdin.readline().strip() # for str iia=lambda:list(map(int,sys.stdin.readline().strip().split())) # for List[int] isa=lambda:sys.stdin.readline().strip().split() # for List[str] mod=int(1e9 + 7);from collections import *;from math import * # abc = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' # sys.setrecursionlimit(500000) ###################### Start Here ###################### # from functools import lru_cache # from collections import defaultdict as dd from collections import deque as dq for _ in range(ii1()): n = ii1() arr = iia() ans = 0 counter = Counter(arr) for key,val in counter.items(): ans+=val//key print(ans) ```
instruction
0
37,874
3
75,748
No
output
1
37,874
3
75,749
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` from collections import deque from collections import OrderedDict import math import sys import os from io import BytesIO import threading import bisect import heapq #sys.stdin = open("F:\PY\\test.txt", "r") input = sys.stdin.readline #file = open("F:\PY\\test.txt", "r") #import file.readline as input def run(val): array = [] while(val>0): array.append(val%10) val=val//10 minElv = 9999999999 maxElv = 0 for i in range(len(array)): minElv= min(array[i], minElv) maxElv = max(array[i], maxElv) return minElv*maxElv for t in range(int(input())): n = int(input()) iA = list(map(int, input().split())) #cV = [0]*300005 cD = dict() for i in range(n): if iA[i] in cD: cD[iA[i]]+=1 else: cD[iA[i]]=1 answer = 0 sL = 0 sortDic = OrderedDict(sorted(cD.items())) it=1 for i in sortDic.values(): #print(i) answer+=i//it sL+= i%it if sL//it>0: answer+=sL//it sL=sL//it it+=1 print(answer) ```
instruction
0
37,875
3
75,750
No
output
1
37,875
3
75,751
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties... Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter e_i — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e or more people. Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him. Input The first line contains the number of independent test cases T(1 ≤ T ≤ 2 ⋅ 10^5). Next 2T lines contain description of test cases. The first line of description of each test case contains the number of young explorers N (1 ≤ N ≤ 2 ⋅ 10^5). The second line contains N integers e_1, e_2, …, e_N (1 ≤ e_i ≤ N), where e_i is the inexperience of the i-th explorer. It's guaranteed that sum of all N doesn't exceed 3 ⋅ 10^5. Output Print T numbers, each number on a separate line. In i-th line print the maximum number of groups Russell can form in i-th test case. Example Input 2 3 1 1 1 5 2 3 1 2 2 Output 3 2 Note In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1, so it's not less than the size of his group. In the second example we can organize two groups. Explorers with inexperience 1, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2 will form the second group. This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group. Submitted Solution: ``` def main(): t=int(input()) while(t>0): solve() t-=1 def solve(): n=int(input()) l=list(map(int,input().strip().split()))[:n] u=len(set(l)) if u==1: print(len(l)) else: print(len(l)-u) main() ```
instruction
0
37,876
3
75,752
No
output
1
37,876
3
75,753
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Two polar bears Menshykov and Uslada from the St.Petersburg zoo and elephant Horace from the Kiev zoo got six sticks to play with and assess the animals' creativity. Menshykov, Uslada and Horace decided to make either an elephant or a bear from those sticks. They can make an animal from sticks in the following way: * Four sticks represent the animal's legs, these sticks should have the same length. * Two remaining sticks represent the animal's head and body. The bear's head stick must be shorter than the body stick. The elephant, however, has a long trunk, so his head stick must be as long as the body stick. Note that there are no limits on the relations between the leg sticks and the head and body sticks. Your task is to find out which animal can be made from the given stick set. The zoo keeper wants the sticks back after the game, so they must never be broken, even bears understand it. Input The single line contains six space-separated integers li (1 ≤ li ≤ 9) — the lengths of the six sticks. It is guaranteed that the input is such that you cannot make both animals from the sticks. Output If you can make a bear from the given set, print string "Bear" (without the quotes). If you can make an elephant, print string "Elephant" (wıthout the quotes). If you can make neither a bear nor an elephant, print string "Alien" (without the quotes). Examples Input 4 2 5 4 4 4 Output Bear Input 4 4 5 4 4 5 Output Elephant Input 1 2 3 4 5 6 Output Alien Note If you're out of creative ideas, see instructions below which show how to make a bear and an elephant in the first two samples. The stick of length 2 is in red, the sticks of length 4 are in green, the sticks of length 5 are in blue. <image> Submitted Solution: ``` arr = list(map(int, input().split())) h = {} for n in arr: if n not in h: h[n] = 1 else: h[n] += 1 k = 4 if len(h)==1: print('Elephant') elif k+1 in h.values(): print('Bear') elif k in h.values(): if len(h)==2: print('Elephant') elif len(h)==3: print('Bear') else: print('Alien') ```
instruction
0
38,057
3
76,114
Yes
output
1
38,057
3
76,115