Minimum Value to Get Positive Step by Step Sum

class Solution {
public:
    int minInitialValue(vector<int>& numbers) {
        int leastTotal = 0;
        int cumulativeSum = 0;
        
        for (int value : numbers) {
            cumulativeSum += value;
            leastTotal = min(leastTotal, cumulativeSum);
        }
        
        return -leastTotal + 1;
    }
};

The provided C++ solution addresses the problem of finding the minimum initial value such that the cumulative sum of an array remains positive when incremented step by step. Here’s an outline of how the solution efficiently solves the problem:

• A function named minInitialValue is defined, which receives a vector of integers numbers.
• Two integer variables, leastTotal and cumulativeSum, are initialized to zero. These variables track the minimum sum encountered during the sequence and the ongoing cumulative sum, respectively.
• The function iterates through each element in the numbers vector, updating the cumulativeSum with the current value and subsequently adjusting leastTotal to capture the lesser of its current value or the new cumulativeSum.
• The smallest starting value required to keep the cumulative sum positive throughout the sequence is calculated by returning the negation of leastTotal plus one. This effectively ensures that even with the lowest cumulative sum, by starting at this value, all subsequent sums remain non-negative.
• The core operation of finding the minimum in each step ensures efficiency, handling each number in the array only once, resulting in a linear time complexity relative to the size of the input.

This approach leverages straightforward logic and efficient iteration to accurately determine the minimum value needed for the desired condition.

class Solution {
    public int minimumStartValue(int[] values) {
        int leastTotal = 0;
        int cumulativeTotal = 0;

        for (int value : values) {
            cumulativeTotal += value;
            leastTotal = Math.min(leastTotal, cumulativeTotal);
        }

        return -leastTotal + 1;
    }
}

The solution you provided in Java addresses the problem of finding the minimum initial value that can be added to a series of integer steps (given in the array values), such that the running total never drops below 1. Here's a concise walkthrough of how the code achieves this:

• Define two integer variables, leastTotal to track the minimum cumulative total encountered, and cumulativeTotal to store the running total as you iterate through the array.
• Traverse the values array using a for-each loop. For each element, add it to cumulativeTotal.
• Update leastTotal with the lesser value between the current leastTotal and cumulativeTotal after each addition.
• Finally, calculate the required minimum start value by negating leastTotal and adding 1. This adjustment ensures the step-by-step sum remains positive.

To summarize, by iterating through the array and continuously updating the running total and its minimum value, the code calculates how much deficit has been accumulated. It then returns the value needed to offset this deficit, thus ensuring all cumulative sums remain positive when this start value is added.

var calculateMinStartValue = function(elements) {
    var minValue = 0;
    var sum = 0;

    for (var index = 0; index < elements.length; ++index) {
        sum += elements[index];
        minValue = Math.min(minValue, sum);
    }

    return -minValue + 1;
};

This solution tackles the problem of finding the minimum initial value such that the step-by-step sum of elements in an array remains positive. The function calculateMinStartValue utilizes an array called elements.

• Initialize minValue to 0 to store the minimum sum obtained during the iteration.
• Initialize sum to 0 to calculate the ongoing sum of the array elements.

The function iterates through the elements array:

1. For each element, add its value to sum.
2. Update minValue to be the lesser of its current value or sum.

After completing the iteration over the array, the function determines the minimum starting value needed:

• It calculates this by negating minValue and adding 1.

This calculation ensures that when starting with the computed initial value, the sum of the array when added incrementally from this initial value will always remain positive. This approach effectively utilizes a straightforward iteration and basic arithmetic to solve the problem efficiently.