/**
 * Max Sub Sum
 * CS 2240
 * University of Vermont
 * Lisa Dion
 * 2019-???-??
 *
 * Clayton Cafiero
 * 2020-Jun-25
 * Revisions:
 *   - Avoid use of using namespace std; but leave note that safe in context
 *   - Include Kadane's algorithm
 *   - Add step counter and revise each algorithm to count steps
 *   - Display answer and number of steps taken
 *   - Make use of random number generation to create array for testing
 *   - Additional comments
 *   - Minor changes to formatting
 */

#include <iostream>
#include <vector>
#include "randi.h"

#define SIZE 1000
#define RANGE 20

int steps;

/**
 * Brute force, O(n^3)
 * @param a
 * @return
 */
int maxSubSum1(const std::vector<int> &a) {
    int maxSum = 0;
    for (int i = 0; i < a.size(); ++i) {
        for (int j = i; j < a.size(); ++j) {
            int thisSum = 0;
            for (int k = i; k <= j; ++k) {
                thisSum += a[k];
                steps++;
            }
            if (thisSum > maxSum) {
                maxSum = thisSum;
            }
        }
    }
    return maxSum;
}

/**
 * Improved, O(n^2)
 * @param a
 * @return
 */
int maxSubSum2(const std::vector<int> &a) {
    int maxSum = 0;
    for (int i = 0; i < a.size(); ++i) {
        int thisSum = 0;
        for (int j = i; j < a.size(); ++j) {
            thisSum += a[j];
            steps++;
            if (thisSum > maxSum) {
                maxSum = thisSum;
            }
        }
    }
    return maxSum;
}

/**
 * Recursive, divide and conquer approach, O(n log n)
 * After Shamos
 * @param a
 * @param left
 * @param right
 * @return
 */
int maxSumRec(const std::vector<int> &a, int left, int right) {
    // base case for recursion, when we have one element
    if (left == right) {
        if (a[left] > 0) {
            return a[left];
        } else {
            return 0;
        }
    }
    // divide into two halves
    int center = (left + right) / 2;
    // get the max subsequence sum from each of the two halves
    int maxLeftSum = maxSumRec(a, left, center);  // recursive call
    int maxRightSum = maxSumRec(a, center + 1, right);  // recursive call

    // starting from the center and working toward left boundary
    int maxLeftBorderSum = 0, leftBorderSum = 0;
    for (int i = center; i >= left; --i) {
        leftBorderSum += a[i];
        steps++;
        if (leftBorderSum > maxLeftBorderSum) {
            maxLeftBorderSum = leftBorderSum;
        }
    }
    // starting from the center and working toward right boundary
    int maxRightBorderSum = 0, rightBorderSum = 0;
    for (int j = center + 1; j <= right; ++j) {
        rightBorderSum += a[j];
        steps++;
        if (rightBorderSum > maxRightBorderSum) {
            maxRightBorderSum = rightBorderSum;
        }
    }
    int combined = maxLeftBorderSum + maxRightBorderSum;

    // return the max of the three subsequence sums
    return std::max(maxLeftSum, std::max(maxRightSum, combined));
}

/**
 * Kadane's algorithm, O(n)
 */
int kadanesAlgo(const std::vector<int> &a) {
    int bestSum = 0;
    int currentSum = 0;
    for (int i = 0; i < a.size(); ++i) {
        currentSum = std::max(0, currentSum + a[i]);
        bestSum = std::max(bestSum, currentSum);
        steps++;
    }
    return bestSum;
}


int main() {
    std::vector<int> a;

    // populate array with SIZE random integers between -RANGE and RANGE
    randPopulateArray(a, SIZE, RANGE);

    steps = 0;
    std::cout << "Brute force, O(n^3)" << std::endl;
    std::cout << "Answer: " << maxSubSum1(a) << std::endl;
    std::cout << "Steps: " << steps << std::endl << std::endl;

    steps = 0;
    std::cout << "Improved, O(n^2)" << std::endl;
    std::cout << "Answer: " << maxSubSum2(a) << std::endl;
    std::cout << "Steps: " << steps << std::endl << std::endl;

    steps = 0;
    std::cout << "Shamos' divide and conquer, O(n log(n))" << std::endl;
    std::cout << "Answer: " << maxSumRec(a, 0, a.size() - 1) << std::endl;
    std::cout << "Steps: " << steps << std::endl << std::endl;

    steps = 0;
    std::cout << "Kadane's Algorithm, O(n)" << std::endl;
    std::cout << "Answer: " << kadanesAlgo(a) << std::endl;
    std::cout << "Steps: " << steps << std::endl;

    return 0;
}