Every Sublist Min Sum- Google Top Interview Questions


Problem Statement :


You are given a list of integers nums. 
Return the sum of min(x) for every sublist x in nums. 
Mod the result by 10 ** 9 + 7.

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [1, 2, 4, 3]

Output

20

Explanation

We have the following sublists and their mins:


min([1]) = 1

min([1, 2]) = 1

min([1, 2, 4]) = 1

min([1, 2, 4, 3]) = 1

min([2]) = 2

min([2, 4]) = 2

min([2, 4, 3]) = 2

min([4]) = 4

min([4, 3]) = 3

min([3]) = 3



Solution :



title-img




                        Solution in C++ :

int solve(vector<int>& nums) {
    int n = nums.size();
    int pref[n + 1] = {};
    stack<int> s;  // Initialising prefix  array and stack
    int ans = 0, j = 0, mod = 1e9 + 7;
    for (int i = 0; i < n; i++) {
        while (!s.empty() && nums[s.top()] >= nums[i])
            s.pop();  // iterating back till we find an index where the minimum of the list if we go
                      // any further left will change

        if (s.empty())
            j = -1;  // we are calculating j just for calculating the count for which nums[i] will
                     // appear  as minimum in the sublist we have created by going left
        else
            j = s.top();
        s.push(i);

        pref[i + 1] = (pref[j + 1] + (i - j) * nums[i]) %
                      mod;  // here maintaining prefix array--Read the implementation part
        ans = (ans + pref[i + 1]) % mod;
    }
    return ans;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[] nums) {
        int n = nums.length;
        int[] next_smaller = new int[n];
        int[] prev_smaller = new int[n];
        Arrays.fill(next_smaller, n);
        Arrays.fill(prev_smaller, -1);

        // compute and fill in the next_smaller
        Stack<Integer> stack = new Stack();
        for (int i = 0; i < n; i++) {
            int cur = nums[i];
            while (stack.size() > 0 && cur < nums[stack.peek()]) {
                next_smaller[stack.pop()] = i;
            }
            stack.push(i);
        }
        // compute and fill in the prev_smaller
        stack = new Stack();
        for (int i = 0; i < n; i++) {
            int cur = nums[i];
            while (stack.size() > 0 && nums[stack.peek()] > cur) {
                stack.pop();
            }
            if (stack.size() > 0)
                prev_smaller[i] = stack.peek();
            stack.push(i);
        }

        // compute the answer
        long res = 0;
        long mod = (long) 1e9 + 7;
        for (int i = 0; i < n; i++) {
            int subarray_min = nums[i];

            int left_count = i - prev_smaller[i]; // number of greater elements on the left
            int right_count =
                next_smaller[i] - i; // number of greater than or equal to  elements on right
            res = res + (subarray_min * (left_count * right_count)) % mod;
            res = res % mod;
        }
        return (int) res;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):
        ans = 0
        s = []  # stack of (index, value, sum)
        currentSum = 0
        for index, value in enumerate(nums):
            while s and value <= s[-1][1]:
                currentSum -= s[-1][2]
                s.pop()
            if not s:
                s.append([index, value, (index + 1) * value])
            else:
                s.append([index, value, (index - s[-1][0]) * value])
            currentSum += s[-1][2]
            ans += currentSum
        return ans % (10 ** 9 + 7)
                    


View More Similar Problems

Kundu and Tree

Kundu is true tree lover. Tree is a connected graph having N vertices and N-1 edges. Today when he got a tree, he colored each edge with one of either red(r) or black(b) color. He is interested in knowing how many triplets(a,b,c) of vertices are there , such that, there is atleast one edge having red color on all the three paths i.e. from vertex a to b, vertex b to c and vertex c to a . Note that

View Solution →

Super Maximum Cost Queries

Victoria has a tree, T , consisting of N nodes numbered from 1 to N. Each edge from node Ui to Vi in tree T has an integer weight, Wi. Let's define the cost, C, of a path from some node X to some other node Y as the maximum weight ( W ) for any edge in the unique path from node X to Y node . Victoria wants your help processing Q queries on tree T, where each query contains 2 integers, L and

View Solution →

Contacts

We're going to make our own Contacts application! The application must perform two types of operations: 1 . add name, where name is a string denoting a contact name. This must store name as a new contact in the application. find partial, where partial is a string denoting a partial name to search the application for. It must count the number of contacts starting partial with and print the co

View Solution →

No Prefix Set

There is a given list of strings where each string contains only lowercase letters from a - j, inclusive. The set of strings is said to be a GOOD SET if no string is a prefix of another string. In this case, print GOOD SET. Otherwise, print BAD SET on the first line followed by the string being checked. Note If two strings are identical, they are prefixes of each other. Function Descriptio

View Solution →

Cube Summation

You are given a 3-D Matrix in which each block contains 0 initially. The first block is defined by the coordinate (1,1,1) and the last block is defined by the coordinate (N,N,N). There are two types of queries. UPDATE x y z W updates the value of block (x,y,z) to W. QUERY x1 y1 z1 x2 y2 z2 calculates the sum of the value of blocks whose x coordinate is between x1 and x2 (inclusive), y coor

View Solution →

Direct Connections

Enter-View ( EV ) is a linear, street-like country. By linear, we mean all the cities of the country are placed on a single straight line - the x -axis. Thus every city's position can be defined by a single coordinate, xi, the distance from the left borderline of the country. You can treat all cities as single points. Unfortunately, the dictator of telecommunication of EV (Mr. S. Treat Jr.) do

View Solution →