_523.java

package com.fishercoder.solutions;

import java.util.HashMap;
import java.util.Map;

/**
 * 523. Continuous Subarray Sum
 *
 * Given a list of non-negative numbers and a target integer k,
 * write a function to check if the array has a continuous subarray of size at least 2
 * that sums up to the multiple of k, that is, sums up to n*k where n is also an integer.

 Example 1:
 Input: [23, 2, 4, 6, 7],  k=6
 Output: True
 Explanation: Because [2, 4] is a continuous subarray of size 2 and sums up to 6.

 Example 2:
 Input: [23, 2, 6, 4, 7],  k=6
 Output: True
 Explanation: Because [23, 2, 6, 4, 7] is an continuous subarray of size 5 and sums up to 42.

 Note:
 The length of the array won't exceed 10,000.
 You may assume the sum of all the numbers is in the range of a signed 32-bit integer.

 */
public class _523 {

    /**reference: https://discuss.leetcode.com/topic/80793/java-o-n-time-o-k-space/20
     *
     * "The reason we use modulus is:
     * (a+(n*x))%x is same as (a%x)
     * e.g. in case of the array [23,2,6,4,7] the running sum is [23,25,31,35,42]
     * and the remainders are [5,1,1,5,0].
     * We got reminder 5 at index 0 and at index 3.
     * That means, in between these two indexes we must have added a number which is multiple of the k.
     * Hope this clarifies your doubt :)"*/
    public boolean checkSubarraySumOnTimeO1Space(int[] nums, int k) {
        Map<Integer, Integer> map = new HashMap<>();
        map.put(0, -1);
        int sum = 0;
        for (int i = 0; i < nums.length; i++) {
            sum += nums[i];
            if (k != 0) {
                /**Because if k == 0, sum %= k will throw ArithmeticException.*/
                sum %= k;
            }
            Integer prev = map.get(sum);
            if (prev != null) {
                if (i - prev > 1) {
                    /**This makes sure that it has length at least 2*/
                    return true;
                }
            } else {
                map.put(sum, i);
            }
        }
        return false;
    }

    public boolean checkSubarraySum(int[] nums, int k) {
        if (nums == null || nums.length == 0) {
            return false;
        }

        //Two continuous zeroes will form a subarray of length 2 with sum 0, 0*k = 0 will always be true
        for (int i = 0; i < nums.length - 1; i++) {
            if (nums[i] == 0 && nums[i + 1] == 0) {
                return true;
            }
        }

        //then k cannot be zero any more
        if (k == 0 || nums.length < 2) {
            return false;
        }

        int[] preSums = new int[nums.length + 1];
        for (int i = 1; i <= nums.length; i++) {
            preSums[i] = preSums[i - 1] + nums[i - 1];
        }

        for (int i = 1; i <= nums.length; i++) {
            for (int j = 0; j < i - 1; j++) {
                if ((preSums[i] - preSums[j]) % k == 0) {
                    return true;
                }
            }
        }
        return false;
    }

}