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Suppose we have an array called stones where stones[i] represents the value of the ith stone from the left. Two friends Amal and Bimal are playing a turn-based game with these stones and Amal starts first always. There are n stones arranged in a row. Each player can remove either the leftmost stone or the rightmost stone from the row and get points equal to the sum of the remaining stones' values in the row. The player with the higher score wins. Bimal found that he will always lose this game, so he decided to minimize the score's difference. ... Read More
Suppose we have a number n, we have to check whether it is possible to represent n as the sum of distinct powers of three or not. An integer y is said to be power of three if there exists an integer x such that y = 3^x. So, if the input is like n = 117, then the output will be True because 117 = 3^4 + 3^3 + 3^2 = 81 + 27 + 9. Algorithm To solve this, we will follow these steps ? for i in range 16 to 0, decrease ... Read More
Given a decimal number as a string, we need to find the minimum number of deci-binary numbers whose sum equals the given number. A deci-binary number contains only digits 0 and 1. For example, if the input is "132", the output will be 3 because 132 can be expressed as the sum of three deci-binary numbers: 100 + 11 + 21 = 132. Algorithm The key insight is that the minimum number of deci-binary numbers needed equals the maximum digit in the input number. This is because: Each deci-binary number can contribute at most 1 ... Read More
Suppose Amal and Bimal are playing a stone game where Amal goes first. The game works as follows − There are n stones in a pile. Each player can take a stone and receive points based on their individual valuation of that stone. We have two arrays A_Values and B_Values where A_Values[i] and B_Values[i] represent how Amal and Bimal value the ith stone respectively. The player with the highest total score wins. If scores are equal, it's a draw. Both players play optimally and know each other's valuations. Return 1 if Amal wins, -1 if Bimal wins, and ... Read More
A ramp in an array is a pair of indices (i, j) where i < j and nums[i] ≤ nums[j]. The width of a ramp is the difference (j - i). We need to find the maximum width ramp in the given array. For example, in the array [6, 0, 8, 2, 1, 5], the maximum width ramp is at indices (1, 5) where nums[1] = 0 and nums[5] = 5, giving us a width of 4. Approach The solution uses a value-to-indices mapping approach ? Group indices by their values in a dictionary Process ... Read More
Given a sorted array in non-decreasing order, we need to create a result array where each element contains the sum of absolute differences between that element and all other elements in the array. For example, with nums = [5, 7, 12], the result will be [9, 7, 12] because: |5−5| + |5−7| + |5−12| = 0+2+7 = 9 |7−5| + |7−7| + |7−12| = 2+0+5 = 7 |12−5| + |12−7| + |12−12| = 7+5+0 = 12 Naive Approach The straightforward approach calculates absolute differences for each element ? def solve_naive(nums): ... Read More
We are given two arrays nums1 and nums2 with values between 1 and 6 (inclusive). In one operation, we can update any value in either array to any value between 1 and 6. Our goal is to find the minimum number of operations needed to make the sum of values in nums1 equal to the sum of values in nums2. So, if the input is like nums1 = [1, 5, 6], nums2 = [4, 1, 1], then the output will be 2 because we can change nums2 from [4, 1, 1] to [4, 1, 6] in first operation, and ... Read More
When working with binary representations, we often need to concatenate binary strings of consecutive numbers. This problem asks us to find the decimal value of a binary string formed by concatenating binary representations of numbers from 1 to n. So, if the input is like n = 4, then the output will be 220 because concatenating binary representations from 1 to 4 gives us "1" + "10" + "11" + "100" = "1101111100", which equals 220 in decimal. Algorithm Steps To solve this problem, we follow these steps − Initialize ans := 1 (binary representation ... Read More
In Python, we can solve the closest dessert cost problem by systematically exploring all possible combinations of bases and toppings. Given arrays of baseCosts and toppingCosts with a target value, we need to find the dessert cost closest to the target. Problem Rules There must be exactly one base We can add zero, one, or more toppings At most two of each type of topping can be used If multiple costs are equally close to target, return the lower one Algorithm Approach We use a bitmask approach to represent topping combinations. Each position in ... Read More
Suppose we have an array called nums and another value k. In one operation, we can select two elements from nums whose sum equals k and remove them from the array. We have to find the maximum number of operations we can perform on the array. So, if the input is like nums = [8, 3, 6, 1, 5] and k = 9, then the output will be 2 as we can delete [3, 6] whose sum is 9, then remove [8, 1] whose sum is also 9. Algorithm To solve this, we will follow these steps: ... Read More