2612. Minimum Reverse Operations

Description

You are given an integer n and an integer p representing an array arr of length n where all elements are set to 0's, except position p which is set to 1. You are also given an integer array banned containing restricted positions. Perform the following operation on arr:

• Reverse a subarray with size k if the single 1 is not set to a position in banned.

Return an integer array answer with n results where the ith result is the minimum number of operations needed to bring the single 1 to position i in arr, or -1 if it is impossible.

 

Example 1:

Input: n = 4, p = 0, banned = [1,2], k = 4

Output: [0,-1,-1,1]

Explanation:

• Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.
• We can never place 1 on the banned positions, so the answer for positions 1 and 2 is -1.
• Perform the operation of size 4 to reverse the whole array.
• After a single operation 1 is at position 3 so the answer for position 3 is 1.

Example 2:

Input: n = 5, p = 0, banned = [2,4], k = 3

Output: [0,-1,-1,-1,-1]

Explanation:

• Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.
• We cannot perform the operation on the subarray positions [0, 2] because position 2 is in banned.
• Because 1 cannot be set at position 2, it is impossible to set 1 at other positions in more operations.

Example 3:

Input: n = 4, p = 2, banned = [0,1,3], k = 1

Output: [-1,-1,0,-1]

Explanation:

Perform operations of size 1 and 1 never changes its position.

 

Constraints:

• 1 <= n <= 105
• 0 <= p <= n - 1
• 0 <= banned.length <= n - 1
• 0 <= banned[i] <= n - 1
• 1 <= k <= n 
• banned[i] != p
• all values in banned are unique 

Solutions

Solution 1: Ordered Set + BFS

We notice that for any index \(i\) in the subarray interval \([l,..r]\), the flipped index \(j = l + r - i\).

If the subarray moves one position to the right, then \(j = l + 1 + r + 1 - i = l + r - i + 2\), that is, \(j\) will increase by \(2\).

Similarly, if the subarray moves one position to the left, then \(j = l - 1 + r - 1 - i = l + r - i - 2\), that is, \(j\) will decrease by \(2\).

Therefore, for a specific index \(i\), all its flipped indices form an arithmetic progression with common difference \(2\), that is, all the flipped indices have the same parity.

Next, we consider the range of values ​​of the index \(i\) after flipping \(j\).

• If the boundary is not considered, the range of values ​​of \(j\) is \([i - k + 1, i + k - 1]\).
• If the subarray is on the left, then \([l, r] = [0, k - 1]\), so the flipped index \(j\) of \(i\) is \(0 + k - 1 - i\), that is, \(j = k - i - 1\), so the left boundary \(mi = max(i - k + 1, k - i - 1)\).
• If the subarray is on the right, then \([l, r] = [n - k, n - 1]\), so the flipped index \(j= n - k + n - 1 - i\) is \(j = n \times 2 - k - i - 1\), so the right boundary of \(j\) is \(mx = min(i + k - 1, n \times 2 - k - i - 1)\).

We use two ordered sets to store all the odd indices and even indices to be searched, here we need to exclude the indices in the array \(banned\) and the index \(p\).

Then we use BFS to search, each time searching all the flipped indices \(j\) of the current index \(i\), that is, \(j = mi, mi + 2, mi + 4, \dots, mx\), updating the answer of index \(j\) and adding index \(j\) to the search queue, and removing index \(j\) from the corresponding ordered set.

When the search is over, the answer to all indices can be obtained.

The time complexity is \(O(n \times \log n)\) and the space complexity is \(O(n)\). Where \(n\) is the given array length in the problem.

Python3JavaC++GoTypeScriptRust

class Solution:
    def minReverseOperations(
        self, n: int, p: int, banned: List[int], k: int
    ) -> List[int]:
        ans = [-1] * n
        ans[p] = 0
        ts = [SortedSet() for _ in range(2)]
        for i in range(n):
            ts[i % 2].add(i)
        ts[p % 2].remove(p)
        for i in banned:
            ts[i % 2].remove(i)
        ts[0].add(n)
        ts[1].add(n)
        q = deque([p])
        while q:
            i = q.popleft()
            mi = max(i - k + 1, k - i - 1)
            mx = min(i + k - 1, n * 2 - k - i - 1)
            s = ts[mi % 2]
            j = s.bisect_left(mi)
            while s[j] <= mx:
                q.append(s[j])
                ans[s[j]] = ans[i] + 1
                s.remove(s[j])
                j = s.bisect_left(mi)
        return ans

class Solution {
    public int[] minReverseOperations(int n, int p, int[] banned, int k) {
        int[] ans = new int[n];
        TreeSet<Integer>[] ts = new TreeSet[] {new TreeSet<>(), new TreeSet<>()};
        for (int i = 0; i < n; ++i) {
            ts[i % 2].add(i);
            ans[i] = i == p ? 0 : -1;
        }
        ts[p % 2].remove(p);
        for (int i : banned) {
            ts[i % 2].remove(i);
        }
        ts[0].add(n);
        ts[1].add(n);
        Deque<Integer> q = new ArrayDeque<>();
        q.offer(p);
        while (!q.isEmpty()) {
            int i = q.poll();
            int mi = Math.max(i - k + 1, k - i - 1);
            int mx = Math.min(i + k - 1, n * 2 - k - i - 1);
            var s = ts[mi % 2];
            for (int j = s.ceiling(mi); j <= mx; j = s.ceiling(mi)) {
                q.offer(j);
                ans[j] = ans[i] + 1;
                s.remove(j);
            }
        }
        return ans;
    }
}

class Solution {
public:
    vector<int> minReverseOperations(int n, int p, vector<int>& banned, int k) {
        vector<int> ans(n, -1);
        ans[p] = 0;
        set<int> ts[2];
        for (int i = 0; i < n; ++i) {
            ts[i % 2].insert(i);
        }
        ts[p % 2].erase(p);
        for (int i : banned) {
            ts[i % 2].erase(i);
        }
        ts[0].insert(n);
        ts[1].insert(n);
        queue<int> q{{p}};
        while (!q.empty()) {
            int i = q.front();
            q.pop();
            int mi = max(i - k + 1, k - i - 1);
            int mx = min(i + k - 1, n * 2 - k - i - 1);
            auto& s = ts[mi % 2];
            auto it = s.lower_bound(mi);
            while (*it <= mx) {
                int j = *it;
                ans[j] = ans[i] + 1;
                q.push(j);
                it = s.erase(it);
            }
        }
        return ans;
    }
};

func minReverseOperations(n int, p int, banned []int, k int) []int {
    ans := make([]int, n)
    ts := [2]*redblacktree.Tree{redblacktree.NewWithIntComparator(), redblacktree.NewWithIntComparator()}
    for i := 0; i < n; i++ {
        ts[i%2].Put(i, struct{}{})
        ans[i] = -1
    }
    ans[p] = 0
    ts[p%2].Remove(p)
    for _, i := range banned {
        ts[i%2].Remove(i)
    }
    ts[0].Put(n, struct{}{})
    ts[1].Put(n, struct{}{})
    q := []int{p}
    for len(q) > 0 {
        i := q[0]
        q = q[1:]
        mi := max(i-k+1, k-i-1)
        mx := min(i+k-1, n*2-k-i-1)
        s := ts[mi%2]
        for x, _ := s.Ceiling(mi); x.Key.(int) <= mx; x, _ = s.Ceiling(mi) {
            j := x.Key.(int)
            s.Remove(j)
            ans[j] = ans[i] + 1
            q = append(q, j)
        }
    }
    return ans
}

function minReverseOperations(n: number, p: number, banned: number[], k: number): number[] {
    const ans: number[] = Array(n).fill(-1);
    const ts = [new TreeSet<number>(), new TreeSet<number>()];
    for (let i = 0; i < n; ++i) {
        ts[i % 2].add(i);
    }
    ans[p] = 0;
    ts[p % 2].delete(p);
    for (const i of banned) {
        ts[i % 2].delete(i);
    }
    ts[0].add(n);
    ts[1].add(n);
    let q = [p];
    while (q.length) {
        const t: number[] = [];
        for (const i of q) {
            const mi = Math.max(i - k + 1, k - i - 1);
            const mx = Math.min(i + k - 1, n * 2 - k - i - 1);
            const s = ts[mi % 2];
            for (let j = s.ceil(mi)!; j <= mx; j = s.ceil(j)!) {
                t.push(j);
                ans[j] = ans[i] + 1;
                s.delete(j);
            }
        }
        q = t;
    }
    return ans;
}

type Compare<T> = (lhs: T, rhs: T) => number;

class RBTreeNode<T = number> {
    data: T;
    count: number;
    left: RBTreeNode<T> | null;
    right: RBTreeNode<T> | null;
    parent: RBTreeNode<T> | null;
    color: number;
    constructor(data: T) {
        this.data = data;
        this.left = this.right = this.parent = null;
        this.color = 0;
        this.count = 1;
    }

    sibling(): RBTreeNode<T> | null {
        if (!this.parent) return null; // sibling null if no parent
        return this.isOnLeft() ? this.parent.right : this.parent.left;
    }

    isOnLeft(): boolean {
        return this === this.parent!.left;
    }

    hasRedChild(): boolean {
        return (
            Boolean(this.left && this.left.color === 0) ||
            Boolean(this.right && this.right.color === 0)
        );
    }
}

class RBTree<T> {
    root: RBTreeNode<T> | null;
    lt: (l: T, r: T) => boolean;
    constructor(compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0)) {
        this.root = null;
        this.lt = (l: T, r: T) => compare(l, r) < 0;
    }

    rotateLeft(pt: RBTreeNode<T>): void {
        const right = pt.right!;
        pt.right = right.left;

        if (pt.right) pt.right.parent = pt;
        right.parent = pt.parent;

        if (!pt.parent) this.root = right;
        else if (pt === pt.parent.left) pt.parent.left = right;
        else pt.parent.right = right;

        right.left = pt;
        pt.parent = right;
    }

    rotateRight(pt: RBTreeNode<T>): void {
        const left = pt.left!;
        pt.left = left.right;

        if (pt.left) pt.left.parent = pt;
        left.parent = pt.parent;

        if (!pt.parent) this.root = left;
        else if (pt === pt.parent.left) pt.parent.left = left;
        else pt.parent.right = left;

        left.right = pt;
        pt.parent = left;
    }

    swapColor(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.color;
        p1.color = p2.color;
        p2.color = tmp;
    }

    swapData(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.data;
        p1.data = p2.data;
        p2.data = tmp;
    }

    fixAfterInsert(pt: RBTreeNode<T>): void {
        let parent = null;
        let grandParent = null;

        while (pt !== this.root && pt.color !== 1 && pt.parent?.color === 0) {
            parent = pt.parent;
            grandParent = pt.parent.parent;

            /*  Case : A
                Parent of pt is left child of Grand-parent of pt */
            if (parent === grandParent?.left) {
                const uncle = grandParent.right;

                /* Case : 1
                   The uncle of pt is also red
                   Only Recoloring required */
                if (uncle && uncle.color === 0) {
                    grandParent.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent;
                } else {
                    /* Case : 2
                       pt is right child of its parent
                       Left-rotation required */
                    if (pt === parent.right) {
                        this.rotateLeft(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is left child of its parent
                       Right-rotation required */
                    this.rotateRight(grandParent);
                    this.swapColor(parent!, grandParent);
                    pt = parent!;
                }
            } else {
                /* Case : B
               Parent of pt is right child of Grand-parent of pt */
                const uncle = grandParent!.left;

                /*  Case : 1
                    The uncle of pt is also red
                    Only Recoloring required */
                if (uncle != null && uncle.color === 0) {
                    grandParent!.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent!;
                } else {
                    /* Case : 2
                       pt is left child of its parent
                       Right-rotation required */
                    if (pt === parent.left) {
                        this.rotateRight(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is right child of its parent
                       Left-rotation required */
                    this.rotateLeft(grandParent!);
                    this.swapColor(parent!, grandParent!);
                    pt = parent!;
                }
            }
        }
        this.root!.color = 1;
    }

    delete(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        node.count--;
        if (!node.count) this.deleteNode(node);
        return true;
    }

    deleteAll(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        this.deleteNode(node);
        return true;
    }

    deleteNode(v: RBTreeNode<T>): void {
        const u = BSTreplace(v);

        // True when u and v are both black
        const uvBlack = (u === null || u.color === 1) && v.color === 1;
        const parent = v.parent!;

        if (!u) {
            // u is null therefore v is leaf
            if (v === this.root) this.root = null;
            // v is root, making root null
            else {
                if (uvBlack) {
                    // u and v both black
                    // v is leaf, fix double black at v
                    this.fixDoubleBlack(v);
                } else {
                    // u or v is red
                    if (v.sibling()) {
                        // sibling is not null, make it red"
                        v.sibling()!.color = 0;
                    }
                }
                // delete v from the tree
                if (v.isOnLeft()) parent.left = null;
                else parent.right = null;
            }
            return;
        }

        if (!v.left || !v.right) {
            // v has 1 child
            if (v === this.root) {
                // v is root, assign the value of u to v, and delete u
                v.data = u.data;
                v.left = v.right = null;
            } else {
                // Detach v from tree and move u up
                if (v.isOnLeft()) parent.left = u;
                else parent.right = u;
                u.parent = parent;
                if (uvBlack) this.fixDoubleBlack(u);
                // u and v both black, fix double black at u
                else u.color = 1; // u or v red, color u black
            }
            return;
        }

        // v has 2 children, swap data with successor and recurse
        this.swapData(u, v);
        this.deleteNode(u);

        // find node that replaces a deleted node in BST
        function BSTreplace(x: RBTreeNode<T>): RBTreeNode<T> | null {
            // when node have 2 children
            if (x.left && x.right) return successor(x.right);
            // when leaf
            if (!x.left && !x.right) return null;
            // when single child
            return x.left ?? x.right;
        }
        // find node that do not have a left child
        // in the subtree of the given node
        function successor(x: RBTreeNode<T>): RBTreeNode<T> {
            let temp = x;
            while (temp.left) temp = temp.left;
            return temp;
        }
    }

    fixDoubleBlack(x: RBTreeNode<T>): void {
        if (x === this.root) return; // Reached root

        const sibling = x.sibling();
        const parent = x.parent!;
        if (!sibling) {
            // No sibiling, double black pushed up
            this.fixDoubleBlack(parent);
        } else {
            if (sibling.color === 0) {
                // Sibling red
                parent.color = 0;
                sibling.color = 1;
                if (sibling.isOnLeft()) this.rotateRight(parent);
                // left case
                else this.rotateLeft(parent); // right case
                this.fixDoubleBlack(x);
            } else {
                // Sibling black
                if (sibling.hasRedChild()) {
                    // at least 1 red children
                    if (sibling.left && sibling.left.color === 0) {
                        if (sibling.isOnLeft()) {
                            // left left
                            sibling.left.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateRight(parent);
                        } else {
                            // right left
                            sibling.left.color = parent.color;
                            this.rotateRight(sibling);
                            this.rotateLeft(parent);
                        }
                    } else {
                        if (sibling.isOnLeft()) {
                            // left right
                            sibling.right!.color = parent.color;
                            this.rotateLeft(sibling);
                            this.rotateRight(parent);
                        } else {
                            // right right
                            sibling.right!.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateLeft(parent);
                        }
                    }
                    parent.color = 1;
                } else {
                    // 2 black children
                    sibling.color = 0;
                    if (parent.color === 1) this.fixDoubleBlack(parent);
                    else parent.color = 1;
                }
            }
        }
    }

    insert(data: T): boolean {
        // search for a position to insert
        let parent = this.root;
        while (parent) {
            if (this.lt(data, parent.data)) {
                if (!parent.left) break;
                else parent = parent.left;
            } else if (this.lt(parent.data, data)) {
                if (!parent.right) break;
                else parent = parent.right;
            } else break;
        }

        // insert node into parent
        const node = new RBTreeNode(data);
        if (!parent) this.root = node;
        else if (this.lt(node.data, parent.data)) parent.left = node;
        else if (this.lt(parent.data, node.data)) parent.right = node;
        else {
            parent.count++;
            return false;
        }
        node.parent = parent;
        this.fixAfterInsert(node);
        return true;
    }

    find(data: T): RBTreeNode<T> | null {
        let p = this.root;
        while (p) {
            if (this.lt(data, p.data)) {
                p = p.left;
            } else if (this.lt(p.data, data)) {
                p = p.right;
            } else break;
        }
        return p ?? null;
    }

    *inOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.inOrder(root.left!)) yield v;
        yield root.data;
        for (const v of this.inOrder(root.right!)) yield v;
    }

    *reverseInOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.reverseInOrder(root.right!)) yield v;
        yield root.data;
        for (const v of this.reverseInOrder(root.left!)) yield v;
    }
}

class TreeSet<T = number> {
    _size: number;
    tree: RBTree<T>;
    compare: Compare<T>;
    constructor(
        collection: T[] | Compare<T> = [],
        compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0),
    ) {
        if (typeof collection === 'function') {
            compare = collection;
            collection = [];
        }
        this._size = 0;
        this.compare = compare;
        this.tree = new RBTree(compare);
        for (const val of collection) this.add(val);
    }

    size(): number {
        return this._size;
    }

    has(val: T): boolean {
        return !!this.tree.find(val);
    }

    add(val: T): boolean {
        const successful = this.tree.insert(val);
        this._size += successful ? 1 : 0;
        return successful;
    }

    delete(val: T): boolean {
        const deleted = this.tree.deleteAll(val);
        this._size -= deleted ? 1 : 0;
        return deleted;
    }

    ceil(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(p.data, val) >= 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    floor(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(val, p.data) >= 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    higher(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(val, p.data) < 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    lower(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(p.data, val) < 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    first(): T | undefined {
        return this.tree.inOrder().next().value;
    }

    last(): T | undefined {
        return this.tree.reverseInOrder().next().value;
    }

    shift(): T | undefined {
        const first = this.first();
        if (first === undefined) return undefined;
        this.delete(first);
        return first;
    }

    pop(): T | undefined {
        const last = this.last();
        if (last === undefined) return undefined;
        this.delete(last);
        return last;
    }

    *[Symbol.iterator](): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *keys(): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *values(): Generator<T, undefined, void> {
        for (const val of this.tree.inOrder()) yield val;
        return undefined;
    }

    /**
     * Return a generator for reverse order traversing the set
     */
    *rvalues(): Generator<T, undefined, void> {
        for (const val of this.tree.reverseInOrder()) yield val;
        return undefined;
    }
}

class TreeMultiSet<T = number> {
    _size: number;
    tree: RBTree<T>;
    compare: Compare<T>;
    constructor(
        collection: T[] | Compare<T> = [],
        compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0),
    ) {
        if (typeof collection === 'function') {
            compare = collection;
            collection = [];
        }
        this._size = 0;
        this.compare = compare;
        this.tree = new RBTree(compare);
        for (const val of collection) this.add(val);
    }

    size(): number {
        return this._size;
    }

    has(val: T): boolean {
        return !!this.tree.find(val);
    }

    add(val: T): boolean {
        const successful = this.tree.insert(val);
        this._size++;
        return successful;
    }

    delete(val: T): boolean {
        const successful = this.tree.delete(val);
        if (!successful) return false;
        this._size--;
        return true;
    }

    count(val: T): number {
        const node = this.tree.find(val);
        return node ? node.count : 0;
    }

    ceil(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(p.data, val) >= 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    floor(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(val, p.data) >= 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    higher(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(val, p.data) < 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    lower(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(p.data, val) < 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    first(): T | undefined {
        return this.tree.inOrder().next().value;
    }

    last(): T | undefined {
        return this.tree.reverseInOrder().next().value;
    }

    shift(): T | undefined {
        const first = this.first();
        if (first === undefined) return undefined;
        this.delete(first);
        return first;
    }

    pop(): T | undefined {
        const last = this.last();
        if (last === undefined) return undefined;
        this.delete(last);
        return last;
    }

    *[Symbol.iterator](): Generator<T, void, void> {
        yield* this.values();
    }

    *keys(): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *values(): Generator<T, undefined, void> {
        for (const val of this.tree.inOrder()) {
            let count = this.count(val);
            while (count--) yield val;
        }
        return undefined;
    }

    /**
     * Return a generator for reverse order traversing the multi-set
     */
    *rvalues(): Generator<T, undefined, void> {
        for (const val of this.tree.reverseInOrder()) {
            let count = this.count(val);
            while (count--) yield val;
        }
        return undefined;
    }
}

use std::collections::{BTreeSet, VecDeque};

impl Solution {
    pub fn min_reverse_operations(n: i32, p: i32, banned: Vec<i32>, k: i32) -> Vec<i32> {
        let mut ans = vec![-1; n as usize];
        let mut ts = [BTreeSet::new(), BTreeSet::new()];

        for i in 0..n {
            ts[(i % 2) as usize].insert(i);
        }
        ans[p as usize] = 0;
        ts[(p % 2) as usize].remove(&p);

        for &b in &banned {
            ts[(b % 2) as usize].remove(&b);
        }

        ts[0].insert(n);
        ts[1].insert(n);
        let mut q = VecDeque::new();
        q.push_back(p);

        while let Some(i) = q.pop_front() {
            let mi = (i - k + 1).max(k - i - 1);
            let mx = (i + k - 1).min(2 * n - k - i - 1);
            let s = &mut ts[(mi % 2) as usize];

            while let Some(&j) = s.range(mi..=mx).next() {
                q.push_back(j);
                ans[j as usize] = ans[i as usize] + 1;
                s.remove(&j);
            }
        }

        ans
    }
}

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