Problem:


Score: 500 points

Problem Statement

Given is a permutation P of \{1, 2, \ldots, N\}.

For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.

Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Constraints

 2 \le N \le 10^5 

 1 \le P_i \le N 

 P_i \neq P_j  (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Sample Input 1

3
2 3 1

Sample Output 1

5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

30

Sample Input 3

8
8 2 7 3 4 5 6 1

Sample Output 3

136



Sample input:
3
2 3 1


Sample output:
5

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
import sys
from bisect import bisect_left, bisect_right
from operator import itemgetter
from fractions import gcd
from math import ceil, floor, sqrt
from copy import deepcopy
from collections import Counter, deque
import heapq
from functools import reduce
sys.setrecursionlimit(200000)
# local only
# if not __debug__:
#     fin = open('in_1.txt', 'r')
#     sys.stdin = fin
# local only
input = sys.stdin.readline
def ii(): return int(input())
def mi(): return map(int, input().rstrip().split())
def lmi(): return list(map(int, input().rstrip().split()))
def li(): return list(input().rstrip())
def debug(*args, sep=" ", end="\n"): print("debug:", *args, file=sys.stderr, sep=sep, end=end) if not __debug__ else None
def exit(*arg): print(*arg); sys.exit()
# template

class Avltree:
    """
    AVL木

    Methods
    -------
        search(x: int) -> Union(int)
            ◯.data == x のものが存在するある場合それを出力、ない場合 None を返す
        insert(x: int) -> None
            ◯.data == x がない場合 ◯.data == x なる頂点を作る。ある場合はなにもしない（上書きしない）
        y.to_s() -> int
            頂点yのdataを返す
        y.left_s() -> Union(int, key=None)
            頂点yのleftを返す(ない場合は key)
        search_lower(x: int, key_lower) -> int
            ○.data が x より小さいものの中で最も大きいものを出力、ない場合 key_lower を返す
        search_higher(x:int , key_higher) -> int
            ○.data が x より大きいものの中で最も小さいものを出力、ない場合 key_higher を返す
    """

    def __init__(self, key=None):
        self.key = key
        self.left = None
        self.right = None
        self.balance = "Even"
    def search(self, key):
        if self.key is None:
            return None
        if self.key > key:
            if self.left is None:
                return None
            else:
                return self.left.search(key)
        if self.key < key:
            if self.right is None:
                return None
            else:
                return self.right.search(key)
        return self  # self.key == keyの場合

    def search_lower(self, key, key_lower):
        if self.key is None:
            return key_lower
        if self.key > key:
            if self.left is None:
                return key_lower
            else:
                return self.left.search_lower(key, key_lower)
        if self.key < key:
            key_lower = self.key
            if self.right is None:
                return key_lower
            else:
                return self.right.search_lower(key, key_lower)
        # self.key == keyの場合
        if self.left is None:
            return key_lower
        else:
            if key_lower is None:
                return self.left.end_higher(self.left.key)
            else:
                return max(key_lower, self.left.end_higher(self.left.key))

    def search_higher(self, key, key_higher):
        if self.key is None:
            return key_higher
        if self.key > key:
            key_higher = self.key
            if self.left is None:
                return key_higher
            else:
                return self.left.search_higher(key, key_higher)
        if self.key < key:
            if self.right is None:
                return key_higher
            else:
                return self.right.search_higher(key, key_higher)
        # self.key == keyの場合
        if self.right is None:
            return key_higher
        else:
            if key_higher is None:
                return self.right.end_lower(self.right.key)
            else:
                return min(key_higher, self.right.end_lower(self.right.key))


    def end_lower(self, end_lower_key):
        if self.left is None:
            return end_lower_key
        else:
            end_lower_key = self.left.key
            return self.left.end_lower(end_lower_key)
    def end_higher(self, end_higher_key):
        if self.right is None:
            return end_higher_key
        else:
            end_higher_key = self.right.key
            return self.right.end_higher(end_higher_key)


    def DoubleRightRotation(self):
        tl = self.left
        self.left = tl.right.right
        tl.right.right = self  # selfはそのノード
        tlr = tl.right
        tl.right = tlr.left
        tlr.left = tl
        if tlr.balance == "Left":
            tlr.right.balance = "Right"
            tlr.left.balance = "Even"
        elif tlr.balance == "Right":
            tlr.right.balance = "Even"
            tlr.left.balance = "Left"
        elif tlr.balance == "Even":
            tlr.right.balance = "Even"
            tlr.left.balance = "Even"
        tlr.balance = "Even"
        return tlr
    def DoubleLeftRotation(self):
        tr = self.right
        self.right = tr.left.left
        tr.left.left = self
        trl = tr.left
        tr.left = trl.right
        trl.right = tr
        if trl.balance == "Right":
            trl.left.balance = "Left"
            trl.right.balance = "Even"
        elif trl.balance == "Left":
            trl.left.balance = "Even"
            trl.right.balance = "Right"
        elif trl.balance == "Even":
            trl.left.balance = "Even"
            trl.right.balance = "Even"
        trl.balance = "Even"
        return trl
    def SingleLeftRotation(self):
        tr = self.right
        tr.balance = "Even"
        self.balance = "Even"
        self.right = tr.left
        tr.left = self
        return tr
    def SingleRightRotation(self):
        tl = self.left
        tl.balance = "Even"
        self.balance = "Even"
        self.left = tl.right
        tl.right = self
        return tl
    def replace(self, p, v):  # 親ノードpの下にある自分(self)をvに置き換える。
        if p.left == self:
            p.left = v
        else:
            p.right = v
    def insert(self, key):  # rootでのみ呼ばれる挿入
        if self.key is None:  # rootを含むrotationはしないことにする。
            self.key = key
            return self
        if key < self.key:
            if self.left is None:
                self.left = Avltree(key)
            else:
                self.left.insertx(self, key)
        elif key > self.key:
            if self.right is None:
                self.right = Avltree(key)
            else:
                self.right.insertx(self, key)
        else:  # key == self.key:
            pass  # do not overwrite
    def insertx(self, p, key):  # replaceを呼ぶために一つ上の親を持っているinsert
        if self.key > key:
            if self.left is None:
                self.left = Avltree(key)
            else:
                if not self.left.insertx(self, key):  # 左の木が生長しなければ、
                    return False  # 成長しない
            if self.balance == "Right":
                self.balance = "Even"
                return False
            elif self.balance == "Even":
                self.balance = "Left"
                return True  # 成長した
            elif self.balance == "Left":
                if self.left.balance == "Right":
                    self.replace(p, self.DoubleRightRotation())
                elif self.left.balance == "Left":
                    self.replace(p, self.SingleRightRotation())
                return False  # rotationを行うと成長しない
        if self.key < key:
            if self.right is None:
                self.right = Avltree(key)
            else:
                if not self.right.insertx(self, key):
                    return False
            if self.balance == "Left":
                self.balance = "Even"
                return False
            elif self.balance == "Even":
                self.balance = "Right"
                return True
            elif self.balance == "Right":
                if self.right.balance == "Left":
                    self.replace(p, self.DoubleLeftRotation())
                elif self.right.balance == "Right":
                    self.replace(p, self.SingleLeftRotation())
                return False
        return False  # self.key == key の時は何もしないので成長もしない

    def to_s(self):
        return self.key
    def left_s(self):
        if self.left is None:
            return None
        return (self.left).key
    def right_s(self):
        if self.right is None:
            return None
        return (self.right).key

"""
Implementation of Red-Black tree.
"""


class RBNode:
    def __init__(self, val, is_red, parent=None, left=None, right=None):
        self.val = val
        self.parent = parent
        self.left = left
        self.right = right
        self.color = is_red


class RBTree:
    def __init__(self):
        self.root = None

    def left_rotate(self, node):
        # set the node as the left child node of the current node's right node
        right_node = node.right
        if right_node is None:
            return
        else:
            # right node's left node become the right node of current node
            node.right = right_node.left
            if right_node.left is not None:
                right_node.left.parent = node
            right_node.parent = node.parent
            # check the parent case
            if node.parent is None:
                self.root = right_node
            elif node is node.parent.left:
                node.parent.left = right_node
            else:
                node.parent.right = right_node
            right_node.left = node
            node.parent = right_node

    def right_rotate(self, node):
        # set the node as the right child node of the current node's left node
        left_node = node.left
        if left_node is None:
            return
        else:
            # left node's right  node become the left node of current node
            node.left = left_node.right
            if left_node.right is not None:
                left_node.right.parent = node
            left_node.parent = node.parent
            # check the parent case
            if node.parent is None:
                self.root = left_node
            elif node is node.parent.left:
                node.parent.left = left_node
            else:
                node.parent.right = left_node
            left_node.right = node
            node.parent = left_node

    def insert(self, node):
        # the inserted node's color is default is red
        root = self.root
        insert_node_parent = None
        # find the position of inserted node
        while root is not None:
            insert_node_parent = root
            if insert_node_parent.val < node.val:
                root = root.right
            else:
                root = root.left
        # set the n ode's parent node
        node.parent = insert_node_parent
        if insert_node_parent is None:
            # case 1  inserted tree is null
            self.root = node
        elif insert_node_parent.val > node.val:
            # case 2 not null and find left or right
            insert_node_parent.left = node
        else:
            insert_node_parent.right = node
        node.left = None
        node.right = None
        node.color = 1
        # fix the tree to
        self.fix_insert(node)

    def fix_insert(self, node):
        # case 1 the parent is null, then set the inserted node as root and color = 0
        if node.parent is None:
            node.color = 0
            self.root = node
            return
            # case 2 the parent color is black, do nothing
        # case 3 the parent color is red
        while node.parent and node.parent.color is 1:
            if node.parent is node.parent.parent.left:
                uncle_node = node.parent.parent.right
                if uncle_node and uncle_node.color is 1:
                    # case 3.1 the uncle node is red
                    # then set parent and uncle color is black and grandparent is red
                    # then node => node.parent
                    node.parent.color = 0
                    node.parent.parent.right.color = 0
                    node.parent.parent.color = 1
                    node = node.parent.parent
                    continue
                elif node is node.parent.right:
                    # case 3.2 the uncle node is black or null, and the node is right of parent
                    # then set his parent node is current node
                    # left rotate the node and continue the next
                    node = node.parent
                    self.left_rotate(node)
                # case 3.3 the uncle node is black and parent node is left
                # then parent node set black and grandparent set red
                node.parent.color = 0
                node.parent.parent.color = 1
                self.right_rotate(node.parent.parent)
            else:
                uncle_node = node.parent.parent.left
                if uncle_node and uncle_node.color is 1:
                    # case 3.1 the uncle node is red
                    # then set parent and uncle color is black and grandparent is red
                    # then node => node.parent
                    node.parent.color = 0
                    node.parent.parent.left.color = 0
                    node.parent.parent.color = 1
                    node = node.parent.parent
                    continue
                elif node is node.parent.left:
                    # case 3.2 the uncle node is black or null, and the node is right of parent
                    # then set his parent node is current node
                    # left rotate the node and continue the next
                    node = node.parent
                    self.right_rotate(node)
                # case 3.3 the uncle node is black and parent node is left
                # then parent node set black and grandparent set red
                node.parent.color = 0
                node.parent.parent.color = 1
                self.left_rotate(node.parent.parent)
        self.root.color = 0

    def transplant(self, node_u, node_v):
        """
        replace u with v
        :param node_u: replaced node
        :param node_v:
        :return: None
        """
        if node_u.parent is None:
            self.root = node_v
        elif node_u is node_u.parent.left:
            node_u.parent.left = node_v
        elif node_u is node_u.parent.right:
            node_u.parent.right = node_v
        # check is node_v is None
        if node_v:
            node_v.parent = node_u.parent

    def find(self, key):
        node = self.root
        while node is not None:
            if node.val < key:
                node = node.right
            elif node.val > key:
                node = node.left
            else:
                return node
        return None

    def maximum(self, node):
        """
        find the max node when node regard as a root node
        :param node:
        :return: max node
        """
        temp_node = node
        while temp_node.right is not None:
            temp_node = temp_node.right
        return temp_node

    def minimum(self, node):
        """
        find the minimum node when node regard as a root node
        :param node:
        :return: minimum node
        """
        temp_node = node
        while temp_node.left:
            temp_node = temp_node.left
        return temp_node

    def search_higher(self, key, key_higher=None, node=None):
        if node is None:
            node = self.root
        if node.val is None:
            return key_higher
        if node.val > key:
            key_higher = node.val
            if node.left is None:
                return key_higher
            else:
                return self.search_higher(key, key_higher, node.left)
        if node.val < key:
            if node.right is None:
                return key_higher
            else:
                return self.search_higher(key, key_higher, node.right)
        # node.val == keyの場合
        if node.right is None:
            return key_higher
        else:
            if key_higher is None:
                return self.minimum(node.right).val
            else:
                return min(key_higher, self.minimum(node.right).val)

    def search_lower(self, key, key_lower=None, node=None):
        if node is None:
            node = self.root
        if node.val is None:
            return key_lower
        if node.val > key:
            if node.left is None:
                return key_lower
            else:
                return self.search_lower(key, key_lower, node.left)
        if node.val < key:
            key_lower = node.val
            if node.right is None:
                return key_lower
            else:
                return self.search_lower(key, key_lower, node.right)
        # node.val == keyの場合
        if node.left is None:
            return key_lower
        else:
            if key_lower is None:
                return self.maximum(node.left).val
            else:
                return max(key_lower, self.maximum(node.left).val)

    def delete(self, node):
        # find the node position
        node_color = node.color
        if node.left is None:
            temp_node = node.right
            self.transplant(node, node.right)
        elif node.right is None:
            temp_node = node.left
            self.transplant(node, node.left)
        else:
            # both child exits ,and find minimum child of right child
            node_min = self.minimum(node.right)
            node_color = node_min.color
            temp_node = node_min.right
            ##
            if node_min.parent != node:
                self.transplant(node_min, node_min.right)
                node_min.right = node.right
                node_min.right.parent = node_min
            self.transplant(node, node_min)
            node_min.left = node.left
            node_min.left.parent = node_min
            node_min.color = node.color
        # when node is black, then need to fix it with 4 cases
        if node_color == 0:
            self.delete_fixup(temp_node)

    def delete_fixup(self, node):
        # 4 cases
        while node != self.root and node.color == 0:
            # node is not root and color is black
            if node == node.parent.left:
                # node is left node
                node_brother = node.parent.right

                # case 1: node's red, can not get black node
                # set brother is black and parent is red
                if node_brother.color == 1:
                    node_brother.color = 0
                    node.parent.color = 1
                    self.left_rotate(node.parent)
                    node_brother = node.parent.right

                # case 2: brother node is black, and its children node is both black
                if (node_brother.left is None or node_brother.left.color == 0) and (
                        node_brother.right is None or node_brother.right.color == 0):
                    node_brother.color = 1
                    node = node.parent
                else:

                    # case 3: brother node is black , and its left child node is red and right is black
                    if node_brother.right is None or node_brother.right.color == 0:
                        node_brother.color = 1
                        node_brother.left.color = 0
                        self.right_rotate(node_brother)
                        node_brother = node.parent.right

                    # case 4: brother node is black, and right is red, and left is any color
                    node_brother.color = node.parent.color
                    node.parent.color = 0
                    node_brother.right.color = 0
                    self.left_rotate(node.parent)
                node = self.root
                break
            else:
                node_brother = node.parent.left
                if node_brother.color == 1:
                    node_brother.color = 0
                    node.parent.color = 1
                    self.left_rotate(node.parent)
                    node_brother = node.parent.right
                if (node_brother.left is None or node_brother.left.color == 0) and (
                        node_brother.right is None or node_brother.right.color == 0):
                    node_brother.color = 1
                    node = node.parent
                else:
                    if node_brother.left is None or node_brother.left.color == 0:
                        node_brother.color = 1
                        node_brother.right.color = 0
                        self.left_rotate(node_brother)
                        node_brother = node.parent.left
                    node_brother.color = node.parent.color
                    node.parent.color = 0
                    node_brother.left.color = 0
                    self.right_rotate(node.parent)
                node = self.root
                break
        node.color = 0

    def inorder(self):
        res = []
        if not self.root:
            return res
        stack = []
        root = self.root
        stack.append(root)
        while stack:
            root = stack.pop()
            res.append({'val': root.val, 'color': root.color})
            if root.left:
                stack.append(root.left)
            if root.right:
                stack.append(root.right)
        # while root or stack:
        #     while root:
        #         stack.append(root)
        #         root = root.left
        #     root = stack.pop()
        #     res.append({'val': root.val, 'color': root.color})
        #     root = root.right
        return res



def main():
    N = ii()
    P = lmi()
    L = []
    for i in range(N):
        L.append((P[i], i))
    L.sort(key=itemgetter(0), reverse=True)
    # print(L)
    ans = 0
    rb = RBTree()
    for x, i in L:
        rb.insert(RBNode(i, 1))
        l1 = rb.search_lower(i, -1)
        l2 = rb.search_lower(l1, -1)
        r1 = rb.search_higher(i, N)
        r2 = rb.search_higher(r1, N)
        # print(l2, l1, r1, r2)
        ans += (abs(i - l1) * abs(r2 - r1) + abs(l1 - l2) * abs(r1 - i)) * x
    print(ans)
    # rb = Avltree()
    # for x, i in L:
    #     rb.insert(i)
    #     l1 = rb.search_lower(i, -1)
    #     l2 = rb.search_lower(l1, -1)
    #     r1 = rb.search_higher(i, N)
    #     r2 = rb.search_higher(r1, N)
    #     print(l2, l1, r1, r2)
    #     ans += (abs(i - l1) * abs(r2 - r1) + abs(l1 - l2) * abs(r1 - i)) * x
    return



if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
n=int(input())
a=list(map(int,input().split()))[::-1]



result=0

for i in range(n-1):
  maxV=max(a[i],a[i+1])
  temp=min(a[i],a[i+1])
  result+=temp
  for j in range(i+2,n):
    if temp>a[j]:
      result+=temp
      #print(i,j)
    else:
      if a[j]>maxV:
        temp=maxV
        result+=temp
        maxV=a[j]
      else:
        temp=a[j]
        result+=temp
    #print(i,j,temp)
        

  
print(result)

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
P = list(map(int, input().split()))

score = 0
for l in range(1, N):
  for r in range(l+1, N+1):
    new_list = sorted(P[l-1:r], reverse=True)
    score += new_list[1]
print(score)

Submission status: Time Limit Exceeded

Solution code:
import sys
from bisect import *

input=sys.stdin.readline

def main():
    n = int(input()[:-1])
    aa = list(map(int, input().split()))
    ans = 0
    pos = [0] * n
    for i, a in enumerate(aa):
        pos[a - 1] = i
    # print(pos)
    fin = [-1, -1, n, n]
    for a in range(n - 1, -1, -1):
        i = pos[a]
        insort(fin,i)
        j = bisect_left(fin, i)
        ans += (a + 1) * ((fin[j - 1] - fin[j - 2]) * (fin[j + 1] - fin[j])
                          + (fin[j] - fin[j - 1]) * (fin[j + 2] - fin[j + 1]))
        # print(a, ans, fin)
    print(ans)

main()