560. Subarray Sum Equals K

Given an array of integers and an integer k, you need to find the total number of continuous subarrays whose sum equals to k.

Example 1:

Input:nums = [1,1,1], k = 2
Output: 2

 Note:

1. The length of the array is in range [1, 20,000].
2. The range of numbers in the array is [-1000, 1000] and the range of the integer k is [-1e7, 1e7].

题目含义：求和为k的连续子数组的个数

 思路：最直观的想法是遍历数组并依次加当前位置的数字，同时用数组preSum记录下当前位置之前所有数字的相加和，这样下标[i, j)之间的数字之和就可以用preSum[j]-preSum]来计算，然后通过双层循环，遍历所有情况来统计满足条件的子数组个数

    public int subarraySum(int[] nums, int k) {
        int[] preSum = new int[nums.length];  //dp数组，位置i上存储从0到i个元素总和
        preSum[0] = nums[0];  
        for (int i = 1; i < nums.length; i++) preSum[i] = preSum[i - 1] + nums[i];
        int result = 0;
        for (int i = 0; i < preSum.length; i++) {
            if (preSum[i] == k) result++;
            for (int j = i + 1; j < preSum.length; j++) {
                if (preSum[j] - preSum[i] == k) result++;   //线段2-线段1==长度k
            }
        }
        return result;
    }