Problem: There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x\- or y\- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:    * If d_i = `R`, the i-th point moves in the positive x direction;   * If d_i = `L`, the i-th point moves in the negative x direction;   * If d_i = `U`, the i-th point moves in the positive y direction;   * If d_i = `D`, the i-th point moves in the negative y direction.  You can stop all the points at some moment of your choice after they start moving (including the moment they start moving). Then, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.  Find the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}) and print it.

Submission attempts (in order):
import sys
input = sys.stdin.readline

N = int(input())
ptss = [[] for _ in range(4)]
convs = dict(zip('LRUD', range(4)))
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    ptss[convs[d]].append((x, y, d))

pts = []
for pt2s in ptss:
    if not pt2s: continue
    pt2s.sort(key=lambda x: x[0])
    pts.append(pt2s[0])
    pts.append(pt2s[-1])
    pt2s.sort(key=lambda x: x[1])
    pts.append(pt2s[0])
    pts.append(pt2s[-1])

def getDiffX(t):
    xs = []
    for x, _, d in pts:
        if d == 'L':
            x -= t
        elif d == 'R':
            x += t
        xs.append(x)
    return max(xs) - min(xs)

def getDiffY(t):
    ys = []
    for _, y, d in pts:
        if d == 'U':
            y += t
        elif d == 'D':
            y -= t
        ys.append(y)
    return max(ys) - min(ys)

def ternarySearchDesc(f):
    L, R = 0, 10**9
    while R-L > 10**-9:
        x1, x2 = (2*L+R)/3, (2*R+L)/3
        f1, f2 = f(x1), f(x2)
        if f1 <= f2:
            R = x2
        else:
            L = x1
    return L

def ternarySearchAsc(f):
    L, R = 0, 10**9
    while R-L > 10**-9:
        x1, x2 = (2*L+R)/3, (2*R+L)/3
        f1, f2 = f(x1), f(x2)
        if f1 < f2:
            R = x2
        else:
            L = x1
    return L

ts = [ternarySearchDesc(getDiffX), ternarySearchAsc(getDiffX), ternarySearchDesc(getDiffY), ternarySearchAsc(getDiffY)]

scores = []
for t in ts:
    diffX = getDiffX(t)
    diffY = getDiffY(t)
    scores.append(diffX * diffY)

print(min(scores))


import sys
input = sys.stdin.readline

N = int(input())
ptss = [[] for _ in range(4)]
convs = dict(zip('LRUD', range(4)))
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    ptss[convs[d]].append((x, y, d))

pts = []
for pt2s in ptss:
    if not pt2s: continue
    pt2s.sort(key=lambda x: x[0])
    pts.append(pt2s[0])
    pts.append(pt2s[-1])
    pt2s.sort(key=lambda x: x[1])
    pts.append(pt2s[0])
    pts.append(pt2s[-1])

def getDiffX(t):
    xs = []
    for x, _, d in pts:
        if d == 'L':
            x -= t
        elif d == 'R':
            x += t
        xs.append(x)
    return max(xs) - min(xs)

def getDiffY(t):
    ys = []
    for _, y, d in pts:
        if d == 'U':
            y += t
        elif d == 'D':
            y -= t
        ys.append(y)
    return max(ys) - min(ys)

def ternarySearchDesc(f):
    L, R = 0, 10**12
    while R-L > 10**-12:
        x1, x2 = (2*L+R)/3, (2*R+L)/3
        f1, f2 = f(x1), f(x2)
        if f1 <= f2:
            R = x2
        else:
            L = x1
    return L

def ternarySearchAsc(f):
    L, R = 0, 10**12
    while R-L > 10**-12:
        x1, x2 = (2*L+R)/3, (2*R+L)/3
        f1, f2 = f(x1), f(x2)
        if f1 < f2:
            R = x2
        else:
            L = x1
    return L

ts = [ternarySearchDesc(getDiffX), ternarySearchAsc(getDiffX), ternarySearchDesc(getDiffY), ternarySearchAsc(getDiffY)]

scores = []
for t in ts:
    diffX = getDiffX(t)
    diffY = getDiffY(t)
    scores.append(diffX * diffY)

print(min(scores))


INF = float('inf')

N = int(input())

xConstMin, xConstMax = INF, -INF
xAscMin, xAscMax = INF, -INF
xDescMin, xDescMax = INF, -INF
yConstMin, yConstMax = INF, -INF
yAscMin, yAscMax = INF, -INF
yDescMin, yDescMax = INF, -INF
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    if d == 'R':
        xAscMax = max(xAscMax, x)
        xAscMin = min(xAscMin, x)
        yConstMax = max(yConstMax, y)
        yConstMin = min(yConstMin, y)
    elif d == 'L':
        xDescMax = max(xDescMax, x)
        xDescMin = min(xDescMin, x)
        yConstMax = max(yConstMax, y)
        yConstMin = min(yConstMin, y)
    elif d == 'U':
        xConstMax = max(xConstMax, x)
        xConstMin = min(xConstMin, x)
        yAscMax = max(yAscMax, y)
        yAscMin = min(yAscMin, y)
    elif d == 'D':
        xConstMax = max(xConstMax, x)
        xConstMin = min(xConstMin, x)
        yDescMax = max(yDescMax, y)
        yDescMin = min(yDescMin, y)

tms = []

t1 = max(0, xDescMax - xConstMax)
t2 = max(0, xConstMax - xAscMax)
if t1 >= t2:
    t = max(0, (xDescMax-xAscMax)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, xConstMin - xAscMin)
t2 = max(0, xDescMin - xConstMin)
if t1 >= t2:
    t = max(0, (xDescMin-xAscMin)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, yDescMax - yConstMax)
t2 = max(0, yConstMax - yAscMax)
if t1 >= t2:
    t = max(0, (yDescMax-yAscMax)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

t1 = max(0, yConstMin - yAscMin)
t2 = max(0, yDescMin - yConstMin)
if t1 >= t2:
    t = max(0, (yDescMin-yAscMin)/2)
    tms.append(t)
else:
    tms.append(t1)
    tms.append(t2)

ans = INF
for tm in tms:
    if tm == INF: continue

    xs = [xConstMin, xConstMax, xAscMin+tm, xAscMax+tm, xDescMin-tm, xDescMax-tm]
    ys = [yConstMin, yConstMax, yAscMin+tm, yAscMax+tm, yDescMin-tm, yDescMax-tm]

    xMin, xMax = INF, -INF
    for x in xs:
        if x == INF or x == -INF: continue
        xMin = min(xMin, x)
        xMax = max(xMax, x)

    yMin, yMax = INF, -INF
    for y in ys:
        if y == INF or y == -INF: continue
        yMin = min(yMin, y)
        yMax = max(yMax, y)

    ans = min(ans, (xMax-xMin)*(yMax-yMin))

print(ans)


Verdicts: Wrong Answer

Wrong Answer

Accepted