LeetCode 327. 区间和的个数-蒲公英云

LeetCode 327. 区间和的个数

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//解法一：分治 68%
class Solution {
    public int countRangeSum(int[] nums, int lower, int upper) {
        int n = nums.length;
        long[] sum = new long[n + 1];
        for(int i = 1; i <= n; i++){
            sum[i] = sum[i - 1] + nums[i - 1]; 
        }
        return countRangeSumRecursive(sum, lower, upper, 0, sum.length - 1);
    }
    public int countRangeSumRecursive(long[] sum, int lower, int upper, int left, int right){
        if(left == right)
            return 0;
        int mid = left + right >> 1;
        int n1 = countRangeSumRecursive(sum, lower, upper, left, mid);
        int n2 = countRangeSumRecursive(sum, lower, upper, mid + 1, right);
        int ret = n1 + n2;
        int i = left;
        int l = mid + 1, r = mid + 1;
        while(i <= mid){
            while(l <= right && sum[l] - sum[i] < lower) l++;
            while(r <= right && sum[r] - sum[i] <= upper) r++;
            ret += (r - l);
            i++;
        }
        int p = 0;
        int p1 = left, p2 = mid + 1;
        long[] sorted = new long[right - left + 1];
        while(p1 <= mid || p2 <= right){
            if(p1 > mid){
                sorted[p++] = sum[p2++];
            }else if(p2 > right){
                sorted[p++] = sum[p1++];
            }else{
                if (sum[p1] < sum[p2]) {
                        sorted[p++] = sum[p1++];
                    } else {
                        sorted[p++] = sum[p2++];
                    }
            }
        }
        for (int k = 0; k < sorted.length; k++) {
                sum[left + k] = sorted[k];
            }
        return ret;
    }
}
//解法二：树状数组
class Solution {
    public int countRangeSum(int[] nums, int lower, int upper) {
        long sum = 0;
        long[] preSum = new long[nums.length + 1];
        for(int i = 0; i < nums.length; i++){
            sum += nums[i];
            preSum[i + 1] = sum;
        }
        Set<Long> allNumbers = new TreeSet<Long>();
        for(long x : preSum){
            allNumbers.add(x - lower);
            allNumbers.add(x - upper);
            allNumbers.add(x);
        }
        Map<Long, Integer> values = new HashMap<Long, Integer>();
        int idx = 1;
        for(long x : allNumbers){
            values.put(x, idx);
            idx++;
        }
        int ret = 0;
        BIT bit = new BIT(values.size() + 1);
        for(int i = 0; i < preSum.length; i++){
            int left = values.get(preSum[i] - upper), right = values.get(preSum[i] - lower);
            ret += bit.query(right) - bit.query(left - 1);
            bit.update(values.get(preSum[i]), 1);
        }
        return ret;
    }
}
class BIT {
    int[] tree;
    int n;
    public BIT(int n) {
        this.n = n;
        this.tree = new int[n + 1];
    }
    public static int lowbit(int x) {
        return x & (-x);
    }
    public void update(int x, int d) {
        while (x <= n) {
            tree[x] += d;
            x += lowbit(x);
        }
    }
    public int query(int x) {
        int ans = 0;
        while (x != 0) {
            ans += tree[x];
            x -= lowbit(x);
        }
        return ans;
    }
}
//解法三：线段树
class Solution {
    public int countRangeSum(int[] nums, int lower, int upper) {
        long sum = 0;
        long[] preSum = new long[nums.length + 1];
        for (int i = 0; i < nums.length; ++i) {
            sum += nums[i];
            preSum[i + 1] = sum;
        }
        Set<Long> allNumbers = new TreeSet<Long>();
        for (long x : preSum) {
            allNumbers.add(x);
            allNumbers.add(x - lower);
            allNumbers.add(x - upper);
        }
        // 利用哈希表进行离散化
        Map<Long, Integer> values = new HashMap<Long, Integer>();
        int idx = 0;
        for (long x : allNumbers) {
            values.put(x, idx);
            idx++;
        }
        int[] a = new int[values.size()];
        TreeNode root = buildTree(a, 0, values.size() - 1);
        int ret = 0;
        for (long x : preSum) {
            int left = values.get(x - upper), right = values.get(x - lower);
            ret += queryTree(root, left, right);
            updateTree(root, values.get(x), 1);
        }
        return ret;
    }
    class TreeNode {
        int val;
        int start;
        int end;
        TreeNode left;
        TreeNode right;
        public TreeNode(int start, int end) {
            left = null;
            right = null;
            this.start = start;
            this.end = end;
        }
    }
    private TreeNode buildTree(int[] nums, int start, int end) {
        if (start > end) return null;
        TreeNode curr = new TreeNode(start, end);
        if (start == end) curr.val = nums[start];
        else {
            int mid = start + (end - start) / 2;
            curr.left = buildTree(nums, start, mid);
            curr.right = buildTree(nums, mid + 1, end);
            curr.val = curr.left.val + curr.right.val;
        }
        return curr;
    }
    public void updateTree(TreeNode node, int i, int val) {
        if (node.start == node.end) {
            node.val += val;
        } else {
            int mid = node.start + (node.end - node.start) / 2;
            if (i <= mid) updateTree(node.left, i, val);
            else updateTree(node.right, i, val);
            node.val = node.left.val + node.right.val;
        }
    }
    public int queryTree(TreeNode node, int i, int j) {
        if(i > j)
            return 0;
        if (node.start == i && node.end == j) return node.val;
        else {
            int mid = node.start + (node.end - node.start) / 2;
            if (j <= mid) {
                return queryTree(node.left, i, j);
            } else if (i >= (mid + 1)) {
                return queryTree(node.right, i, j);
            } else {
                return queryTree(node.left, i, mid) + queryTree(node.right, mid + 1, j);
            }
        }
    }
}