Problem:


Convex Hull

Find the convex hull of a given set of points P. In other words, find the smallest convex polygon containing all the points of P. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

Please note that you should find all the points of P on both corner and boundary of the convex polygon.

Input

n
x1 y1 
x2 y2
:
xn yn

The first integer n is the number of points in P. The coordinate of the i-th point pi is given by two integers xi and yi. 

Output

In the first line, print the number of points on the corner/boundary of the convex polygon. In the following lines, print x y coordinates of the set of points.
The coordinates should be given in the order of counter-clockwise visit of them starting from the point in P with the minimum y-coordinate, or the leftmost such point in case of a tie.

Constraints

3 ≤ n ≤ 100000

-10000 ≤ xi, yi ≤ 10000

No point in the P will occur more than once.

Sample Input 1

7
2 1
0 0
1 2
2 2
4 2
1 3
3 3

Sample Output 1

5
0 0
2 1
4 2
3 3
1 3

Sample Input 2

4
0 0
2 2
0 2
0 1

Sample Output 2

4
0 0
2 2
0 2
0 1



Sample input:
7
2 1
0 0
1 2
2 2
4 2
1 3
3 3


Sample output:
5
0 0
2 1
4 2
3 3
1 3

Submission status: Accepted

Solution code:
#CGL_4-A Convex Polygon - Convex Hull
def isCLKWISE(ph):
    if (ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0 : return False
    return True
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph):
    if (ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) >= 0 : return True
    return False
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph):
    return (ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) >= 0
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P.sort()
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n : P.append([int(x) for x in input().split()])
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:] :
        phU.append(p)
        while(True) :
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1] :
        phL.append(p)
        while(True) :
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            if len(phU) == 2 : break
            else :
                if isCLKWISE(phU) : break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            if len(phL) == 2 : break
            else :
                if isCLKWISE(phL) : break

                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError:
                break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError:
                break
                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:] :
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1] :
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(y) for y in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = []
    phU.append(P[0])
    phU.append(P[1])
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = []
    phL.append(P[-1])
    phL.append(P[-2])
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True):
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 ph = phU + phL[1:-1]
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True) :
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 ph = phU + phL[1:-1]
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True) :
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 ph = phU + phL[1:-1]
 return ph
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True):
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 ph = phU + phL[1:-1]
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True):
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 del phL[0]
 del phL[-1]
 ph = phU + phL
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = [P[0],P[1]]
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True):
   del phU[-2]
   try:
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = [P[-1],P[-2]]
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 del phL[0]
 del phL[-1]
 ph = phU + phL
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
#sort ??§??????????????????????????????
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True) :
   del phU[-2]
   try :
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 del phL[0]
 del phL[-1]
 ph = phU + phL
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True) :
   del phU[-2]
   try :
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 ph = phU + phL[1:-1]
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
 P = sorted(P)
 phU = []
 phU.append(P[0])
 phU.append(P[1])
 for p in P[2:] :
  phU.append(p)
  if isCLKWISE(phU) : continue
  while(True) :
   del phU[-2]
   try :
    if isCLKWISE(phU) : break
   except IndexError : break
 phL = []
 phL.append(P[-1])
 phL.append(P[-2])
 for p in P[-3::-1] :
  phL.append(p)
  if isCLKWISE(phL) : continue
  while(True) :
   del phL[-2]
   try:
    if isCLKWISE(phL) : break
   except IndexError : break
 del phL[0]
 del phL[-1]
 ph = phU + phL
 return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
P = [[int(x) for x in input().split()] for _ in range(int(input()))]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
for p in P[idx:] + P[:idx] : print(p[0],p[1])

Submission status: Accepted

Solution code:
from functools import reduce
 
 
def cross(a, b):
    return a.real * b.imag - a.imag * b.real
 
 
def graham_scan(points):
    points.sort(key=lambda p: (p.real, p.imag))
    lh = reduce(keep_left, points, [])
    uh = reduce(keep_left, reversed(points), [])
    lh.extend(uh[1:-1])
    return lh
 
 
def keep_left(hull, r):
    if hull:
        prev = hull.pop()
        while hull:
            p = hull[-1]
            if cross(prev - p, r - p) >= 0:
                hull.append(prev)
                break
            prev = hull.pop()
        else:
            hull.append(prev)
    if not hull or hull[-1] != r:
        hull.append(r)
    return hull
 
 
n = int(input())
points = [complex(*map(int, input().split())) for _ in range(n)]
result = graham_scan(points)
lr = len(result)
print(lr)
s = min(range(lr), key=lambda i: (result[i].imag, result[i].real))
for p in (result[s:] + result[:s]):
    print(int(p.real), int(p.imag))