Problem:
 Score : 1000 points    Problem Statement You are given a sequence a = \{a_1, ..., a_N\} with all zeros, and a sequence b = \{b_1, ..., b_N\} consisting of 0 and 1 . The length of both is N .  You can perform Q kinds of operations. The i -th operation is as follows:   Replace each of a_{l_i}, a_{l_i + 1}, ..., a_{r_i} with 1 .   Minimize the hamming distance between a and b , that is, the number of i such that a_i \neq b_i , by performing some of the Q operations.      Constraints  1 \leq N \leq 200,000  b consists of 0 and 1 .  1 \leq Q \leq 200,000  1 \leq l_i \leq r_i \leq N  If i \neq j , either l_i \neq l_j or r_i \neq r_j .         Input Input is given from Standard Input in the following format:  N  b_1  b_2  ...  b_N  Q  l_1  r_1  l_2  r_2  :  l_Q  r_Q       Output Print the minimum possible hamming distance.        Sample Input 1 3
1 0 1
1
1 3      Sample Output 1 1  If you choose to perform the operation, a will become \{1, 1, 1\} , for a hamming distance of 1 .       Sample Input 2 3
1 0 1
2
1 1
3 3      Sample Output 2 0  If both operations are performed, a will become \{1, 0, 1\} , for a hamming distance of 0 .       Sample Input 3 3
1 0 1
2
1 1
2 3      Sample Output 3 1       Sample Input 4 5
0 1 0 1 0
1
1 5      Sample Output 4 2  It may be optimal to perform no operation.       Sample Input 5 9
0 1 0 1 1 1 0 1 0
3
1 4
5 8
6 7      Sample Output 5 3       Sample Input 6 15
1 1 0 0 0 0 0 0 1 0 1 1 1 0 0
9
4 10
13 14
1 7
4 14
9 11
2 6
7 8
3 12
7 13      Sample Output 6 5       Sample Input 7 10
0 0 0 1 0 0 1 1 1 0
7
1 4
2 5
1 3
6 7
9 9
1 5
7 9      Sample Output 7 1

Solution (Python):
import sys

input=sys.stdin.readline

n=int(input())
b=list(map(int,input().split()))
ope=[[] for i in range(n)]
Q=int(input())
for i in range(Q):
    l,r=map(int,input().split())
    ope[r-1].append(l-1)

res=b.count(0)

Data=[(-1)**((b[i]==1)+1) for i in range(n)]
for i in range(1,n):
    Data[i]+=Data[i-1]
Data=[0]+Data

for i in range(n):
    ope[i].sort(reverse=True)


N=n+1
N0 = 2**(N-1).bit_length()
data = [None]*(2*N0)
INF = (-2**31, -2**31)


def update(l, r, v):
    L = l + N0; R = r + N0
    while L < R:
        if R & 1:
            R -= 1
            if data[R-1]:
                data[R-1] = max(v,data[R-1])
            else:
                data[R-1]=v

        if L & 1:
            if data[L-1]:
                data[L-1] = max(v,data[L-1])
            else:
                data[L-1]=v
            L += 1
        L >>= 1; R >>= 1

def _query(k):
    k += N0-1
    s = INF
    while k >= 0:
        if data[k]:
            s = max(s, data[k])
        k = (k - 1) // 2
    return s

def query(k):
    return _query(k)[1]

for i in range(n+1):
    update(i,i+1,(-Data[i],-Data[i]))
if ope[0]:
    update(1,2,(0,0))

for i in range(1,n):
    val=query(i)
    update(i+1,i+2,(val+Data[i]-Data[i+1],val+Data[i]-Data[i+1]))
    for l in ope[i]:
        val=query(l)
        update(l+1,i+2,(val,val))



print(n-(res+query(n)+Data[n]))

Solution (Python):
n=int(input())
b=list(map(int,input().split()))
ope=[[] for i in range(n)]
Q=int(input())
for i in range(Q):
    l,r=map(int,input().split())
    ope[r-1].append(l-1)

res=b.count(0)

Data=[(-1)**((b[i]==1)+1) for i in range(n)]
for i in range(1,n):
    Data[i]+=Data[i-1]
Data=[0]+Data

for i in range(n):
    ope[i].sort(reverse=True)


N=n+1
N0 = 2**(N-1).bit_length()
data = [None]*(2*N0)
INF = (-2**31, -2**31)


def update(l, r, v):
    L = l + N0; R = r + N0
    while L < R:
        if R & 1:
            R -= 1
            if data[R-1]:
                data[R-1] = max(v,data[R-1])
            else:
                data[R-1]=v

        if L & 1:
            if data[L-1]:
                data[L-1] = max(v,data[L-1])
            else:
                data[L-1]=v
            L += 1
        L >>= 1; R >>= 1

def _query(k):
    k += N0-1
    s = INF
    while k >= 0:
        if data[k]:
            s = max(s, data[k])
        k = (k - 1) // 2
    return s

def query(k):
    return _query(k)[1]

for i in range(n+1):
    update(i,i+1,(-Data[i],-Data[i]))
if ope[0]:
    update(1,2,(0,0))

for i in range(1,n):
    val=query(i)
    update(i+1,i+2,(val+Data[i]-Data[i+1],val+Data[i]-Data[i+1]))
    for l in ope[i]:
        val=query(l)
        update(l+1,i+2,(val,val))



print(n-(res+query(n)+Data[n]))

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N = int(readline())
B = list(map(int,readline().split()))
Q = int(readline())
m = map(int,read().split())
LR = sorted(zip(m,m))

class MaxSegTree():
    def __init__(self,raw_data):
        N = len(raw_data)
        self.size = 1<<(N.bit_length()) 
        self.data = [0] * (2*self.size)
        self.build(raw_data)
        
    def build(self,raw_data):
        for i,x in enumerate(raw_data):
            self.data[self.size+i] = x
        for i in range(self.size-1,0,-1):
            x = self.data[i+i]; y = self.data[i+i+1]
            self.data[i] = x if x>y else y
    
    def update(self,i,x):
        i += self.size
        self.data[i] = x
        i >>= 1
        while i:
            x = self.data[i+i]; y = self.data[i+i+1]
            self.data[i] = x if x>y else y
            i >>= 1
    
    def get_data(self,i):
        return self.data[i+self.size]

    def get_max(self,L,R):
        
        L += self.size
        R += self.size + 1
        
        x = 0
        while L < R:
            if L&1:
                y = self.data[L]
                if x < y: x = y
                L += 1
                
            if R&1:
                R -= 1
                y = self.data[R]
                if x < y: x = y
            L >>= 1; R >>= 1
        return x

"""
・あるから先を全て0で埋めた場合
・あるから先を全て1で埋めた場合
"""
add1 = [0] * (N+1)
add1[0] = sum(B)
for i,x in enumerate(B,1):
    if x:
        add1[i] = add1[i-1] - 1
    else:
        add1[i] = add1[i-1]
add0 = [N - i - x for i,x in enumerate(add1)]

add0,add1


dp0 = MaxSegTree([0] * (N+1))
dp1 = MaxSegTree([0] * (N+1))
dp0.update(0,add0[0])
dp1.update(0,add1[0])

for L,R in LR:
    a = dp1.get_data(R)
    b = dp0.get_max(0,L-1) + add1[L-1] - add0[L-1]
    c = dp1.get_max(L,R-1)
    if b < c:
        b = c
    if a < b:
        dp1.update(R, b)
        dp0.update(R, b - add1[R] + add0[R])

answer = N - dp0.get_max(0,N)
print(answer)

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N = int(readline())
B = list(map(int,readline().split()))
Q = int(readline())
m = map(int,read().split())
LR = sorted(zip(m,m))

class MaxSegTree():
    def __init__(self,N):
        self.Nelem = N
        self.size = 1<<(N.bit_length()) 
        self.data = [0] * (2*self.size)
        
    def build(self,raw_data):
        
        for i,x in enumerate(raw_data):
            self.data[self.size+i] = x
        for i in range(self.size-1,0,-1):
            x = self.data[i+i]; y = self.data[i+i+1]
            self.data[i] = x if x>y else y
    
    def update(self,i,x):
        i += self.size
        self.data[i] = x
        i >>= 1
        while i:
            x = self.data[i+i]; y = self.data[i+i+1]
            self.data[i] = x if x>y else y
            i >>= 1
    
    def get_data(self,i):
        return self.data[i+self.size]

    def get_max(self,L,R):
        
        L += self.size
        R += self.size + 1
        
        x = 0
        while L < R:
            if L&1:
                y = self.data[L]
                if x < y: x = y
                L += 1
                
            if R&1:
                R -= 1
                y = self.data[R]
                if x < y: x = y
            L >>= 1; R >>= 1
        return x

"""
・ある場所まで確定して、そこから先を全て1で埋めた場合
・ある場所まで確定して、そこから先を全て0で埋めた場合
の加算スコア
"""
add0 = [0] * (N+1)
add1 = [0] * (N+1)
x = sum(B)
add1[0] = x
add0[0] = N-x
for i,x in enumerate(B,1):
    if x == 0:
        add0[i]=add0[i-1]-1; add1[i] = add1[i-1]
    else:
        add1[i]=add1[i-1]-1; add0[i] = add0[i-1]

"""
ある場所を右端としてとった時点での
・残りをすべて0で埋めたときのスコア
・残りをすべて1で埋めたときのスコア
dp0, dp1 をseg木で管理
"""

dp0 = MaxSegTree(N+1)
dp0.build([add0[0]] + [0] * N)
dp1 = MaxSegTree(N+1)
dp1.build([add1[0]] + [0] * N)

for L,R in LR:
    
    x = dp1.get_data(R)
    y = dp0.get_max(0,L-1) + add1[L-1] - add0[L-1] 
    z = dp1.get_max(L,R-1) 
    if y < z: y = z
    if x < y:
        dp1.update(R,y)
        dp0.update(R,y - add1[R] + add0[R])


answer = N - dp0.data[1]
print(answer)