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2,923
Find Champion I
Easy
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament.</p> <p>Given a <strong>0-indexed</strong> 2D boolean matrix <code>grid</code> of size <code>n * n</code>. For all <code>i, j</code> that <code>0 &lt;= i, j &lt;= n - 1</code> and <code>i != j</code> team <code>i</code> is <strong>stronger</strong> than team <code>j</code> if <code>grid[i][j] == 1</code>, otherwise, team <code>j</code> is <strong>stronger</strong> than team <code>i</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is stronger than team <code>a</code>.</p> <p>Return <em>the team that will be the champion of the tournament.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> grid = [[0,1],[0,0]] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are two teams in this tournament. grid[0][1] == 1 means that team 0 is stronger than team 1. So team 0 will be the champion. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> grid = [[0,0,1],[1,0,1],[0,0,0]] <strong>Output:</strong> 1 <strong>Explanation:</strong> There are three teams in this tournament. grid[1][0] == 1 means that team 1 is stronger than team 0. grid[1][2] == 1 means that team 1 is stronger than team 2. So team 1 will be the champion. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == grid.length</code></li> <li><code>n == grid[i].length</code></li> <li><code>2 &lt;= n &lt;= 100</code></li> <li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li> <li>For all <code>i grid[i][i]</code> is <code>0.</code></li> <li>For all <code>i, j</code> that <code>i != j</code>, <code>grid[i][j] != grid[j][i]</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Array; Matrix
Go
func findChampion(grid [][]int) int { n := len(grid) for i := 0; ; i++ { cnt := 0 for j, x := range grid[i] { if i != j && x == 1 { cnt++ } } if cnt == n-1 { return i } } }
2,923
Find Champion I
Easy
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament.</p> <p>Given a <strong>0-indexed</strong> 2D boolean matrix <code>grid</code> of size <code>n * n</code>. For all <code>i, j</code> that <code>0 &lt;= i, j &lt;= n - 1</code> and <code>i != j</code> team <code>i</code> is <strong>stronger</strong> than team <code>j</code> if <code>grid[i][j] == 1</code>, otherwise, team <code>j</code> is <strong>stronger</strong> than team <code>i</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is stronger than team <code>a</code>.</p> <p>Return <em>the team that will be the champion of the tournament.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> grid = [[0,1],[0,0]] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are two teams in this tournament. grid[0][1] == 1 means that team 0 is stronger than team 1. So team 0 will be the champion. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> grid = [[0,0,1],[1,0,1],[0,0,0]] <strong>Output:</strong> 1 <strong>Explanation:</strong> There are three teams in this tournament. grid[1][0] == 1 means that team 1 is stronger than team 0. grid[1][2] == 1 means that team 1 is stronger than team 2. So team 1 will be the champion. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == grid.length</code></li> <li><code>n == grid[i].length</code></li> <li><code>2 &lt;= n &lt;= 100</code></li> <li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li> <li>For all <code>i grid[i][i]</code> is <code>0.</code></li> <li>For all <code>i, j</code> that <code>i != j</code>, <code>grid[i][j] != grid[j][i]</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Array; Matrix
Java
class Solution { public int findChampion(int[][] grid) { int n = grid.length; for (int i = 0;; ++i) { int cnt = 0; for (int j = 0; j < n; ++j) { if (i != j && grid[i][j] == 1) { ++cnt; } } if (cnt == n - 1) { return i; } } } }
2,923
Find Champion I
Easy
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament.</p> <p>Given a <strong>0-indexed</strong> 2D boolean matrix <code>grid</code> of size <code>n * n</code>. For all <code>i, j</code> that <code>0 &lt;= i, j &lt;= n - 1</code> and <code>i != j</code> team <code>i</code> is <strong>stronger</strong> than team <code>j</code> if <code>grid[i][j] == 1</code>, otherwise, team <code>j</code> is <strong>stronger</strong> than team <code>i</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is stronger than team <code>a</code>.</p> <p>Return <em>the team that will be the champion of the tournament.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> grid = [[0,1],[0,0]] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are two teams in this tournament. grid[0][1] == 1 means that team 0 is stronger than team 1. So team 0 will be the champion. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> grid = [[0,0,1],[1,0,1],[0,0,0]] <strong>Output:</strong> 1 <strong>Explanation:</strong> There are three teams in this tournament. grid[1][0] == 1 means that team 1 is stronger than team 0. grid[1][2] == 1 means that team 1 is stronger than team 2. So team 1 will be the champion. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == grid.length</code></li> <li><code>n == grid[i].length</code></li> <li><code>2 &lt;= n &lt;= 100</code></li> <li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li> <li>For all <code>i grid[i][i]</code> is <code>0.</code></li> <li>For all <code>i, j</code> that <code>i != j</code>, <code>grid[i][j] != grid[j][i]</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Array; Matrix
Python
class Solution: def findChampion(self, grid: List[List[int]]) -> int: for i, row in enumerate(grid): if all(x == 1 for j, x in enumerate(row) if i != j): return i
2,923
Find Champion I
Easy
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament.</p> <p>Given a <strong>0-indexed</strong> 2D boolean matrix <code>grid</code> of size <code>n * n</code>. For all <code>i, j</code> that <code>0 &lt;= i, j &lt;= n - 1</code> and <code>i != j</code> team <code>i</code> is <strong>stronger</strong> than team <code>j</code> if <code>grid[i][j] == 1</code>, otherwise, team <code>j</code> is <strong>stronger</strong> than team <code>i</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is stronger than team <code>a</code>.</p> <p>Return <em>the team that will be the champion of the tournament.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> grid = [[0,1],[0,0]] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are two teams in this tournament. grid[0][1] == 1 means that team 0 is stronger than team 1. So team 0 will be the champion. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> grid = [[0,0,1],[1,0,1],[0,0,0]] <strong>Output:</strong> 1 <strong>Explanation:</strong> There are three teams in this tournament. grid[1][0] == 1 means that team 1 is stronger than team 0. grid[1][2] == 1 means that team 1 is stronger than team 2. So team 1 will be the champion. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == grid.length</code></li> <li><code>n == grid[i].length</code></li> <li><code>2 &lt;= n &lt;= 100</code></li> <li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li> <li>For all <code>i grid[i][i]</code> is <code>0.</code></li> <li>For all <code>i, j</code> that <code>i != j</code>, <code>grid[i][j] != grid[j][i]</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Array; Matrix
TypeScript
function findChampion(grid: number[][]): number { for (let i = 0, n = grid.length; ; ++i) { let cnt = 0; for (let j = 0; j < n; ++j) { if (i !== j && grid[i][j] === 1) { ++cnt; } } if (cnt === n - 1) { return i; } } }
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
C++
class Solution { public: int findChampion(int n, vector<vector<int>>& edges) { int indeg[n]; memset(indeg, 0, sizeof(indeg)); for (auto& e : edges) { ++indeg[e[1]]; } int ans = -1, cnt = 0; for (int i = 0; i < n; ++i) { if (indeg[i] == 0) { ++cnt; ans = i; } } return cnt == 1 ? ans : -1; } };
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
Go
func findChampion(n int, edges [][]int) int { indeg := make([]int, n) for _, e := range edges { indeg[e[1]]++ } ans, cnt := -1, 0 for i, x := range indeg { if x == 0 { cnt++ ans = i } } if cnt == 1 { return ans } return -1 }
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
Java
class Solution { public int findChampion(int n, int[][] edges) { int[] indeg = new int[n]; for (var e : edges) { ++indeg[e[1]]; } int ans = -1, cnt = 0; for (int i = 0; i < n; ++i) { if (indeg[i] == 0) { ++cnt; ans = i; } } return cnt == 1 ? ans : -1; } }
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
JavaScript
function findChampion(n, edges) { const indeg = Array(n).fill(0); for (const [_, v] of edges) { ++indeg[v]; } let [ans, cnt] = [-1, 0]; for (let i = 0; i < n; ++i) { if (indeg[i] === 0) { ++cnt; ans = i; } } return cnt === 1 ? ans : -1; }
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
Python
class Solution: def findChampion(self, n: int, edges: List[List[int]]) -> int: indeg = [0] * n for _, v in edges: indeg[v] += 1 return -1 if indeg.count(0) != 1 else indeg.index(0)
2,924
Find Champion II
Medium
<p>There are <code>n</code> teams numbered from <code>0</code> to <code>n - 1</code> in a tournament; each team is also a node in a <strong>DAG</strong>.</p> <p>You are given the integer <code>n</code> and a <strong>0-indexed</strong> 2D integer array <code>edges</code> of length <code><font face="monospace">m</font></code> representing the <strong>DAG</strong>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is a directed edge from team <code>u<sub>i</sub></code> to team <code>v<sub>i</sub></code> in the graph.</p> <p>A directed edge from <code>a</code> to <code>b</code> in the graph means that team <code>a</code> is <strong>stronger</strong> than team <code>b</code> and team <code>b</code> is <strong>weaker</strong> than team <code>a</code>.</p> <p>Team <code>a</code> will be the <strong>champion</strong> of the tournament if there is no team <code>b</code> that is <strong>stronger</strong> than team <code>a</code>.</p> <p>Return <em>the team that will be the <strong>champion</strong> of the tournament if there is a <strong>unique</strong> champion, otherwise, return </em><code>-1</code><em>.</em></p> <p><strong>Notes</strong></p> <ul> <li>A <strong>cycle</strong> is a series of nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub>, a<sub>n+1</sub></code> such that node <code>a<sub>1</sub></code> is the same node as node <code>a<sub>n+1</sub></code>, the nodes <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code> are distinct, and there is a directed edge from the node <code>a<sub>i</sub></code> to node <code>a<sub>i+1</sub></code> for every <code>i</code> in the range <code>[1, n]</code>.</li> <li>A <strong>DAG</strong> is a directed graph that does not have any <strong>cycle</strong>.</li> </ul> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-3.png" width="300" /></p> <pre> <strong>Input:</strong> n = 3, edges = [[0,1],[1,2]] <strong>Output:</strong> 0 <strong>Explanation: </strong>Team 1 is weaker than team 0. Team 2 is weaker than team 1. So the champion is team 0. </pre> <p><strong class="example">Example 2:</strong></p> <p><img height="300" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2924.Find%20Champion%20II/images/graph-4.png" width="300" /></p> <pre> <strong>Input:</strong> n = 4, edges = [[0,2],[1,3],[1,2]] <strong>Output:</strong> -1 <strong>Explanation:</strong> Team 2 is weaker than team 0 and team 1. Team 3 is weaker than team 1. But team 1 and team 0 are not weaker than any other teams. So the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 100</code></li> <li><code>m == edges.length</code></li> <li><code>0 &lt;= m &lt;= n * (n - 1) / 2</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= edge[i][j] &lt;= n - 1</code></li> <li><code>edges[i][0] != edges[i][1]</code></li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code>, team <code>b</code> is not stronger than team <code>a</code>.</li> <li>The input is generated such that if team <code>a</code> is stronger than team <code>b</code> and team <code>b</code> is stronger than team <code>c</code>, then team <code>a</code> is stronger than team <code>c</code>.</li> </ul>
Graph
TypeScript
function findChampion(n: number, edges: number[][]): number { const indeg: number[] = Array(n).fill(0); for (const [_, v] of edges) { ++indeg[v]; } let [ans, cnt] = [-1, 0]; for (let i = 0; i < n; ++i) { if (indeg[i] === 0) { ++cnt; ans = i; } } return cnt === 1 ? ans : -1; }
2,925
Maximum Score After Applying Operations on a Tree
Medium
<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p> <p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p> <p>You start with a score of <code>0</code>. In one operation, you can:</p> <ul> <li>Pick any node <code>i</code>.</li> <li>Add <code>values[i]</code> to your score.</li> <li>Set <code>values[i]</code> to <code>0</code>.</li> </ul> <p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p> <p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-13-1.png" style="width: 515px; height: 443px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1] <strong>Output:</strong> 11 <strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11. It can be shown that 11 is the maximum score obtainable after any number of operations on the tree. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-14-2.png" style="width: 522px; height: 245px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5] <strong>Output:</strong> 40 <strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4. - The sum of values on the path from 0 to 4 is equal to 10. - The sum of values on the path from 0 to 3 is equal to 10. - The sum of values on the path from 0 to 5 is equal to 3. - The sum of values on the path from 0 to 6 is equal to 5. Therefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40. It can be shown that 40 is the maximum score obtainable after any number of operations on the tree. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li> <li><code>values.length == n</code></li> <li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that <code>edges</code> represents a valid tree.</li> </ul>
Tree; Depth-First Search; Dynamic Programming
C++
class Solution { public: long long maximumScoreAfterOperations(vector<vector<int>>& edges, vector<int>& values) { int n = values.size(); vector<int> g[n]; for (auto& e : edges) { int a = e[0], b = e[1]; g[a].emplace_back(b); g[b].emplace_back(a); } using ll = long long; function<pair<ll, ll>(int, int)> dfs = [&](int i, int fa) -> pair<ll, ll> { ll a = 0, b = 0; bool leaf = true; for (int j : g[i]) { if (j != fa) { auto [aa, bb] = dfs(j, i); a += aa; b += bb; leaf = false; } } if (leaf) { return {values[i], 0LL}; } return {values[i] + a, max(values[i] + b, a)}; }; auto [_, b] = dfs(0, -1); return b; } };
2,925
Maximum Score After Applying Operations on a Tree
Medium
<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p> <p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p> <p>You start with a score of <code>0</code>. In one operation, you can:</p> <ul> <li>Pick any node <code>i</code>.</li> <li>Add <code>values[i]</code> to your score.</li> <li>Set <code>values[i]</code> to <code>0</code>.</li> </ul> <p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p> <p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-13-1.png" style="width: 515px; height: 443px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1] <strong>Output:</strong> 11 <strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11. It can be shown that 11 is the maximum score obtainable after any number of operations on the tree. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-14-2.png" style="width: 522px; height: 245px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5] <strong>Output:</strong> 40 <strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4. - The sum of values on the path from 0 to 4 is equal to 10. - The sum of values on the path from 0 to 3 is equal to 10. - The sum of values on the path from 0 to 5 is equal to 3. - The sum of values on the path from 0 to 6 is equal to 5. Therefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40. It can be shown that 40 is the maximum score obtainable after any number of operations on the tree. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li> <li><code>values.length == n</code></li> <li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that <code>edges</code> represents a valid tree.</li> </ul>
Tree; Depth-First Search; Dynamic Programming
Go
func maximumScoreAfterOperations(edges [][]int, values []int) int64 { g := make([][]int, len(values)) for _, e := range edges { a, b := e[0], e[1] g[a] = append(g[a], b) g[b] = append(g[b], a) } var dfs func(int, int) (int64, int64) dfs = func(i, fa int) (int64, int64) { a, b := int64(0), int64(0) leaf := true for _, j := range g[i] { if j != fa { leaf = false aa, bb := dfs(j, i) a += aa b += bb } } if leaf { return int64(values[i]), int64(0) } return int64(values[i]) + a, max(int64(values[i])+b, a) } _, b := dfs(0, -1) return b }
2,925
Maximum Score After Applying Operations on a Tree
Medium
<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p> <p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p> <p>You start with a score of <code>0</code>. In one operation, you can:</p> <ul> <li>Pick any node <code>i</code>.</li> <li>Add <code>values[i]</code> to your score.</li> <li>Set <code>values[i]</code> to <code>0</code>.</li> </ul> <p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p> <p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-13-1.png" style="width: 515px; height: 443px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1] <strong>Output:</strong> 11 <strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11. It can be shown that 11 is the maximum score obtainable after any number of operations on the tree. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-14-2.png" style="width: 522px; height: 245px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5] <strong>Output:</strong> 40 <strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4. - The sum of values on the path from 0 to 4 is equal to 10. - The sum of values on the path from 0 to 3 is equal to 10. - The sum of values on the path from 0 to 5 is equal to 3. - The sum of values on the path from 0 to 6 is equal to 5. Therefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40. It can be shown that 40 is the maximum score obtainable after any number of operations on the tree. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li> <li><code>values.length == n</code></li> <li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that <code>edges</code> represents a valid tree.</li> </ul>
Tree; Depth-First Search; Dynamic Programming
Java
class Solution { private List<Integer>[] g; private int[] values; public long maximumScoreAfterOperations(int[][] edges, int[] values) { int n = values.length; g = new List[n]; this.values = values; Arrays.setAll(g, k -> new ArrayList<>()); for (var e : edges) { int a = e[0], b = e[1]; g[a].add(b); g[b].add(a); } return dfs(0, -1)[1]; } private long[] dfs(int i, int fa) { long a = 0, b = 0; boolean leaf = true; for (int j : g[i]) { if (j != fa) { leaf = false; var t = dfs(j, i); a += t[0]; b += t[1]; } } if (leaf) { return new long[] {values[i], 0}; } return new long[] {values[i] + a, Math.max(values[i] + b, a)}; } }
2,925
Maximum Score After Applying Operations on a Tree
Medium
<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p> <p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p> <p>You start with a score of <code>0</code>. In one operation, you can:</p> <ul> <li>Pick any node <code>i</code>.</li> <li>Add <code>values[i]</code> to your score.</li> <li>Set <code>values[i]</code> to <code>0</code>.</li> </ul> <p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p> <p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-13-1.png" style="width: 515px; height: 443px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1] <strong>Output:</strong> 11 <strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11. It can be shown that 11 is the maximum score obtainable after any number of operations on the tree. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-14-2.png" style="width: 522px; height: 245px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5] <strong>Output:</strong> 40 <strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4. - The sum of values on the path from 0 to 4 is equal to 10. - The sum of values on the path from 0 to 3 is equal to 10. - The sum of values on the path from 0 to 5 is equal to 3. - The sum of values on the path from 0 to 6 is equal to 5. Therefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40. It can be shown that 40 is the maximum score obtainable after any number of operations on the tree. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li> <li><code>values.length == n</code></li> <li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that <code>edges</code> represents a valid tree.</li> </ul>
Tree; Depth-First Search; Dynamic Programming
Python
class Solution: def maximumScoreAfterOperations( self, edges: List[List[int]], values: List[int] ) -> int: def dfs(i: int, fa: int = -1) -> (int, int): a = b = 0 leaf = True for j in g[i]: if j != fa: leaf = False aa, bb = dfs(j, i) a += aa b += bb if leaf: return values[i], 0 return values[i] + a, max(values[i] + b, a) g = [[] for _ in range(len(values))] for a, b in edges: g[a].append(b) g[b].append(a) return dfs(0)[1]
2,925
Maximum Score After Applying Operations on a Tree
Medium
<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p> <p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p> <p>You start with a score of <code>0</code>. In one operation, you can:</p> <ul> <li>Pick any node <code>i</code>.</li> <li>Add <code>values[i]</code> to your score.</li> <li>Set <code>values[i]</code> to <code>0</code>.</li> </ul> <p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p> <p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-13-1.png" style="width: 515px; height: 443px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1] <strong>Output:</strong> 11 <strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11. It can be shown that 11 is the maximum score obtainable after any number of operations on the tree. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/images/graph-14-2.png" style="width: 522px; height: 245px;" /> <pre> <strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5] <strong>Output:</strong> 40 <strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4. - The sum of values on the path from 0 to 4 is equal to 10. - The sum of values on the path from 0 to 3 is equal to 10. - The sum of values on the path from 0 to 5 is equal to 3. - The sum of values on the path from 0 to 6 is equal to 5. Therefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40. It can be shown that 40 is the maximum score obtainable after any number of operations on the tree. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[i].length == 2</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li> <li><code>values.length == n</code></li> <li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that <code>edges</code> represents a valid tree.</li> </ul>
Tree; Depth-First Search; Dynamic Programming
TypeScript
function maximumScoreAfterOperations(edges: number[][], values: number[]): number { const g: number[][] = Array.from({ length: values.length }, () => []); for (const [a, b] of edges) { g[a].push(b); g[b].push(a); } const dfs = (i: number, fa: number): [number, number] => { let [a, b] = [0, 0]; let leaf = true; for (const j of g[i]) { if (j !== fa) { const [aa, bb] = dfs(j, i); a += aa; b += bb; leaf = false; } } if (leaf) { return [values[i], 0]; } return [values[i] + a, Math.max(values[i] + b, a)]; }; return dfs(0, -1)[1]; }
2,926
Maximum Balanced Subsequence Sum
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub>&nbsp;&lt;&nbsp;i<sub>1</sub> &lt;&nbsp;... &lt; i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p> <ul> <li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] &gt;= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li> </ul> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p> <p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,5,6] <strong>Output:</strong> 14 <strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected. nums[2] - nums[0] &gt;= 2 - 0. nums[3] - nums[2] &gt;= 3 - 2. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. The subsequence consisting of indices 1, 2, and 3 is also valid. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,-1,-3,8] <strong>Output:</strong> 13 <strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected. nums[3] - nums[0] &gt;= 3 - 0. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [-2,-1] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, the subsequence [-1] can be selected. It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li> <li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> </ul>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Dynamic Programming
C++
class BinaryIndexedTree { private: int n; vector<long long> c; const long long inf = 1e18; public: BinaryIndexedTree(int n) { this->n = n; c.resize(n + 1, -inf); } void update(int x, long long v) { while (x <= n) { c[x] = max(c[x], v); x += x & -x; } } long long query(int x) { long long mx = -inf; while (x > 0) { mx = max(mx, c[x]); x -= x & -x; } return mx; } }; class Solution { public: long long maxBalancedSubsequenceSum(vector<int>& nums) { int n = nums.size(); vector<int> arr(n); for (int i = 0; i < n; ++i) { arr[i] = nums[i] - i; } sort(arr.begin(), arr.end()); arr.erase(unique(arr.begin(), arr.end()), arr.end()); int m = arr.size(); BinaryIndexedTree tree(m); for (int i = 0; i < n; ++i) { int j = lower_bound(arr.begin(), arr.end(), nums[i] - i) - arr.begin() + 1; long long v = max(tree.query(j), 0LL) + nums[i]; tree.update(j, v); } return tree.query(m); } };
2,926
Maximum Balanced Subsequence Sum
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub>&nbsp;&lt;&nbsp;i<sub>1</sub> &lt;&nbsp;... &lt; i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p> <ul> <li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] &gt;= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li> </ul> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p> <p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,5,6] <strong>Output:</strong> 14 <strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected. nums[2] - nums[0] &gt;= 2 - 0. nums[3] - nums[2] &gt;= 3 - 2. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. The subsequence consisting of indices 1, 2, and 3 is also valid. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,-1,-3,8] <strong>Output:</strong> 13 <strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected. nums[3] - nums[0] &gt;= 3 - 0. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [-2,-1] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, the subsequence [-1] can be selected. It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li> <li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> </ul>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Dynamic Programming
Go
const inf int = 1e18 type BinaryIndexedTree struct { n int c []int } func NewBinaryIndexedTree(n int) BinaryIndexedTree { c := make([]int, n+1) for i := range c { c[i] = -inf } return BinaryIndexedTree{n: n, c: c} } func (bit *BinaryIndexedTree) update(x, v int) { for x <= bit.n { bit.c[x] = max(bit.c[x], v) x += x & -x } } func (bit *BinaryIndexedTree) query(x int) int { mx := -inf for x > 0 { mx = max(mx, bit.c[x]) x -= x & -x } return mx } func maxBalancedSubsequenceSum(nums []int) int64 { n := len(nums) arr := make([]int, n) for i, x := range nums { arr[i] = x - i } sort.Ints(arr) m := 0 for i, x := range arr { if i == 0 || x != arr[i-1] { arr[m] = x m++ } } arr = arr[:m] tree := NewBinaryIndexedTree(m) for i, x := range nums { j := sort.SearchInts(arr, x-i) + 1 v := max(tree.query(j), 0) + x tree.update(j, v) } return int64(tree.query(m)) }
2,926
Maximum Balanced Subsequence Sum
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub>&nbsp;&lt;&nbsp;i<sub>1</sub> &lt;&nbsp;... &lt; i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p> <ul> <li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] &gt;= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li> </ul> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p> <p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,5,6] <strong>Output:</strong> 14 <strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected. nums[2] - nums[0] &gt;= 2 - 0. nums[3] - nums[2] &gt;= 3 - 2. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. The subsequence consisting of indices 1, 2, and 3 is also valid. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,-1,-3,8] <strong>Output:</strong> 13 <strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected. nums[3] - nums[0] &gt;= 3 - 0. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [-2,-1] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, the subsequence [-1] can be selected. It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li> <li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> </ul>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Dynamic Programming
Java
class BinaryIndexedTree { private int n; private long[] c; private final long inf = 1L << 60; public BinaryIndexedTree(int n) { this.n = n; c = new long[n + 1]; Arrays.fill(c, -inf); } public void update(int x, long v) { while (x <= n) { c[x] = Math.max(c[x], v); x += x & -x; } } public long query(int x) { long mx = -inf; while (x > 0) { mx = Math.max(mx, c[x]); x -= x & -x; } return mx; } } class Solution { public long maxBalancedSubsequenceSum(int[] nums) { int n = nums.length; int[] arr = new int[n]; for (int i = 0; i < n; ++i) { arr[i] = nums[i] - i; } Arrays.sort(arr); int m = 0; for (int i = 0; i < n; ++i) { if (i == 0 || arr[i] != arr[i - 1]) { arr[m++] = arr[i]; } } BinaryIndexedTree tree = new BinaryIndexedTree(m); for (int i = 0; i < n; ++i) { int j = search(arr, nums[i] - i, m) + 1; long v = Math.max(tree.query(j), 0) + nums[i]; tree.update(j, v); } return tree.query(m); } private int search(int[] nums, int x, int r) { int l = 0; while (l < r) { int mid = (l + r) >> 1; if (nums[mid] >= x) { r = mid; } else { l = mid + 1; } } return l; } }
2,926
Maximum Balanced Subsequence Sum
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub>&nbsp;&lt;&nbsp;i<sub>1</sub> &lt;&nbsp;... &lt; i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p> <ul> <li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] &gt;= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li> </ul> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p> <p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,5,6] <strong>Output:</strong> 14 <strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected. nums[2] - nums[0] &gt;= 2 - 0. nums[3] - nums[2] &gt;= 3 - 2. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. The subsequence consisting of indices 1, 2, and 3 is also valid. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,-1,-3,8] <strong>Output:</strong> 13 <strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected. nums[3] - nums[0] &gt;= 3 - 0. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [-2,-1] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, the subsequence [-1] can be selected. It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li> <li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> </ul>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Dynamic Programming
Python
class BinaryIndexedTree: def __init__(self, n: int): self.n = n self.c = [-inf] * (n + 1) def update(self, x: int, v: int): while x <= self.n: self.c[x] = max(self.c[x], v) x += x & -x def query(self, x: int) -> int: mx = -inf while x: mx = max(mx, self.c[x]) x -= x & -x return mx class Solution: def maxBalancedSubsequenceSum(self, nums: List[int]) -> int: arr = [x - i for i, x in enumerate(nums)] s = sorted(set(arr)) tree = BinaryIndexedTree(len(s)) for i, x in enumerate(nums): j = bisect_left(s, x - i) + 1 v = max(tree.query(j), 0) + x tree.update(j, v) return tree.query(len(s))
2,926
Maximum Balanced Subsequence Sum
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub>&nbsp;&lt;&nbsp;i<sub>1</sub> &lt;&nbsp;... &lt; i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p> <ul> <li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] &gt;= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li> </ul> <p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p> <p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,5,6] <strong>Output:</strong> 14 <strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected. nums[2] - nums[0] &gt;= 2 - 0. nums[3] - nums[2] &gt;= 3 - 2. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. The subsequence consisting of indices 1, 2, and 3 is also valid. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,-1,-3,8] <strong>Output:</strong> 13 <strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected. nums[3] - nums[0] &gt;= 3 - 0. Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [-2,-1] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, the subsequence [-1] can be selected. It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li> <li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> </ul>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Dynamic Programming
TypeScript
class BinaryIndexedTree { private n: number; private c: number[]; constructor(n: number) { this.n = n; this.c = Array(n + 1).fill(-Infinity); } update(x: number, v: number): void { while (x <= this.n) { this.c[x] = Math.max(this.c[x], v); x += x & -x; } } query(x: number): number { let mx = -Infinity; while (x > 0) { mx = Math.max(mx, this.c[x]); x -= x & -x; } return mx; } } function maxBalancedSubsequenceSum(nums: number[]): number { const n = nums.length; const arr = Array(n).fill(0); for (let i = 0; i < n; ++i) { arr[i] = nums[i] - i; } arr.sort((a, b) => a - b); let m = 0; for (let i = 0; i < n; ++i) { if (i === 0 || arr[i] !== arr[i - 1]) { arr[m++] = arr[i]; } } arr.length = m; const tree = new BinaryIndexedTree(m); const search = (nums: number[], x: number): number => { let [l, r] = [0, nums.length]; while (l < r) { const mid = (l + r) >> 1; if (nums[mid] >= x) { r = mid; } else { l = mid + 1; } } return l; }; for (let i = 0; i < n; ++i) { const j = search(arr, nums[i] - i) + 1; const v = Math.max(tree.query(j), 0) + nums[i]; tree.update(j, v); } return tree.query(m); }
2,927
Distribute Candies Among Children III
Hard
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>8</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>8</sup></code></li> </ul>
Math; Combinatorics
C++
class Solution { public: long long distributeCandies(int n, int limit) { auto comb2 = [](int n) { return 1LL * n * (n - 1) / 2; }; if (n > 3 * limit) { return 0; } long long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; } };
2,927
Distribute Candies Among Children III
Hard
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>8</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>8</sup></code></li> </ul>
Math; Combinatorics
Go
func distributeCandies(n int, limit int) int64 { comb2 := func(n int) int { return n * (n - 1) / 2 } if n > 3*limit { return 0 } ans := comb2(n + 2) if n > limit { ans -= 3 * comb2(n-limit+1) } if n-2 >= 2*limit { ans += 3 * comb2(n-2*limit) } return int64(ans) }
2,927
Distribute Candies Among Children III
Hard
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>8</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>8</sup></code></li> </ul>
Math; Combinatorics
Java
class Solution { public long distributeCandies(int n, int limit) { if (n > 3 * limit) { return 0; } long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; } private long comb2(int n) { return 1L * n * (n - 1) / 2; } }
2,927
Distribute Candies Among Children III
Hard
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>8</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>8</sup></code></li> </ul>
Math; Combinatorics
Python
class Solution: def distributeCandies(self, n: int, limit: int) -> int: if n > 3 * limit: return 0 ans = comb(n + 2, 2) if n > limit: ans -= 3 * comb(n - limit + 1, 2) if n - 2 >= 2 * limit: ans += 3 * comb(n - 2 * limit, 2) return ans
2,927
Distribute Candies Among Children III
Hard
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>8</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>8</sup></code></li> </ul>
Math; Combinatorics
TypeScript
function distributeCandies(n: number, limit: number): number { const comb2 = (n: number) => (n * (n - 1)) / 2; if (n > 3 * limit) { return 0; } let ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; }
2,928
Distribute Candies Among Children I
Easy
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 50</code></li> <li><code>1 &lt;= limit &lt;= 50</code></li> </ul>
Math; Combinatorics; Enumeration
C++
class Solution { public: int distributeCandies(int n, int limit) { auto comb2 = [](int n) { return 1LL * n * (n - 1) / 2; }; if (n > 3 * limit) { return 0; } long long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; } };
2,928
Distribute Candies Among Children I
Easy
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 50</code></li> <li><code>1 &lt;= limit &lt;= 50</code></li> </ul>
Math; Combinatorics; Enumeration
Go
func distributeCandies(n int, limit int) int { comb2 := func(n int) int { return n * (n - 1) / 2 } if n > 3*limit { return 0 } ans := comb2(n + 2) if n > limit { ans -= 3 * comb2(n-limit+1) } if n-2 >= 2*limit { ans += 3 * comb2(n-2*limit) } return ans }
2,928
Distribute Candies Among Children I
Easy
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 50</code></li> <li><code>1 &lt;= limit &lt;= 50</code></li> </ul>
Math; Combinatorics; Enumeration
Java
class Solution { public int distributeCandies(int n, int limit) { if (n > 3 * limit) { return 0; } long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return (int) ans; } private long comb2(int n) { return 1L * n * (n - 1) / 2; } }
2,928
Distribute Candies Among Children I
Easy
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 50</code></li> <li><code>1 &lt;= limit &lt;= 50</code></li> </ul>
Math; Combinatorics; Enumeration
Python
class Solution: def distributeCandies(self, n: int, limit: int) -> int: if n > 3 * limit: return 0 ans = comb(n + 2, 2) if n > limit: ans -= 3 * comb(n - limit + 1, 2) if n - 2 >= 2 * limit: ans += 3 * comb(n - 2 * limit, 2) return ans
2,928
Distribute Candies Among Children I
Easy
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 50</code></li> <li><code>1 &lt;= limit &lt;= 50</code></li> </ul>
Math; Combinatorics; Enumeration
TypeScript
function distributeCandies(n: number, limit: number): number { const comb2 = (n: number) => (n * (n - 1)) / 2; if (n > 3 * limit) { return 0; } let ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; }
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
C++
class Solution { public: long long distributeCandies(int n, int limit) { auto comb2 = [](int n) { return 1LL * n * (n - 1) / 2; }; if (n > 3 * limit) { return 0; } long long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; } };
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
Go
func distributeCandies(n int, limit int) int64 { comb2 := func(n int) int { return n * (n - 1) / 2 } if n > 3*limit { return 0 } ans := comb2(n + 2) if n > limit { ans -= 3 * comb2(n-limit+1) } if n-2 >= 2*limit { ans += 3 * comb2(n-2*limit) } return int64(ans) }
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
Java
class Solution { public long distributeCandies(int n, int limit) { if (n > 3 * limit) { return 0; } long ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; } private long comb2(int n) { return 1L * n * (n - 1) / 2; } }
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
Python
class Solution: def distributeCandies(self, n: int, limit: int) -> int: if n > 3 * limit: return 0 ans = comb(n + 2, 2) if n > limit: ans -= 3 * comb(n - limit + 1, 2) if n - 2 >= 2 * limit: ans += 3 * comb(n - 2 * limit, 2) return ans
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
Rust
impl Solution { pub fn distribute_candies(n: i32, limit: i32) -> i64 { if n > 3 * limit { return 0; } let mut ans = Self::comb2(n + 2); if n > limit { ans -= 3 * Self::comb2(n - limit + 1); } if n - 2 >= 2 * limit { ans += 3 * Self::comb2(n - 2 * limit); } ans } fn comb2(n: i32) -> i64 { (n as i64) * (n as i64 - 1) / 2 } }
2,929
Distribute Candies Among Children II
Medium
<p>You are given two positive integers <code>n</code> and <code>limit</code>.</p> <p>Return <em>the <strong>total number</strong> of ways to distribute </em><code>n</code> <em>candies among </em><code>3</code><em> children such that no child gets more than </em><code>limit</code><em> candies.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 5, limit = 2 <strong>Output:</strong> 3 <strong>Explanation:</strong> There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 3, limit = 3 <strong>Output:</strong> 10 <strong>Explanation:</strong> There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0). </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= limit &lt;= 10<sup>6</sup></code></li> </ul>
Math; Combinatorics; Enumeration
TypeScript
function distributeCandies(n: number, limit: number): number { const comb2 = (n: number) => (n * (n - 1)) / 2; if (n > 3 * limit) { return 0; } let ans = comb2(n + 2); if (n > limit) { ans -= 3 * comb2(n - limit + 1); } if (n - 2 >= 2 * limit) { ans += 3 * comb2(n - 2 * limit); } return ans; }
2,930
Number of Strings Which Can Be Rearranged to Contain Substring
Medium
<p>You are given an integer <code>n</code>.</p> <p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p> <p>For example:</p> <ul> <li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li> <li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li> </ul> <p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p> <p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p> <p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p> <div class="notranslate" style="all: initial;">&nbsp;</div> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 12 <strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 83943898 <strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> </ul>
Math; Dynamic Programming; Combinatorics
C++
class Solution { public: int stringCount(int n) { const int mod = 1e9 + 7; using ll = long long; ll f[n + 1][2][3][2]; memset(f, -1, sizeof(f)); function<ll(int, int, int, int)> dfs = [&](int i, int l, int e, int t) -> ll { if (i == 0) { return l == 1 && e == 2 && t == 1 ? 1 : 0; } if (f[i][l][e][t] != -1) { return f[i][l][e][t]; } ll a = dfs(i - 1, l, e, t) * 23 % mod; ll b = dfs(i - 1, min(1, l + 1), e, t) % mod; ll c = dfs(i - 1, l, min(2, e + 1), t) % mod; ll d = dfs(i - 1, l, e, min(1, t + 1)) % mod; return f[i][l][e][t] = (a + b + c + d) % mod; }; return dfs(n, 0, 0, 0); } };
2,930
Number of Strings Which Can Be Rearranged to Contain Substring
Medium
<p>You are given an integer <code>n</code>.</p> <p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p> <p>For example:</p> <ul> <li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li> <li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li> </ul> <p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p> <p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p> <p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p> <div class="notranslate" style="all: initial;">&nbsp;</div> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 12 <strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 83943898 <strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> </ul>
Math; Dynamic Programming; Combinatorics
Go
func stringCount(n int) int { const mod int = 1e9 + 7 f := make([][2][3][2]int, n+1) for i := range f { for j := range f[i] { for k := range f[i][j] { for l := range f[i][j][k] { f[i][j][k][l] = -1 } } } } var dfs func(i, l, e, t int) int dfs = func(i, l, e, t int) int { if i == 0 { if l == 1 && e == 2 && t == 1 { return 1 } return 0 } if f[i][l][e][t] == -1 { a := dfs(i-1, l, e, t) * 23 % mod b := dfs(i-1, min(1, l+1), e, t) c := dfs(i-1, l, min(2, e+1), t) d := dfs(i-1, l, e, min(1, t+1)) f[i][l][e][t] = (a + b + c + d) % mod } return f[i][l][e][t] } return dfs(n, 0, 0, 0) }
2,930
Number of Strings Which Can Be Rearranged to Contain Substring
Medium
<p>You are given an integer <code>n</code>.</p> <p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p> <p>For example:</p> <ul> <li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li> <li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li> </ul> <p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p> <p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p> <p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p> <div class="notranslate" style="all: initial;">&nbsp;</div> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 12 <strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 83943898 <strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> </ul>
Math; Dynamic Programming; Combinatorics
Java
class Solution { private final int mod = (int) 1e9 + 7; private Long[][][][] f; public int stringCount(int n) { f = new Long[n + 1][2][3][2]; return (int) dfs(n, 0, 0, 0); } private long dfs(int i, int l, int e, int t) { if (i == 0) { return l == 1 && e == 2 && t == 1 ? 1 : 0; } if (f[i][l][e][t] != null) { return f[i][l][e][t]; } long a = dfs(i - 1, l, e, t) * 23 % mod; long b = dfs(i - 1, Math.min(1, l + 1), e, t); long c = dfs(i - 1, l, Math.min(2, e + 1), t); long d = dfs(i - 1, l, e, Math.min(1, t + 1)); return f[i][l][e][t] = (a + b + c + d) % mod; } }
2,930
Number of Strings Which Can Be Rearranged to Contain Substring
Medium
<p>You are given an integer <code>n</code>.</p> <p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p> <p>For example:</p> <ul> <li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li> <li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li> </ul> <p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p> <p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p> <p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p> <div class="notranslate" style="all: initial;">&nbsp;</div> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 12 <strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 83943898 <strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> </ul>
Math; Dynamic Programming; Combinatorics
Python
class Solution: def stringCount(self, n: int) -> int: @cache def dfs(i: int, l: int, e: int, t: int) -> int: if i == 0: return int(l == 1 and e == 2 and t == 1) a = dfs(i - 1, l, e, t) * 23 % mod b = dfs(i - 1, min(1, l + 1), e, t) c = dfs(i - 1, l, min(2, e + 1), t) d = dfs(i - 1, l, e, min(1, t + 1)) return (a + b + c + d) % mod mod = 10**9 + 7 return dfs(n, 0, 0, 0)
2,930
Number of Strings Which Can Be Rearranged to Contain Substring
Medium
<p>You are given an integer <code>n</code>.</p> <p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p> <p>For example:</p> <ul> <li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li> <li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li> </ul> <p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p> <p>Since the answer may be large, return it <strong>modulo </strong><code>10<sup>9</sup> + 7</code>.</p> <p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p> <div class="notranslate" style="all: initial;">&nbsp;</div> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 12 <strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 83943898 <strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> </ul>
Math; Dynamic Programming; Combinatorics
TypeScript
function stringCount(n: number): number { const mod = 10 ** 9 + 7; const f: number[][][][] = Array.from({ length: n + 1 }, () => Array.from({ length: 2 }, () => Array.from({ length: 3 }, () => Array.from({ length: 2 }, () => -1)), ), ); const dfs = (i: number, l: number, e: number, t: number): number => { if (i === 0) { return l === 1 && e === 2 && t === 1 ? 1 : 0; } if (f[i][l][e][t] !== -1) { return f[i][l][e][t]; } const a = (dfs(i - 1, l, e, t) * 23) % mod; const b = dfs(i - 1, Math.min(1, l + 1), e, t); const c = dfs(i - 1, l, Math.min(2, e + 1), t); const d = dfs(i - 1, l, e, Math.min(1, t + 1)); return (f[i][l][e][t] = (a + b + c + d) % mod); }; return dfs(n, 0, 0, 0); }
2,931
Maximum Spending After Buying Items
Hard
<p>You are given a <strong>0-indexed</strong> <code>m * n</code> integer matrix <code>values</code>, representing the values of <code>m * n</code> different items in <code>m</code> different shops. Each shop has <code>n</code> items where the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> shop has a value of <code>values[i][j]</code>. Additionally, the items in the <code>i<sup>th</sup></code> shop are sorted in non-increasing order of value. That is, <code>values[i][j] &gt;= values[i][j + 1]</code> for all <code>0 &lt;= j &lt; n - 1</code>.</p> <p>On each day, you would like to buy a single item from one of the shops. Specifically, On the <code>d<sup>th</sup></code> day you can:</p> <ul> <li>Pick any shop <code>i</code>.</li> <li>Buy the rightmost available item <code>j</code> for the price of <code>values[i][j] * d</code>. That is, find the greatest index <code>j</code> such that item <code>j</code> was never bought before, and buy it for the price of <code>values[i][j] * d</code>.</li> </ul> <p><strong>Note</strong> that all items are pairwise different. For example, if you have bought item <code>0</code> from shop <code>1</code>, you can still buy item <code>0</code> from any other shop.</p> <p>Return <em>the <strong>maximum amount of money that can be spent</strong> on buying all </em> <code>m * n</code> <em>products</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> values = [[8,5,2],[6,4,1],[9,7,3]] <strong>Output:</strong> 285 <strong>Explanation:</strong> On the first day, we buy product 2 from shop 1 for a price of values[1][2] * 1 = 1. On the second day, we buy product 2 from shop 0 for a price of values[0][2] * 2 = 4. On the third day, we buy product 2 from shop 2 for a price of values[2][2] * 3 = 9. On the fourth day, we buy product 1 from shop 1 for a price of values[1][1] * 4 = 16. On the fifth day, we buy product 1 from shop 0 for a price of values[0][1] * 5 = 25. On the sixth day, we buy product 0 from shop 1 for a price of values[1][0] * 6 = 36. On the seventh day, we buy product 1 from shop 2 for a price of values[2][1] * 7 = 49. On the eighth day, we buy product 0 from shop 0 for a price of values[0][0] * 8 = 64. On the ninth day, we buy product 0 from shop 2 for a price of values[2][0] * 9 = 81. Hence, our total spending is equal to 285. It can be shown that 285 is the maximum amount of money that can be spent buying all m * n products. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> values = [[10,8,6,4,2],[9,7,5,3,2]] <strong>Output:</strong> 386 <strong>Explanation:</strong> On the first day, we buy product 4 from shop 0 for a price of values[0][4] * 1 = 2. On the second day, we buy product 4 from shop 1 for a price of values[1][4] * 2 = 4. On the third day, we buy product 3 from shop 1 for a price of values[1][3] * 3 = 9. On the fourth day, we buy product 3 from shop 0 for a price of values[0][3] * 4 = 16. On the fifth day, we buy product 2 from shop 1 for a price of values[1][2] * 5 = 25. On the sixth day, we buy product 2 from shop 0 for a price of values[0][2] * 6 = 36. On the seventh day, we buy product 1 from shop 1 for a price of values[1][1] * 7 = 49. On the eighth day, we buy product 1 from shop 0 for a price of values[0][1] * 8 = 64 On the ninth day, we buy product 0 from shop 1 for a price of values[1][0] * 9 = 81. On the tenth day, we buy product 0 from shop 0 for a price of values[0][0] * 10 = 100. Hence, our total spending is equal to 386. It can be shown that 386 is the maximum amount of money that can be spent buying all m * n products. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= m == values.length &lt;= 10</code></li> <li><code>1 &lt;= n == values[i].length &lt;= 10<sup>4</sup></code></li> <li><code>1 &lt;= values[i][j] &lt;= 10<sup>6</sup></code></li> <li><code>values[i]</code> are sorted in non-increasing order.</li> </ul>
Greedy; Array; Matrix; Sorting; Heap (Priority Queue)
C++
class Solution { public: long long maxSpending(vector<vector<int>>& values) { priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq; int m = values.size(), n = values[0].size(); for (int i = 0; i < m; ++i) { pq.emplace(values[i][n - 1], i, n - 1); } long long ans = 0; for (int d = 1; pq.size(); ++d) { auto [v, i, j] = pq.top(); pq.pop(); ans += 1LL * v * d; if (j) { pq.emplace(values[i][j - 1], i, j - 1); } } return ans; } };
2,931
Maximum Spending After Buying Items
Hard
<p>You are given a <strong>0-indexed</strong> <code>m * n</code> integer matrix <code>values</code>, representing the values of <code>m * n</code> different items in <code>m</code> different shops. Each shop has <code>n</code> items where the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> shop has a value of <code>values[i][j]</code>. Additionally, the items in the <code>i<sup>th</sup></code> shop are sorted in non-increasing order of value. That is, <code>values[i][j] &gt;= values[i][j + 1]</code> for all <code>0 &lt;= j &lt; n - 1</code>.</p> <p>On each day, you would like to buy a single item from one of the shops. Specifically, On the <code>d<sup>th</sup></code> day you can:</p> <ul> <li>Pick any shop <code>i</code>.</li> <li>Buy the rightmost available item <code>j</code> for the price of <code>values[i][j] * d</code>. That is, find the greatest index <code>j</code> such that item <code>j</code> was never bought before, and buy it for the price of <code>values[i][j] * d</code>.</li> </ul> <p><strong>Note</strong> that all items are pairwise different. For example, if you have bought item <code>0</code> from shop <code>1</code>, you can still buy item <code>0</code> from any other shop.</p> <p>Return <em>the <strong>maximum amount of money that can be spent</strong> on buying all </em> <code>m * n</code> <em>products</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> values = [[8,5,2],[6,4,1],[9,7,3]] <strong>Output:</strong> 285 <strong>Explanation:</strong> On the first day, we buy product 2 from shop 1 for a price of values[1][2] * 1 = 1. On the second day, we buy product 2 from shop 0 for a price of values[0][2] * 2 = 4. On the third day, we buy product 2 from shop 2 for a price of values[2][2] * 3 = 9. On the fourth day, we buy product 1 from shop 1 for a price of values[1][1] * 4 = 16. On the fifth day, we buy product 1 from shop 0 for a price of values[0][1] * 5 = 25. On the sixth day, we buy product 0 from shop 1 for a price of values[1][0] * 6 = 36. On the seventh day, we buy product 1 from shop 2 for a price of values[2][1] * 7 = 49. On the eighth day, we buy product 0 from shop 0 for a price of values[0][0] * 8 = 64. On the ninth day, we buy product 0 from shop 2 for a price of values[2][0] * 9 = 81. Hence, our total spending is equal to 285. It can be shown that 285 is the maximum amount of money that can be spent buying all m * n products. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> values = [[10,8,6,4,2],[9,7,5,3,2]] <strong>Output:</strong> 386 <strong>Explanation:</strong> On the first day, we buy product 4 from shop 0 for a price of values[0][4] * 1 = 2. On the second day, we buy product 4 from shop 1 for a price of values[1][4] * 2 = 4. On the third day, we buy product 3 from shop 1 for a price of values[1][3] * 3 = 9. On the fourth day, we buy product 3 from shop 0 for a price of values[0][3] * 4 = 16. On the fifth day, we buy product 2 from shop 1 for a price of values[1][2] * 5 = 25. On the sixth day, we buy product 2 from shop 0 for a price of values[0][2] * 6 = 36. On the seventh day, we buy product 1 from shop 1 for a price of values[1][1] * 7 = 49. On the eighth day, we buy product 1 from shop 0 for a price of values[0][1] * 8 = 64 On the ninth day, we buy product 0 from shop 1 for a price of values[1][0] * 9 = 81. On the tenth day, we buy product 0 from shop 0 for a price of values[0][0] * 10 = 100. Hence, our total spending is equal to 386. It can be shown that 386 is the maximum amount of money that can be spent buying all m * n products. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= m == values.length &lt;= 10</code></li> <li><code>1 &lt;= n == values[i].length &lt;= 10<sup>4</sup></code></li> <li><code>1 &lt;= values[i][j] &lt;= 10<sup>6</sup></code></li> <li><code>values[i]</code> are sorted in non-increasing order.</li> </ul>
Greedy; Array; Matrix; Sorting; Heap (Priority Queue)
Go
func maxSpending(values [][]int) (ans int64) { pq := hp{} n := len(values[0]) for i, row := range values { heap.Push(&pq, tuple{row[n-1], i, n - 1}) } for d := 1; len(pq) > 0; d++ { p := heap.Pop(&pq).(tuple) ans += int64(p.v * d) if p.j > 0 { heap.Push(&pq, tuple{values[p.i][p.j-1], p.i, p.j - 1}) } } return } type tuple struct{ v, i, j int } type hp []tuple func (h hp) Len() int { return len(h) } func (h hp) Less(i, j int) bool { return h[i].v < h[j].v } func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] } func (h *hp) Push(v any) { *h = append(*h, v.(tuple)) } func (h *hp) Pop() any { a := *h; v := a[len(a)-1]; *h = a[:len(a)-1]; return v }
2,931
Maximum Spending After Buying Items
Hard
<p>You are given a <strong>0-indexed</strong> <code>m * n</code> integer matrix <code>values</code>, representing the values of <code>m * n</code> different items in <code>m</code> different shops. Each shop has <code>n</code> items where the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> shop has a value of <code>values[i][j]</code>. Additionally, the items in the <code>i<sup>th</sup></code> shop are sorted in non-increasing order of value. That is, <code>values[i][j] &gt;= values[i][j + 1]</code> for all <code>0 &lt;= j &lt; n - 1</code>.</p> <p>On each day, you would like to buy a single item from one of the shops. Specifically, On the <code>d<sup>th</sup></code> day you can:</p> <ul> <li>Pick any shop <code>i</code>.</li> <li>Buy the rightmost available item <code>j</code> for the price of <code>values[i][j] * d</code>. That is, find the greatest index <code>j</code> such that item <code>j</code> was never bought before, and buy it for the price of <code>values[i][j] * d</code>.</li> </ul> <p><strong>Note</strong> that all items are pairwise different. For example, if you have bought item <code>0</code> from shop <code>1</code>, you can still buy item <code>0</code> from any other shop.</p> <p>Return <em>the <strong>maximum amount of money that can be spent</strong> on buying all </em> <code>m * n</code> <em>products</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> values = [[8,5,2],[6,4,1],[9,7,3]] <strong>Output:</strong> 285 <strong>Explanation:</strong> On the first day, we buy product 2 from shop 1 for a price of values[1][2] * 1 = 1. On the second day, we buy product 2 from shop 0 for a price of values[0][2] * 2 = 4. On the third day, we buy product 2 from shop 2 for a price of values[2][2] * 3 = 9. On the fourth day, we buy product 1 from shop 1 for a price of values[1][1] * 4 = 16. On the fifth day, we buy product 1 from shop 0 for a price of values[0][1] * 5 = 25. On the sixth day, we buy product 0 from shop 1 for a price of values[1][0] * 6 = 36. On the seventh day, we buy product 1 from shop 2 for a price of values[2][1] * 7 = 49. On the eighth day, we buy product 0 from shop 0 for a price of values[0][0] * 8 = 64. On the ninth day, we buy product 0 from shop 2 for a price of values[2][0] * 9 = 81. Hence, our total spending is equal to 285. It can be shown that 285 is the maximum amount of money that can be spent buying all m * n products. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> values = [[10,8,6,4,2],[9,7,5,3,2]] <strong>Output:</strong> 386 <strong>Explanation:</strong> On the first day, we buy product 4 from shop 0 for a price of values[0][4] * 1 = 2. On the second day, we buy product 4 from shop 1 for a price of values[1][4] * 2 = 4. On the third day, we buy product 3 from shop 1 for a price of values[1][3] * 3 = 9. On the fourth day, we buy product 3 from shop 0 for a price of values[0][3] * 4 = 16. On the fifth day, we buy product 2 from shop 1 for a price of values[1][2] * 5 = 25. On the sixth day, we buy product 2 from shop 0 for a price of values[0][2] * 6 = 36. On the seventh day, we buy product 1 from shop 1 for a price of values[1][1] * 7 = 49. On the eighth day, we buy product 1 from shop 0 for a price of values[0][1] * 8 = 64 On the ninth day, we buy product 0 from shop 1 for a price of values[1][0] * 9 = 81. On the tenth day, we buy product 0 from shop 0 for a price of values[0][0] * 10 = 100. Hence, our total spending is equal to 386. It can be shown that 386 is the maximum amount of money that can be spent buying all m * n products. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= m == values.length &lt;= 10</code></li> <li><code>1 &lt;= n == values[i].length &lt;= 10<sup>4</sup></code></li> <li><code>1 &lt;= values[i][j] &lt;= 10<sup>6</sup></code></li> <li><code>values[i]</code> are sorted in non-increasing order.</li> </ul>
Greedy; Array; Matrix; Sorting; Heap (Priority Queue)
Java
class Solution { public long maxSpending(int[][] values) { int m = values.length, n = values[0].length; PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]); for (int i = 0; i < m; ++i) { pq.offer(new int[] {values[i][n - 1], i, n - 1}); } long ans = 0; for (int d = 1; !pq.isEmpty(); ++d) { var p = pq.poll(); int v = p[0], i = p[1], j = p[2]; ans += (long) v * d; if (j > 0) { pq.offer(new int[] {values[i][j - 1], i, j - 1}); } } return ans; } }
2,931
Maximum Spending After Buying Items
Hard
<p>You are given a <strong>0-indexed</strong> <code>m * n</code> integer matrix <code>values</code>, representing the values of <code>m * n</code> different items in <code>m</code> different shops. Each shop has <code>n</code> items where the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> shop has a value of <code>values[i][j]</code>. Additionally, the items in the <code>i<sup>th</sup></code> shop are sorted in non-increasing order of value. That is, <code>values[i][j] &gt;= values[i][j + 1]</code> for all <code>0 &lt;= j &lt; n - 1</code>.</p> <p>On each day, you would like to buy a single item from one of the shops. Specifically, On the <code>d<sup>th</sup></code> day you can:</p> <ul> <li>Pick any shop <code>i</code>.</li> <li>Buy the rightmost available item <code>j</code> for the price of <code>values[i][j] * d</code>. That is, find the greatest index <code>j</code> such that item <code>j</code> was never bought before, and buy it for the price of <code>values[i][j] * d</code>.</li> </ul> <p><strong>Note</strong> that all items are pairwise different. For example, if you have bought item <code>0</code> from shop <code>1</code>, you can still buy item <code>0</code> from any other shop.</p> <p>Return <em>the <strong>maximum amount of money that can be spent</strong> on buying all </em> <code>m * n</code> <em>products</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> values = [[8,5,2],[6,4,1],[9,7,3]] <strong>Output:</strong> 285 <strong>Explanation:</strong> On the first day, we buy product 2 from shop 1 for a price of values[1][2] * 1 = 1. On the second day, we buy product 2 from shop 0 for a price of values[0][2] * 2 = 4. On the third day, we buy product 2 from shop 2 for a price of values[2][2] * 3 = 9. On the fourth day, we buy product 1 from shop 1 for a price of values[1][1] * 4 = 16. On the fifth day, we buy product 1 from shop 0 for a price of values[0][1] * 5 = 25. On the sixth day, we buy product 0 from shop 1 for a price of values[1][0] * 6 = 36. On the seventh day, we buy product 1 from shop 2 for a price of values[2][1] * 7 = 49. On the eighth day, we buy product 0 from shop 0 for a price of values[0][0] * 8 = 64. On the ninth day, we buy product 0 from shop 2 for a price of values[2][0] * 9 = 81. Hence, our total spending is equal to 285. It can be shown that 285 is the maximum amount of money that can be spent buying all m * n products. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> values = [[10,8,6,4,2],[9,7,5,3,2]] <strong>Output:</strong> 386 <strong>Explanation:</strong> On the first day, we buy product 4 from shop 0 for a price of values[0][4] * 1 = 2. On the second day, we buy product 4 from shop 1 for a price of values[1][4] * 2 = 4. On the third day, we buy product 3 from shop 1 for a price of values[1][3] * 3 = 9. On the fourth day, we buy product 3 from shop 0 for a price of values[0][3] * 4 = 16. On the fifth day, we buy product 2 from shop 1 for a price of values[1][2] * 5 = 25. On the sixth day, we buy product 2 from shop 0 for a price of values[0][2] * 6 = 36. On the seventh day, we buy product 1 from shop 1 for a price of values[1][1] * 7 = 49. On the eighth day, we buy product 1 from shop 0 for a price of values[0][1] * 8 = 64 On the ninth day, we buy product 0 from shop 1 for a price of values[1][0] * 9 = 81. On the tenth day, we buy product 0 from shop 0 for a price of values[0][0] * 10 = 100. Hence, our total spending is equal to 386. It can be shown that 386 is the maximum amount of money that can be spent buying all m * n products. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= m == values.length &lt;= 10</code></li> <li><code>1 &lt;= n == values[i].length &lt;= 10<sup>4</sup></code></li> <li><code>1 &lt;= values[i][j] &lt;= 10<sup>6</sup></code></li> <li><code>values[i]</code> are sorted in non-increasing order.</li> </ul>
Greedy; Array; Matrix; Sorting; Heap (Priority Queue)
Python
class Solution: def maxSpending(self, values: List[List[int]]) -> int: n = len(values[0]) pq = [(row[-1], i, n - 1) for i, row in enumerate(values)] heapify(pq) ans = d = 0 while pq: d += 1 v, i, j = heappop(pq) ans += v * d if j: heappush(pq, (values[i][j - 1], i, j - 1)) return ans
2,931
Maximum Spending After Buying Items
Hard
<p>You are given a <strong>0-indexed</strong> <code>m * n</code> integer matrix <code>values</code>, representing the values of <code>m * n</code> different items in <code>m</code> different shops. Each shop has <code>n</code> items where the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> shop has a value of <code>values[i][j]</code>. Additionally, the items in the <code>i<sup>th</sup></code> shop are sorted in non-increasing order of value. That is, <code>values[i][j] &gt;= values[i][j + 1]</code> for all <code>0 &lt;= j &lt; n - 1</code>.</p> <p>On each day, you would like to buy a single item from one of the shops. Specifically, On the <code>d<sup>th</sup></code> day you can:</p> <ul> <li>Pick any shop <code>i</code>.</li> <li>Buy the rightmost available item <code>j</code> for the price of <code>values[i][j] * d</code>. That is, find the greatest index <code>j</code> such that item <code>j</code> was never bought before, and buy it for the price of <code>values[i][j] * d</code>.</li> </ul> <p><strong>Note</strong> that all items are pairwise different. For example, if you have bought item <code>0</code> from shop <code>1</code>, you can still buy item <code>0</code> from any other shop.</p> <p>Return <em>the <strong>maximum amount of money that can be spent</strong> on buying all </em> <code>m * n</code> <em>products</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> values = [[8,5,2],[6,4,1],[9,7,3]] <strong>Output:</strong> 285 <strong>Explanation:</strong> On the first day, we buy product 2 from shop 1 for a price of values[1][2] * 1 = 1. On the second day, we buy product 2 from shop 0 for a price of values[0][2] * 2 = 4. On the third day, we buy product 2 from shop 2 for a price of values[2][2] * 3 = 9. On the fourth day, we buy product 1 from shop 1 for a price of values[1][1] * 4 = 16. On the fifth day, we buy product 1 from shop 0 for a price of values[0][1] * 5 = 25. On the sixth day, we buy product 0 from shop 1 for a price of values[1][0] * 6 = 36. On the seventh day, we buy product 1 from shop 2 for a price of values[2][1] * 7 = 49. On the eighth day, we buy product 0 from shop 0 for a price of values[0][0] * 8 = 64. On the ninth day, we buy product 0 from shop 2 for a price of values[2][0] * 9 = 81. Hence, our total spending is equal to 285. It can be shown that 285 is the maximum amount of money that can be spent buying all m * n products. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> values = [[10,8,6,4,2],[9,7,5,3,2]] <strong>Output:</strong> 386 <strong>Explanation:</strong> On the first day, we buy product 4 from shop 0 for a price of values[0][4] * 1 = 2. On the second day, we buy product 4 from shop 1 for a price of values[1][4] * 2 = 4. On the third day, we buy product 3 from shop 1 for a price of values[1][3] * 3 = 9. On the fourth day, we buy product 3 from shop 0 for a price of values[0][3] * 4 = 16. On the fifth day, we buy product 2 from shop 1 for a price of values[1][2] * 5 = 25. On the sixth day, we buy product 2 from shop 0 for a price of values[0][2] * 6 = 36. On the seventh day, we buy product 1 from shop 1 for a price of values[1][1] * 7 = 49. On the eighth day, we buy product 1 from shop 0 for a price of values[0][1] * 8 = 64 On the ninth day, we buy product 0 from shop 1 for a price of values[1][0] * 9 = 81. On the tenth day, we buy product 0 from shop 0 for a price of values[0][0] * 10 = 100. Hence, our total spending is equal to 386. It can be shown that 386 is the maximum amount of money that can be spent buying all m * n products. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= m == values.length &lt;= 10</code></li> <li><code>1 &lt;= n == values[i].length &lt;= 10<sup>4</sup></code></li> <li><code>1 &lt;= values[i][j] &lt;= 10<sup>6</sup></code></li> <li><code>values[i]</code> are sorted in non-increasing order.</li> </ul>
Greedy; Array; Matrix; Sorting; Heap (Priority Queue)
TypeScript
function maxSpending(values: number[][]): number { const m = values.length; const n = values[0].length; const pq = new PriorityQueue({ compare: (a, b) => a[0] - b[0] }); for (let i = 0; i < m; ++i) { pq.enqueue([values[i][n - 1], i, n - 1]); } let ans = 0; for (let d = 1; !pq.isEmpty(); ++d) { const [v, i, j] = pq.dequeue()!; ans += v * d; if (j > 0) { pq.enqueue([values[i][j - 1], i, j - 1]); } } return ans; }
2,932
Maximum Strong Pair XOR I
Easy
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array <code>nums</code>: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,25,30] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 6 strong pairs in the array <code>nums</code>: (5, 5), (5, 6), (6, 6), (25, 25), (25, 30) and (30, 30). The maximum XOR possible from these pairs is 25 XOR 30 = 7 since the only other non-zero XOR value is 5 XOR 6 = 3. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 50</code></li> <li><code>1 &lt;= nums[i] &lt;= 100</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
C++
class Solution { public: int maximumStrongPairXor(vector<int>& nums) { int ans = 0; for (int x : nums) { for (int y : nums) { if (abs(x - y) <= min(x, y)) { ans = max(ans, x ^ y); } } } return ans; } };
2,932
Maximum Strong Pair XOR I
Easy
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array <code>nums</code>: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,25,30] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 6 strong pairs in the array <code>nums</code>: (5, 5), (5, 6), (6, 6), (25, 25), (25, 30) and (30, 30). The maximum XOR possible from these pairs is 25 XOR 30 = 7 since the only other non-zero XOR value is 5 XOR 6 = 3. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 50</code></li> <li><code>1 &lt;= nums[i] &lt;= 100</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Go
func maximumStrongPairXor(nums []int) (ans int) { for _, x := range nums { for _, y := range nums { if abs(x-y) <= min(x, y) { ans = max(ans, x^y) } } } return } func abs(x int) int { if x < 0 { return -x } return x }
2,932
Maximum Strong Pair XOR I
Easy
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array <code>nums</code>: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,25,30] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 6 strong pairs in the array <code>nums</code>: (5, 5), (5, 6), (6, 6), (25, 25), (25, 30) and (30, 30). The maximum XOR possible from these pairs is 25 XOR 30 = 7 since the only other non-zero XOR value is 5 XOR 6 = 3. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 50</code></li> <li><code>1 &lt;= nums[i] &lt;= 100</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Java
class Solution { public int maximumStrongPairXor(int[] nums) { int ans = 0; for (int x : nums) { for (int y : nums) { if (Math.abs(x - y) <= Math.min(x, y)) { ans = Math.max(ans, x ^ y); } } } return ans; } }
2,932
Maximum Strong Pair XOR I
Easy
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array <code>nums</code>: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,25,30] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 6 strong pairs in the array <code>nums</code>: (5, 5), (5, 6), (6, 6), (25, 25), (25, 30) and (30, 30). The maximum XOR possible from these pairs is 25 XOR 30 = 7 since the only other non-zero XOR value is 5 XOR 6 = 3. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 50</code></li> <li><code>1 &lt;= nums[i] &lt;= 100</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Python
class Solution: def maximumStrongPairXor(self, nums: List[int]) -> int: return max(x ^ y for x in nums for y in nums if abs(x - y) <= min(x, y))
2,932
Maximum Strong Pair XOR I
Easy
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array <code>nums</code>: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,25,30] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 6 strong pairs in the array <code>nums</code>: (5, 5), (5, 6), (6, 6), (25, 25), (25, 30) and (30, 30). The maximum XOR possible from these pairs is 25 XOR 30 = 7 since the only other non-zero XOR value is 5 XOR 6 = 3. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 50</code></li> <li><code>1 &lt;= nums[i] &lt;= 100</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
TypeScript
function maximumStrongPairXor(nums: number[]): number { let ans = 0; for (const x of nums) { for (const y of nums) { if (Math.abs(x - y) <= Math.min(x, y)) { ans = Math.max(ans, x ^ y); } } } return ans; }
2,933
High-Access Employees
Medium
<p>You are given a 2D <strong>0-indexed</strong> array of strings, <code>access_times</code>, with size <code>n</code>. For each <code>i</code> where <code>0 &lt;= i &lt;= n - 1</code>, <code>access_times[i][0]</code> represents the name of an employee, and <code>access_times[i][1]</code> represents the access time of that employee. All entries in <code>access_times</code> are within the same day.</p> <p>The access time is represented as <strong>four digits</strong> using a <strong>24-hour</strong> time format, for example, <code>&quot;0800&quot;</code> or <code>&quot;2250&quot;</code>.</p> <p>An employee is said to be <strong>high-access</strong> if he has accessed the system <strong>three or more</strong> times within a <strong>one-hour period</strong>.</p> <p>Times with exactly one hour of difference are <strong>not</strong> considered part of the same one-hour period. For example, <code>&quot;0815&quot;</code> and <code>&quot;0915&quot;</code> are not part of the same one-hour period.</p> <p>Access times at the start and end of the day are <strong>not</strong> counted within the same one-hour period. For example, <code>&quot;0005&quot;</code> and <code>&quot;2350&quot;</code> are not part of the same one-hour period.</p> <p>Return <em>a list that contains the names of <strong>high-access</strong> employees with any order you want.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;a&quot;,&quot;0549&quot;],[&quot;b&quot;,&quot;0457&quot;],[&quot;a&quot;,&quot;0532&quot;],[&quot;a&quot;,&quot;0621&quot;],[&quot;b&quot;,&quot;0540&quot;]] <strong>Output:</strong> [&quot;a&quot;] <strong>Explanation:</strong> &quot;a&quot; has three access times in the one-hour period of [05:32, 06:31] which are 05:32, 05:49, and 06:21. But &quot;b&quot; does not have more than two access times at all. So the answer is [&quot;a&quot;].</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;d&quot;,&quot;0002&quot;],[&quot;c&quot;,&quot;0808&quot;],[&quot;c&quot;,&quot;0829&quot;],[&quot;e&quot;,&quot;0215&quot;],[&quot;d&quot;,&quot;1508&quot;],[&quot;d&quot;,&quot;1444&quot;],[&quot;d&quot;,&quot;1410&quot;],[&quot;c&quot;,&quot;0809&quot;]] <strong>Output:</strong> [&quot;c&quot;,&quot;d&quot;] <strong>Explanation:</strong> &quot;c&quot; has three access times in the one-hour period of [08:08, 09:07] which are 08:08, 08:09, and 08:29. &quot;d&quot; has also three access times in the one-hour period of [14:10, 15:09] which are 14:10, 14:44, and 15:08. However, &quot;e&quot; has just one access time, so it can not be in the answer and the final answer is [&quot;c&quot;,&quot;d&quot;].</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;cd&quot;,&quot;1025&quot;],[&quot;ab&quot;,&quot;1025&quot;],[&quot;cd&quot;,&quot;1046&quot;],[&quot;cd&quot;,&quot;1055&quot;],[&quot;ab&quot;,&quot;1124&quot;],[&quot;ab&quot;,&quot;1120&quot;]] <strong>Output:</strong> [&quot;ab&quot;,&quot;cd&quot;] <strong>Explanation:</strong> &quot;ab&quot; has three access times in the one-hour period of [10:25, 11:24] which are 10:25, 11:20, and 11:24. &quot;cd&quot; has also three access times in the one-hour period of [10:25, 11:24] which are 10:25, 10:46, and 10:55. So the answer is [&quot;ab&quot;,&quot;cd&quot;].</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= access_times.length &lt;= 100</code></li> <li><code>access_times[i].length == 2</code></li> <li><code>1 &lt;= access_times[i][0].length &lt;= 10</code></li> <li><code>access_times[i][0]</code> consists only of English small letters.</li> <li><code>access_times[i][1].length == 4</code></li> <li><code>access_times[i][1]</code> is in 24-hour time format.</li> <li><code>access_times[i][1]</code> consists only of <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>.</li> </ul>
Array; Hash Table; String; Sorting
C++
class Solution { public: vector<string> findHighAccessEmployees(vector<vector<string>>& access_times) { unordered_map<string, vector<int>> d; for (auto& e : access_times) { auto name = e[0]; auto s = e[1]; int t = stoi(s.substr(0, 2)) * 60 + stoi(s.substr(2, 2)); d[name].emplace_back(t); } vector<string> ans; for (auto& [name, ts] : d) { sort(ts.begin(), ts.end()); for (int i = 2; i < ts.size(); ++i) { if (ts[i] - ts[i - 2] < 60) { ans.emplace_back(name); break; } } } return ans; } };
2,933
High-Access Employees
Medium
<p>You are given a 2D <strong>0-indexed</strong> array of strings, <code>access_times</code>, with size <code>n</code>. For each <code>i</code> where <code>0 &lt;= i &lt;= n - 1</code>, <code>access_times[i][0]</code> represents the name of an employee, and <code>access_times[i][1]</code> represents the access time of that employee. All entries in <code>access_times</code> are within the same day.</p> <p>The access time is represented as <strong>four digits</strong> using a <strong>24-hour</strong> time format, for example, <code>&quot;0800&quot;</code> or <code>&quot;2250&quot;</code>.</p> <p>An employee is said to be <strong>high-access</strong> if he has accessed the system <strong>three or more</strong> times within a <strong>one-hour period</strong>.</p> <p>Times with exactly one hour of difference are <strong>not</strong> considered part of the same one-hour period. For example, <code>&quot;0815&quot;</code> and <code>&quot;0915&quot;</code> are not part of the same one-hour period.</p> <p>Access times at the start and end of the day are <strong>not</strong> counted within the same one-hour period. For example, <code>&quot;0005&quot;</code> and <code>&quot;2350&quot;</code> are not part of the same one-hour period.</p> <p>Return <em>a list that contains the names of <strong>high-access</strong> employees with any order you want.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;a&quot;,&quot;0549&quot;],[&quot;b&quot;,&quot;0457&quot;],[&quot;a&quot;,&quot;0532&quot;],[&quot;a&quot;,&quot;0621&quot;],[&quot;b&quot;,&quot;0540&quot;]] <strong>Output:</strong> [&quot;a&quot;] <strong>Explanation:</strong> &quot;a&quot; has three access times in the one-hour period of [05:32, 06:31] which are 05:32, 05:49, and 06:21. But &quot;b&quot; does not have more than two access times at all. So the answer is [&quot;a&quot;].</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;d&quot;,&quot;0002&quot;],[&quot;c&quot;,&quot;0808&quot;],[&quot;c&quot;,&quot;0829&quot;],[&quot;e&quot;,&quot;0215&quot;],[&quot;d&quot;,&quot;1508&quot;],[&quot;d&quot;,&quot;1444&quot;],[&quot;d&quot;,&quot;1410&quot;],[&quot;c&quot;,&quot;0809&quot;]] <strong>Output:</strong> [&quot;c&quot;,&quot;d&quot;] <strong>Explanation:</strong> &quot;c&quot; has three access times in the one-hour period of [08:08, 09:07] which are 08:08, 08:09, and 08:29. &quot;d&quot; has also three access times in the one-hour period of [14:10, 15:09] which are 14:10, 14:44, and 15:08. However, &quot;e&quot; has just one access time, so it can not be in the answer and the final answer is [&quot;c&quot;,&quot;d&quot;].</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;cd&quot;,&quot;1025&quot;],[&quot;ab&quot;,&quot;1025&quot;],[&quot;cd&quot;,&quot;1046&quot;],[&quot;cd&quot;,&quot;1055&quot;],[&quot;ab&quot;,&quot;1124&quot;],[&quot;ab&quot;,&quot;1120&quot;]] <strong>Output:</strong> [&quot;ab&quot;,&quot;cd&quot;] <strong>Explanation:</strong> &quot;ab&quot; has three access times in the one-hour period of [10:25, 11:24] which are 10:25, 11:20, and 11:24. &quot;cd&quot; has also three access times in the one-hour period of [10:25, 11:24] which are 10:25, 10:46, and 10:55. So the answer is [&quot;ab&quot;,&quot;cd&quot;].</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= access_times.length &lt;= 100</code></li> <li><code>access_times[i].length == 2</code></li> <li><code>1 &lt;= access_times[i][0].length &lt;= 10</code></li> <li><code>access_times[i][0]</code> consists only of English small letters.</li> <li><code>access_times[i][1].length == 4</code></li> <li><code>access_times[i][1]</code> is in 24-hour time format.</li> <li><code>access_times[i][1]</code> consists only of <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>.</li> </ul>
Array; Hash Table; String; Sorting
Go
func findHighAccessEmployees(access_times [][]string) (ans []string) { d := map[string][]int{} for _, e := range access_times { name, s := e[0], e[1] h, _ := strconv.Atoi(s[:2]) m, _ := strconv.Atoi(s[2:]) t := h*60 + m d[name] = append(d[name], t) } for name, ts := range d { sort.Ints(ts) for i := 2; i < len(ts); i++ { if ts[i]-ts[i-2] < 60 { ans = append(ans, name) break } } } return }
2,933
High-Access Employees
Medium
<p>You are given a 2D <strong>0-indexed</strong> array of strings, <code>access_times</code>, with size <code>n</code>. For each <code>i</code> where <code>0 &lt;= i &lt;= n - 1</code>, <code>access_times[i][0]</code> represents the name of an employee, and <code>access_times[i][1]</code> represents the access time of that employee. All entries in <code>access_times</code> are within the same day.</p> <p>The access time is represented as <strong>four digits</strong> using a <strong>24-hour</strong> time format, for example, <code>&quot;0800&quot;</code> or <code>&quot;2250&quot;</code>.</p> <p>An employee is said to be <strong>high-access</strong> if he has accessed the system <strong>three or more</strong> times within a <strong>one-hour period</strong>.</p> <p>Times with exactly one hour of difference are <strong>not</strong> considered part of the same one-hour period. For example, <code>&quot;0815&quot;</code> and <code>&quot;0915&quot;</code> are not part of the same one-hour period.</p> <p>Access times at the start and end of the day are <strong>not</strong> counted within the same one-hour period. For example, <code>&quot;0005&quot;</code> and <code>&quot;2350&quot;</code> are not part of the same one-hour period.</p> <p>Return <em>a list that contains the names of <strong>high-access</strong> employees with any order you want.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;a&quot;,&quot;0549&quot;],[&quot;b&quot;,&quot;0457&quot;],[&quot;a&quot;,&quot;0532&quot;],[&quot;a&quot;,&quot;0621&quot;],[&quot;b&quot;,&quot;0540&quot;]] <strong>Output:</strong> [&quot;a&quot;] <strong>Explanation:</strong> &quot;a&quot; has three access times in the one-hour period of [05:32, 06:31] which are 05:32, 05:49, and 06:21. But &quot;b&quot; does not have more than two access times at all. So the answer is [&quot;a&quot;].</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;d&quot;,&quot;0002&quot;],[&quot;c&quot;,&quot;0808&quot;],[&quot;c&quot;,&quot;0829&quot;],[&quot;e&quot;,&quot;0215&quot;],[&quot;d&quot;,&quot;1508&quot;],[&quot;d&quot;,&quot;1444&quot;],[&quot;d&quot;,&quot;1410&quot;],[&quot;c&quot;,&quot;0809&quot;]] <strong>Output:</strong> [&quot;c&quot;,&quot;d&quot;] <strong>Explanation:</strong> &quot;c&quot; has three access times in the one-hour period of [08:08, 09:07] which are 08:08, 08:09, and 08:29. &quot;d&quot; has also three access times in the one-hour period of [14:10, 15:09] which are 14:10, 14:44, and 15:08. However, &quot;e&quot; has just one access time, so it can not be in the answer and the final answer is [&quot;c&quot;,&quot;d&quot;].</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;cd&quot;,&quot;1025&quot;],[&quot;ab&quot;,&quot;1025&quot;],[&quot;cd&quot;,&quot;1046&quot;],[&quot;cd&quot;,&quot;1055&quot;],[&quot;ab&quot;,&quot;1124&quot;],[&quot;ab&quot;,&quot;1120&quot;]] <strong>Output:</strong> [&quot;ab&quot;,&quot;cd&quot;] <strong>Explanation:</strong> &quot;ab&quot; has three access times in the one-hour period of [10:25, 11:24] which are 10:25, 11:20, and 11:24. &quot;cd&quot; has also three access times in the one-hour period of [10:25, 11:24] which are 10:25, 10:46, and 10:55. So the answer is [&quot;ab&quot;,&quot;cd&quot;].</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= access_times.length &lt;= 100</code></li> <li><code>access_times[i].length == 2</code></li> <li><code>1 &lt;= access_times[i][0].length &lt;= 10</code></li> <li><code>access_times[i][0]</code> consists only of English small letters.</li> <li><code>access_times[i][1].length == 4</code></li> <li><code>access_times[i][1]</code> is in 24-hour time format.</li> <li><code>access_times[i][1]</code> consists only of <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>.</li> </ul>
Array; Hash Table; String; Sorting
Java
class Solution { public List<String> findHighAccessEmployees(List<List<String>> access_times) { Map<String, List<Integer>> d = new HashMap<>(); for (var e : access_times) { String name = e.get(0), s = e.get(1); int t = Integer.valueOf(s.substring(0, 2)) * 60 + Integer.valueOf(s.substring(2)); d.computeIfAbsent(name, k -> new ArrayList<>()).add(t); } List<String> ans = new ArrayList<>(); for (var e : d.entrySet()) { String name = e.getKey(); var ts = e.getValue(); Collections.sort(ts); for (int i = 2; i < ts.size(); ++i) { if (ts.get(i) - ts.get(i - 2) < 60) { ans.add(name); break; } } } return ans; } }
2,933
High-Access Employees
Medium
<p>You are given a 2D <strong>0-indexed</strong> array of strings, <code>access_times</code>, with size <code>n</code>. For each <code>i</code> where <code>0 &lt;= i &lt;= n - 1</code>, <code>access_times[i][0]</code> represents the name of an employee, and <code>access_times[i][1]</code> represents the access time of that employee. All entries in <code>access_times</code> are within the same day.</p> <p>The access time is represented as <strong>four digits</strong> using a <strong>24-hour</strong> time format, for example, <code>&quot;0800&quot;</code> or <code>&quot;2250&quot;</code>.</p> <p>An employee is said to be <strong>high-access</strong> if he has accessed the system <strong>three or more</strong> times within a <strong>one-hour period</strong>.</p> <p>Times with exactly one hour of difference are <strong>not</strong> considered part of the same one-hour period. For example, <code>&quot;0815&quot;</code> and <code>&quot;0915&quot;</code> are not part of the same one-hour period.</p> <p>Access times at the start and end of the day are <strong>not</strong> counted within the same one-hour period. For example, <code>&quot;0005&quot;</code> and <code>&quot;2350&quot;</code> are not part of the same one-hour period.</p> <p>Return <em>a list that contains the names of <strong>high-access</strong> employees with any order you want.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;a&quot;,&quot;0549&quot;],[&quot;b&quot;,&quot;0457&quot;],[&quot;a&quot;,&quot;0532&quot;],[&quot;a&quot;,&quot;0621&quot;],[&quot;b&quot;,&quot;0540&quot;]] <strong>Output:</strong> [&quot;a&quot;] <strong>Explanation:</strong> &quot;a&quot; has three access times in the one-hour period of [05:32, 06:31] which are 05:32, 05:49, and 06:21. But &quot;b&quot; does not have more than two access times at all. So the answer is [&quot;a&quot;].</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;d&quot;,&quot;0002&quot;],[&quot;c&quot;,&quot;0808&quot;],[&quot;c&quot;,&quot;0829&quot;],[&quot;e&quot;,&quot;0215&quot;],[&quot;d&quot;,&quot;1508&quot;],[&quot;d&quot;,&quot;1444&quot;],[&quot;d&quot;,&quot;1410&quot;],[&quot;c&quot;,&quot;0809&quot;]] <strong>Output:</strong> [&quot;c&quot;,&quot;d&quot;] <strong>Explanation:</strong> &quot;c&quot; has three access times in the one-hour period of [08:08, 09:07] which are 08:08, 08:09, and 08:29. &quot;d&quot; has also three access times in the one-hour period of [14:10, 15:09] which are 14:10, 14:44, and 15:08. However, &quot;e&quot; has just one access time, so it can not be in the answer and the final answer is [&quot;c&quot;,&quot;d&quot;].</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;cd&quot;,&quot;1025&quot;],[&quot;ab&quot;,&quot;1025&quot;],[&quot;cd&quot;,&quot;1046&quot;],[&quot;cd&quot;,&quot;1055&quot;],[&quot;ab&quot;,&quot;1124&quot;],[&quot;ab&quot;,&quot;1120&quot;]] <strong>Output:</strong> [&quot;ab&quot;,&quot;cd&quot;] <strong>Explanation:</strong> &quot;ab&quot; has three access times in the one-hour period of [10:25, 11:24] which are 10:25, 11:20, and 11:24. &quot;cd&quot; has also three access times in the one-hour period of [10:25, 11:24] which are 10:25, 10:46, and 10:55. So the answer is [&quot;ab&quot;,&quot;cd&quot;].</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= access_times.length &lt;= 100</code></li> <li><code>access_times[i].length == 2</code></li> <li><code>1 &lt;= access_times[i][0].length &lt;= 10</code></li> <li><code>access_times[i][0]</code> consists only of English small letters.</li> <li><code>access_times[i][1].length == 4</code></li> <li><code>access_times[i][1]</code> is in 24-hour time format.</li> <li><code>access_times[i][1]</code> consists only of <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>.</li> </ul>
Array; Hash Table; String; Sorting
Python
class Solution: def findHighAccessEmployees(self, access_times: List[List[str]]) -> List[str]: d = defaultdict(list) for name, t in access_times: d[name].append(int(t[:2]) * 60 + int(t[2:])) ans = [] for name, ts in d.items(): ts.sort() if any(ts[i] - ts[i - 2] < 60 for i in range(2, len(ts))): ans.append(name) return ans
2,933
High-Access Employees
Medium
<p>You are given a 2D <strong>0-indexed</strong> array of strings, <code>access_times</code>, with size <code>n</code>. For each <code>i</code> where <code>0 &lt;= i &lt;= n - 1</code>, <code>access_times[i][0]</code> represents the name of an employee, and <code>access_times[i][1]</code> represents the access time of that employee. All entries in <code>access_times</code> are within the same day.</p> <p>The access time is represented as <strong>four digits</strong> using a <strong>24-hour</strong> time format, for example, <code>&quot;0800&quot;</code> or <code>&quot;2250&quot;</code>.</p> <p>An employee is said to be <strong>high-access</strong> if he has accessed the system <strong>three or more</strong> times within a <strong>one-hour period</strong>.</p> <p>Times with exactly one hour of difference are <strong>not</strong> considered part of the same one-hour period. For example, <code>&quot;0815&quot;</code> and <code>&quot;0915&quot;</code> are not part of the same one-hour period.</p> <p>Access times at the start and end of the day are <strong>not</strong> counted within the same one-hour period. For example, <code>&quot;0005&quot;</code> and <code>&quot;2350&quot;</code> are not part of the same one-hour period.</p> <p>Return <em>a list that contains the names of <strong>high-access</strong> employees with any order you want.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;a&quot;,&quot;0549&quot;],[&quot;b&quot;,&quot;0457&quot;],[&quot;a&quot;,&quot;0532&quot;],[&quot;a&quot;,&quot;0621&quot;],[&quot;b&quot;,&quot;0540&quot;]] <strong>Output:</strong> [&quot;a&quot;] <strong>Explanation:</strong> &quot;a&quot; has three access times in the one-hour period of [05:32, 06:31] which are 05:32, 05:49, and 06:21. But &quot;b&quot; does not have more than two access times at all. So the answer is [&quot;a&quot;].</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;d&quot;,&quot;0002&quot;],[&quot;c&quot;,&quot;0808&quot;],[&quot;c&quot;,&quot;0829&quot;],[&quot;e&quot;,&quot;0215&quot;],[&quot;d&quot;,&quot;1508&quot;],[&quot;d&quot;,&quot;1444&quot;],[&quot;d&quot;,&quot;1410&quot;],[&quot;c&quot;,&quot;0809&quot;]] <strong>Output:</strong> [&quot;c&quot;,&quot;d&quot;] <strong>Explanation:</strong> &quot;c&quot; has three access times in the one-hour period of [08:08, 09:07] which are 08:08, 08:09, and 08:29. &quot;d&quot; has also three access times in the one-hour period of [14:10, 15:09] which are 14:10, 14:44, and 15:08. However, &quot;e&quot; has just one access time, so it can not be in the answer and the final answer is [&quot;c&quot;,&quot;d&quot;].</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> access_times = [[&quot;cd&quot;,&quot;1025&quot;],[&quot;ab&quot;,&quot;1025&quot;],[&quot;cd&quot;,&quot;1046&quot;],[&quot;cd&quot;,&quot;1055&quot;],[&quot;ab&quot;,&quot;1124&quot;],[&quot;ab&quot;,&quot;1120&quot;]] <strong>Output:</strong> [&quot;ab&quot;,&quot;cd&quot;] <strong>Explanation:</strong> &quot;ab&quot; has three access times in the one-hour period of [10:25, 11:24] which are 10:25, 11:20, and 11:24. &quot;cd&quot; has also three access times in the one-hour period of [10:25, 11:24] which are 10:25, 10:46, and 10:55. So the answer is [&quot;ab&quot;,&quot;cd&quot;].</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= access_times.length &lt;= 100</code></li> <li><code>access_times[i].length == 2</code></li> <li><code>1 &lt;= access_times[i][0].length &lt;= 10</code></li> <li><code>access_times[i][0]</code> consists only of English small letters.</li> <li><code>access_times[i][1].length == 4</code></li> <li><code>access_times[i][1]</code> is in 24-hour time format.</li> <li><code>access_times[i][1]</code> consists only of <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>.</li> </ul>
Array; Hash Table; String; Sorting
TypeScript
function findHighAccessEmployees(access_times: string[][]): string[] { const d: Map<string, number[]> = new Map(); for (const [name, s] of access_times) { const h = parseInt(s.slice(0, 2), 10); const m = parseInt(s.slice(2), 10); const t = h * 60 + m; if (!d.has(name)) { d.set(name, []); } d.get(name)!.push(t); } const ans: string[] = []; for (const [name, ts] of d) { ts.sort((a, b) => a - b); for (let i = 2; i < ts.length; ++i) { if (ts[i] - ts[i - 2] < 60) { ans.push(name); break; } } } return ans; }
2,934
Minimum Operations to Maximize Last Elements in Arrays
Medium
<p>You are given two <strong>0-indexed</strong> integer arrays, <code>nums1</code> and <code>nums2</code>, both having length <code>n</code>.</p> <p>You are allowed to perform a series of <strong>operations</strong> (<strong>possibly none</strong>).</p> <p>In an operation, you select an index <code>i</code> in the range <code>[0, n - 1]</code> and <strong>swap</strong> the values of <code>nums1[i]</code> and <code>nums2[i]</code>.</p> <p>Your task is to find the <strong>minimum</strong> number of operations required to satisfy the following conditions:</p> <ul> <li><code>nums1[n - 1]</code> is equal to the <strong>maximum value</strong> among all elements of <code>nums1</code>, i.e., <code>nums1[n - 1] = max(nums1[0], nums1[1], ..., nums1[n - 1])</code>.</li> <li><code>nums2[n - 1]</code> is equal to the <strong>maximum</strong> <strong>value</strong> among all elements of <code>nums2</code>, i.e., <code>nums2[n - 1] = max(nums2[0], nums2[1], ..., nums2[n - 1])</code>.</li> </ul> <p>Return <em>an integer denoting the <strong>minimum</strong> number of operations needed to meet <strong>both</strong> conditions</em>, <em>or </em><code>-1</code><em> if it is <strong>impossible</strong> to satisfy both conditions.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,2,7], nums2 = [4,5,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, an operation can be performed using index i = 2. When nums1[2] and nums2[2] are swapped, nums1 becomes [1,2,3] and nums2 becomes [4,5,7]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 1. So, the answer is 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums1 = [2,3,4,5,9], nums2 = [8,8,4,4,4] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, the following operations can be performed: First operation using index i = 4. When nums1[4] and nums2[4] are swapped, nums1 becomes [2,3,4,5,4], and nums2 becomes [8,8,4,4,9]. Another operation using index i = 3. When nums1[3] and nums2[3] are swapped, nums1 becomes [2,3,4,4,4], and nums2 becomes [8,8,4,5,9]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 2. So, the answer is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,5,4], nums2 = [2,5,3] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, it is not possible to satisfy both conditions. So, the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == nums1.length == nums2.length &lt;= 1000</code></li> <li><code>1 &lt;= nums1[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= nums2[i] &lt;= 10<sup>9</sup></code></li> </ul>
Array; Enumeration
C++
class Solution { public: int minOperations(vector<int>& nums1, vector<int>& nums2) { int n = nums1.size(); auto f = [&](int x, int y) { int cnt = 0; for (int i = 0; i < n - 1; ++i) { if (nums1[i] <= x && nums2[i] <= y) { continue; } if (!(nums1[i] <= y && nums2[i] <= x)) { return -1; } ++cnt; } return cnt; }; int a = f(nums1.back(), nums2.back()); int b = f(nums2.back(), nums1.back()); return a + b == -2 ? -1 : min(a, b + 1); } };
2,934
Minimum Operations to Maximize Last Elements in Arrays
Medium
<p>You are given two <strong>0-indexed</strong> integer arrays, <code>nums1</code> and <code>nums2</code>, both having length <code>n</code>.</p> <p>You are allowed to perform a series of <strong>operations</strong> (<strong>possibly none</strong>).</p> <p>In an operation, you select an index <code>i</code> in the range <code>[0, n - 1]</code> and <strong>swap</strong> the values of <code>nums1[i]</code> and <code>nums2[i]</code>.</p> <p>Your task is to find the <strong>minimum</strong> number of operations required to satisfy the following conditions:</p> <ul> <li><code>nums1[n - 1]</code> is equal to the <strong>maximum value</strong> among all elements of <code>nums1</code>, i.e., <code>nums1[n - 1] = max(nums1[0], nums1[1], ..., nums1[n - 1])</code>.</li> <li><code>nums2[n - 1]</code> is equal to the <strong>maximum</strong> <strong>value</strong> among all elements of <code>nums2</code>, i.e., <code>nums2[n - 1] = max(nums2[0], nums2[1], ..., nums2[n - 1])</code>.</li> </ul> <p>Return <em>an integer denoting the <strong>minimum</strong> number of operations needed to meet <strong>both</strong> conditions</em>, <em>or </em><code>-1</code><em> if it is <strong>impossible</strong> to satisfy both conditions.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,2,7], nums2 = [4,5,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, an operation can be performed using index i = 2. When nums1[2] and nums2[2] are swapped, nums1 becomes [1,2,3] and nums2 becomes [4,5,7]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 1. So, the answer is 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums1 = [2,3,4,5,9], nums2 = [8,8,4,4,4] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, the following operations can be performed: First operation using index i = 4. When nums1[4] and nums2[4] are swapped, nums1 becomes [2,3,4,5,4], and nums2 becomes [8,8,4,4,9]. Another operation using index i = 3. When nums1[3] and nums2[3] are swapped, nums1 becomes [2,3,4,4,4], and nums2 becomes [8,8,4,5,9]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 2. So, the answer is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,5,4], nums2 = [2,5,3] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, it is not possible to satisfy both conditions. So, the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == nums1.length == nums2.length &lt;= 1000</code></li> <li><code>1 &lt;= nums1[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= nums2[i] &lt;= 10<sup>9</sup></code></li> </ul>
Array; Enumeration
Go
func minOperations(nums1 []int, nums2 []int) int { n := len(nums1) f := func(x, y int) (cnt int) { for i, a := range nums1[:n-1] { b := nums2[i] if a <= x && b <= y { continue } if !(a <= y && b <= x) { return -1 } cnt++ } return } a, b := f(nums1[n-1], nums2[n-1]), f(nums2[n-1], nums1[n-1]) if a+b == -2 { return -1 } return min(a, b+1) }
2,934
Minimum Operations to Maximize Last Elements in Arrays
Medium
<p>You are given two <strong>0-indexed</strong> integer arrays, <code>nums1</code> and <code>nums2</code>, both having length <code>n</code>.</p> <p>You are allowed to perform a series of <strong>operations</strong> (<strong>possibly none</strong>).</p> <p>In an operation, you select an index <code>i</code> in the range <code>[0, n - 1]</code> and <strong>swap</strong> the values of <code>nums1[i]</code> and <code>nums2[i]</code>.</p> <p>Your task is to find the <strong>minimum</strong> number of operations required to satisfy the following conditions:</p> <ul> <li><code>nums1[n - 1]</code> is equal to the <strong>maximum value</strong> among all elements of <code>nums1</code>, i.e., <code>nums1[n - 1] = max(nums1[0], nums1[1], ..., nums1[n - 1])</code>.</li> <li><code>nums2[n - 1]</code> is equal to the <strong>maximum</strong> <strong>value</strong> among all elements of <code>nums2</code>, i.e., <code>nums2[n - 1] = max(nums2[0], nums2[1], ..., nums2[n - 1])</code>.</li> </ul> <p>Return <em>an integer denoting the <strong>minimum</strong> number of operations needed to meet <strong>both</strong> conditions</em>, <em>or </em><code>-1</code><em> if it is <strong>impossible</strong> to satisfy both conditions.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,2,7], nums2 = [4,5,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, an operation can be performed using index i = 2. When nums1[2] and nums2[2] are swapped, nums1 becomes [1,2,3] and nums2 becomes [4,5,7]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 1. So, the answer is 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums1 = [2,3,4,5,9], nums2 = [8,8,4,4,4] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, the following operations can be performed: First operation using index i = 4. When nums1[4] and nums2[4] are swapped, nums1 becomes [2,3,4,5,4], and nums2 becomes [8,8,4,4,9]. Another operation using index i = 3. When nums1[3] and nums2[3] are swapped, nums1 becomes [2,3,4,4,4], and nums2 becomes [8,8,4,5,9]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 2. So, the answer is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,5,4], nums2 = [2,5,3] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, it is not possible to satisfy both conditions. So, the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == nums1.length == nums2.length &lt;= 1000</code></li> <li><code>1 &lt;= nums1[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= nums2[i] &lt;= 10<sup>9</sup></code></li> </ul>
Array; Enumeration
Java
class Solution { private int n; public int minOperations(int[] nums1, int[] nums2) { n = nums1.length; int a = f(nums1, nums2, nums1[n - 1], nums2[n - 1]); int b = f(nums1, nums2, nums2[n - 1], nums1[n - 1]); return a + b == -2 ? -1 : Math.min(a, b + 1); } private int f(int[] nums1, int[] nums2, int x, int y) { int cnt = 0; for (int i = 0; i < n - 1; ++i) { if (nums1[i] <= x && nums2[i] <= y) { continue; } if (!(nums1[i] <= y && nums2[i] <= x)) { return -1; } ++cnt; } return cnt; } }
2,934
Minimum Operations to Maximize Last Elements in Arrays
Medium
<p>You are given two <strong>0-indexed</strong> integer arrays, <code>nums1</code> and <code>nums2</code>, both having length <code>n</code>.</p> <p>You are allowed to perform a series of <strong>operations</strong> (<strong>possibly none</strong>).</p> <p>In an operation, you select an index <code>i</code> in the range <code>[0, n - 1]</code> and <strong>swap</strong> the values of <code>nums1[i]</code> and <code>nums2[i]</code>.</p> <p>Your task is to find the <strong>minimum</strong> number of operations required to satisfy the following conditions:</p> <ul> <li><code>nums1[n - 1]</code> is equal to the <strong>maximum value</strong> among all elements of <code>nums1</code>, i.e., <code>nums1[n - 1] = max(nums1[0], nums1[1], ..., nums1[n - 1])</code>.</li> <li><code>nums2[n - 1]</code> is equal to the <strong>maximum</strong> <strong>value</strong> among all elements of <code>nums2</code>, i.e., <code>nums2[n - 1] = max(nums2[0], nums2[1], ..., nums2[n - 1])</code>.</li> </ul> <p>Return <em>an integer denoting the <strong>minimum</strong> number of operations needed to meet <strong>both</strong> conditions</em>, <em>or </em><code>-1</code><em> if it is <strong>impossible</strong> to satisfy both conditions.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,2,7], nums2 = [4,5,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, an operation can be performed using index i = 2. When nums1[2] and nums2[2] are swapped, nums1 becomes [1,2,3] and nums2 becomes [4,5,7]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 1. So, the answer is 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums1 = [2,3,4,5,9], nums2 = [8,8,4,4,4] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, the following operations can be performed: First operation using index i = 4. When nums1[4] and nums2[4] are swapped, nums1 becomes [2,3,4,5,4], and nums2 becomes [8,8,4,4,9]. Another operation using index i = 3. When nums1[3] and nums2[3] are swapped, nums1 becomes [2,3,4,4,4], and nums2 becomes [8,8,4,5,9]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 2. So, the answer is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,5,4], nums2 = [2,5,3] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, it is not possible to satisfy both conditions. So, the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == nums1.length == nums2.length &lt;= 1000</code></li> <li><code>1 &lt;= nums1[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= nums2[i] &lt;= 10<sup>9</sup></code></li> </ul>
Array; Enumeration
Python
class Solution: def minOperations(self, nums1: List[int], nums2: List[int]) -> int: def f(x: int, y: int) -> int: cnt = 0 for a, b in zip(nums1[:-1], nums2[:-1]): if a <= x and b <= y: continue if not (a <= y and b <= x): return -1 cnt += 1 return cnt a, b = f(nums1[-1], nums2[-1]), f(nums2[-1], nums1[-1]) return -1 if a + b == -2 else min(a, b + 1)
2,934
Minimum Operations to Maximize Last Elements in Arrays
Medium
<p>You are given two <strong>0-indexed</strong> integer arrays, <code>nums1</code> and <code>nums2</code>, both having length <code>n</code>.</p> <p>You are allowed to perform a series of <strong>operations</strong> (<strong>possibly none</strong>).</p> <p>In an operation, you select an index <code>i</code> in the range <code>[0, n - 1]</code> and <strong>swap</strong> the values of <code>nums1[i]</code> and <code>nums2[i]</code>.</p> <p>Your task is to find the <strong>minimum</strong> number of operations required to satisfy the following conditions:</p> <ul> <li><code>nums1[n - 1]</code> is equal to the <strong>maximum value</strong> among all elements of <code>nums1</code>, i.e., <code>nums1[n - 1] = max(nums1[0], nums1[1], ..., nums1[n - 1])</code>.</li> <li><code>nums2[n - 1]</code> is equal to the <strong>maximum</strong> <strong>value</strong> among all elements of <code>nums2</code>, i.e., <code>nums2[n - 1] = max(nums2[0], nums2[1], ..., nums2[n - 1])</code>.</li> </ul> <p>Return <em>an integer denoting the <strong>minimum</strong> number of operations needed to meet <strong>both</strong> conditions</em>, <em>or </em><code>-1</code><em> if it is <strong>impossible</strong> to satisfy both conditions.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,2,7], nums2 = [4,5,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, an operation can be performed using index i = 2. When nums1[2] and nums2[2] are swapped, nums1 becomes [1,2,3] and nums2 becomes [4,5,7]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 1. So, the answer is 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums1 = [2,3,4,5,9], nums2 = [8,8,4,4,4] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, the following operations can be performed: First operation using index i = 4. When nums1[4] and nums2[4] are swapped, nums1 becomes [2,3,4,5,4], and nums2 becomes [8,8,4,4,9]. Another operation using index i = 3. When nums1[3] and nums2[3] are swapped, nums1 becomes [2,3,4,4,4], and nums2 becomes [8,8,4,5,9]. Both conditions are now satisfied. It can be shown that the minimum number of operations needed to be performed is 2. So, the answer is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums1 = [1,5,4], nums2 = [2,5,3] <strong>Output:</strong> -1 <strong>Explanation:</strong> In this example, it is not possible to satisfy both conditions. So, the answer is -1. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == nums1.length == nums2.length &lt;= 1000</code></li> <li><code>1 &lt;= nums1[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= nums2[i] &lt;= 10<sup>9</sup></code></li> </ul>
Array; Enumeration
TypeScript
function minOperations(nums1: number[], nums2: number[]): number { const n = nums1.length; const f = (x: number, y: number): number => { let cnt = 0; for (let i = 0; i < n - 1; ++i) { if (nums1[i] <= x && nums2[i] <= y) { continue; } if (!(nums1[i] <= y && nums2[i] <= x)) { return -1; } ++cnt; } return cnt; }; const a = f(nums1.at(-1), nums2.at(-1)); const b = f(nums2.at(-1), nums1.at(-1)); return a + b === -2 ? -1 : Math.min(a, b + 1); }
2,935
Maximum Strong Pair XOR II
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [500,520,2500,3000] <strong>Output:</strong> 1020 <strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000). The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
C++
class Trie { public: Trie* children[2]; int cnt; Trie() : cnt(0) { children[0] = nullptr; children[1] = nullptr; } void insert(int x) { Trie* node = this; for (int i = 20; ~i; --i) { int v = (x >> i) & 1; if (node->children[v] == nullptr) { node->children[v] = new Trie(); } node = node->children[v]; ++node->cnt; } } int search(int x) { Trie* node = this; int ans = 0; for (int i = 20; ~i; --i) { int v = (x >> i) & 1; if (node->children[v ^ 1] != nullptr && node->children[v ^ 1]->cnt > 0) { ans |= 1 << i; node = node->children[v ^ 1]; } else { node = node->children[v]; } } return ans; } void remove(int x) { Trie* node = this; for (int i = 20; ~i; --i) { int v = (x >> i) & 1; node = node->children[v]; --node->cnt; } } }; class Solution { public: int maximumStrongPairXor(vector<int>& nums) { sort(nums.begin(), nums.end()); Trie* tree = new Trie(); int ans = 0, i = 0; for (int y : nums) { tree->insert(y); while (y > nums[i] * 2) { tree->remove(nums[i++]); } ans = max(ans, tree->search(y)); } return ans; } };
2,935
Maximum Strong Pair XOR II
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [500,520,2500,3000] <strong>Output:</strong> 1020 <strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000). The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Go
type Trie struct { children [2]*Trie cnt int } func newTrie() *Trie { return &Trie{} } func (t *Trie) insert(x int) { node := t for i := 20; i >= 0; i-- { v := (x >> uint(i)) & 1 if node.children[v] == nil { node.children[v] = newTrie() } node = node.children[v] node.cnt++ } } func (t *Trie) search(x int) int { node := t ans := 0 for i := 20; i >= 0; i-- { v := (x >> uint(i)) & 1 if node.children[v^1] != nil && node.children[v^1].cnt > 0 { ans |= 1 << uint(i) node = node.children[v^1] } else { node = node.children[v] } } return ans } func (t *Trie) remove(x int) { node := t for i := 20; i >= 0; i-- { v := (x >> uint(i)) & 1 node = node.children[v] node.cnt-- } } func maximumStrongPairXor(nums []int) (ans int) { sort.Ints(nums) tree := newTrie() i := 0 for _, y := range nums { tree.insert(y) for ; y > nums[i]*2; i++ { tree.remove(nums[i]) } ans = max(ans, tree.search(y)) } return ans }
2,935
Maximum Strong Pair XOR II
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [500,520,2500,3000] <strong>Output:</strong> 1020 <strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000). The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Java
class Trie { private Trie[] children = new Trie[2]; private int cnt = 0; public Trie() { } public void insert(int x) { Trie node = this; for (int i = 20; i >= 0; --i) { int v = x >> i & 1; if (node.children[v] == null) { node.children[v] = new Trie(); } node = node.children[v]; ++node.cnt; } } public int search(int x) { Trie node = this; int ans = 0; for (int i = 20; i >= 0; --i) { int v = x >> i & 1; if (node.children[v ^ 1] != null && node.children[v ^ 1].cnt > 0) { ans |= 1 << i; node = node.children[v ^ 1]; } else { node = node.children[v]; } } return ans; } public void remove(int x) { Trie node = this; for (int i = 20; i >= 0; --i) { int v = x >> i & 1; node = node.children[v]; --node.cnt; } } } class Solution { public int maximumStrongPairXor(int[] nums) { Arrays.sort(nums); Trie tree = new Trie(); int ans = 0, i = 0; for (int y : nums) { tree.insert(y); while (y > nums[i] * 2) { tree.remove(nums[i++]); } ans = Math.max(ans, tree.search(y)); } return ans; } }
2,935
Maximum Strong Pair XOR II
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [500,520,2500,3000] <strong>Output:</strong> 1020 <strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000). The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
Python
class Trie: __slots__ = ("children", "cnt") def __init__(self): self.children: List[Trie | None] = [None, None] self.cnt = 0 def insert(self, x: int): node = self for i in range(20, -1, -1): v = x >> i & 1 if node.children[v] is None: node.children[v] = Trie() node = node.children[v] node.cnt += 1 def search(self, x: int) -> int: node = self ans = 0 for i in range(20, -1, -1): v = x >> i & 1 if node.children[v ^ 1] and node.children[v ^ 1].cnt: ans |= 1 << i node = node.children[v ^ 1] else: node = node.children[v] return ans def remove(self, x: int): node = self for i in range(20, -1, -1): v = x >> i & 1 node = node.children[v] node.cnt -= 1 class Solution: def maximumStrongPairXor(self, nums: List[int]) -> int: nums.sort() tree = Trie() ans = i = 0 for y in nums: tree.insert(y) while y > nums[i] * 2: tree.remove(nums[i]) i += 1 ans = max(ans, tree.search(y)) return ans
2,935
Maximum Strong Pair XOR II
Hard
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p> <ul> <li><code>|x - y| &lt;= min(x, y)</code></li> </ul> <p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p> <p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p> <p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5] <strong>Output:</strong> 7 <strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5). The maximum XOR possible from these pairs is 3 XOR 4 = 7. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [10,100] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100). The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [500,520,2500,3000] <strong>Output:</strong> 1020 <strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000). The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li> </ul>
Bit Manipulation; Trie; Array; Hash Table; Sliding Window
TypeScript
class Trie { children: (Trie | null)[]; cnt: number; constructor() { this.children = [null, null]; this.cnt = 0; } insert(x: number): void { let node: Trie | null = this; for (let i = 20; i >= 0; i--) { const v = (x >> i) & 1; if (node.children[v] === null) { node.children[v] = new Trie(); } node = node.children[v] as Trie; node.cnt++; } } search(x: number): number { let node: Trie | null = this; let ans = 0; for (let i = 20; i >= 0; i--) { const v = (x >> i) & 1; if (node.children[v ^ 1] !== null && (node.children[v ^ 1] as Trie).cnt > 0) { ans |= 1 << i; node = node.children[v ^ 1] as Trie; } else { node = node.children[v] as Trie; } } return ans; } remove(x: number): void { let node: Trie | null = this; for (let i = 20; i >= 0; i--) { const v = (x >> i) & 1; node = node.children[v] as Trie; node.cnt--; } } } function maximumStrongPairXor(nums: number[]): number { nums.sort((a, b) => a - b); const tree = new Trie(); let ans = 0; let i = 0; for (const y of nums) { tree.insert(y); while (y > nums[i] * 2) { tree.remove(nums[i++]); } ans = Math.max(ans, tree.search(y)); } return ans; }
2,936
Number of Equal Numbers Blocks
Medium
<p>You are given a <strong>0-indexed</strong> array of integers, <code>nums</code>. The following property holds for <code>nums</code>:</p> <ul> <li>All occurrences of a value are adjacent. In other words, if there are two indices <code>i &lt; j</code> such that <code>nums[i] == nums[j]</code>, then for every index <code>k</code> that <code>i &lt; k &lt; j</code>, <code>nums[k] == nums[i]</code>.</li> </ul> <p>Since <code>nums</code> is a very large array, you are given an instance of the class <code>BigArray</code> which has the following functions:</p> <ul> <li><code>int at(long long index)</code>: Returns the value of <code>nums[i]</code>.</li> <li><code>void size()</code>: Returns <code>nums.length</code>.</li> </ul> <p>Let&#39;s partition the array into <strong>maximal</strong> blocks such that each block contains <strong>equal values</strong>. Return<em> the number of these blocks.</em></p> <p><strong>Note</strong> that if you want to test your solution using a custom test, behavior for tests with <code>nums.length &gt; 10</code> is undefined.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,3,3,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> There is only one block here which is the whole array (because all numbers are equal) and that is: [<u>3,3,3,3,3</u>]. So the answer would be 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [1,1,1,3,9,9,9,2,10,10] <strong>Output:</strong> 5 <strong>Explanation:</strong> There are 5 blocks here: Block number 1: [<u>1,1,1</u>,3,9,9,9,2,10,10] Block number 2: [1,1,1,<u>3</u>,9,9,9,2,10,10] Block number 3: [1,1,1,3,<u>9,9,9</u>,2,10,10] Block number 4: [1,1,1,3,9,9,9,<u>2</u>,10,10] Block number 5: [1,1,1,3,9,9,9,2,<u>10,10</u>] So the answer would be 5.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5,6,7] <strong>Output:</strong> 7 <strong>Explanation:</strong> Since all numbers are distinct, there are 7 blocks here and each element representing one block. So the answer would be 7. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>15</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that all equal values are adjacent.</li> <li>The sum of the elements of&nbsp;<code>nums</code>&nbsp;is at most&nbsp;<code>10<sup>15</sup></code>.</li> </ul>
Array; Binary Search; Interactive
C++
/** * Definition for BigArray. * class BigArray { * public: * BigArray(vector<int> elements); * int at(long long index); * long long size(); * }; */ class Solution { public: int countBlocks(BigArray* nums) { int ans = 0; using ll = long long; ll n = nums->size(); auto search = [&](ll l) { ll r = n; int x = nums->at(l); while (l < r) { ll mid = (l + r) >> 1; if (nums->at(mid) != x) { r = mid; } else { l = mid + 1; } } return l; }; for (long long i = 0; i < n; ++ans) { i = search(i); } return ans; } };
2,936
Number of Equal Numbers Blocks
Medium
<p>You are given a <strong>0-indexed</strong> array of integers, <code>nums</code>. The following property holds for <code>nums</code>:</p> <ul> <li>All occurrences of a value are adjacent. In other words, if there are two indices <code>i &lt; j</code> such that <code>nums[i] == nums[j]</code>, then for every index <code>k</code> that <code>i &lt; k &lt; j</code>, <code>nums[k] == nums[i]</code>.</li> </ul> <p>Since <code>nums</code> is a very large array, you are given an instance of the class <code>BigArray</code> which has the following functions:</p> <ul> <li><code>int at(long long index)</code>: Returns the value of <code>nums[i]</code>.</li> <li><code>void size()</code>: Returns <code>nums.length</code>.</li> </ul> <p>Let&#39;s partition the array into <strong>maximal</strong> blocks such that each block contains <strong>equal values</strong>. Return<em> the number of these blocks.</em></p> <p><strong>Note</strong> that if you want to test your solution using a custom test, behavior for tests with <code>nums.length &gt; 10</code> is undefined.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,3,3,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> There is only one block here which is the whole array (because all numbers are equal) and that is: [<u>3,3,3,3,3</u>]. So the answer would be 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [1,1,1,3,9,9,9,2,10,10] <strong>Output:</strong> 5 <strong>Explanation:</strong> There are 5 blocks here: Block number 1: [<u>1,1,1</u>,3,9,9,9,2,10,10] Block number 2: [1,1,1,<u>3</u>,9,9,9,2,10,10] Block number 3: [1,1,1,3,<u>9,9,9</u>,2,10,10] Block number 4: [1,1,1,3,9,9,9,<u>2</u>,10,10] Block number 5: [1,1,1,3,9,9,9,2,<u>10,10</u>] So the answer would be 5.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5,6,7] <strong>Output:</strong> 7 <strong>Explanation:</strong> Since all numbers are distinct, there are 7 blocks here and each element representing one block. So the answer would be 7. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>15</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that all equal values are adjacent.</li> <li>The sum of the elements of&nbsp;<code>nums</code>&nbsp;is at most&nbsp;<code>10<sup>15</sup></code>.</li> </ul>
Array; Binary Search; Interactive
Java
/** * Definition for BigArray. * class BigArray { * public BigArray(int[] elements); * public int at(long index); * public long size(); * } */ class Solution { public int countBlocks(BigArray nums) { int ans = 0; for (long i = 0, n = nums.size(); i < n; ++ans) { i = search(nums, i, n); } return ans; } private long search(BigArray nums, long l, long n) { long r = n; int x = nums.at(l); while (l < r) { long mid = (l + r) >> 1; if (nums.at(mid) != x) { r = mid; } else { l = mid + 1; } } return l; } }
2,936
Number of Equal Numbers Blocks
Medium
<p>You are given a <strong>0-indexed</strong> array of integers, <code>nums</code>. The following property holds for <code>nums</code>:</p> <ul> <li>All occurrences of a value are adjacent. In other words, if there are two indices <code>i &lt; j</code> such that <code>nums[i] == nums[j]</code>, then for every index <code>k</code> that <code>i &lt; k &lt; j</code>, <code>nums[k] == nums[i]</code>.</li> </ul> <p>Since <code>nums</code> is a very large array, you are given an instance of the class <code>BigArray</code> which has the following functions:</p> <ul> <li><code>int at(long long index)</code>: Returns the value of <code>nums[i]</code>.</li> <li><code>void size()</code>: Returns <code>nums.length</code>.</li> </ul> <p>Let&#39;s partition the array into <strong>maximal</strong> blocks such that each block contains <strong>equal values</strong>. Return<em> the number of these blocks.</em></p> <p><strong>Note</strong> that if you want to test your solution using a custom test, behavior for tests with <code>nums.length &gt; 10</code> is undefined.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,3,3,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> There is only one block here which is the whole array (because all numbers are equal) and that is: [<u>3,3,3,3,3</u>]. So the answer would be 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [1,1,1,3,9,9,9,2,10,10] <strong>Output:</strong> 5 <strong>Explanation:</strong> There are 5 blocks here: Block number 1: [<u>1,1,1</u>,3,9,9,9,2,10,10] Block number 2: [1,1,1,<u>3</u>,9,9,9,2,10,10] Block number 3: [1,1,1,3,<u>9,9,9</u>,2,10,10] Block number 4: [1,1,1,3,9,9,9,<u>2</u>,10,10] Block number 5: [1,1,1,3,9,9,9,2,<u>10,10</u>] So the answer would be 5.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5,6,7] <strong>Output:</strong> 7 <strong>Explanation:</strong> Since all numbers are distinct, there are 7 blocks here and each element representing one block. So the answer would be 7. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>15</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that all equal values are adjacent.</li> <li>The sum of the elements of&nbsp;<code>nums</code>&nbsp;is at most&nbsp;<code>10<sup>15</sup></code>.</li> </ul>
Array; Binary Search; Interactive
Python
# Definition for BigArray. # class BigArray: # def at(self, index: long) -> int: # pass # def size(self) -> long: # pass class Solution(object): def countBlocks(self, nums: Optional["BigArray"]) -> int: i, n = 0, nums.size() ans = 0 while i < n: ans += 1 x = nums.at(i) if i + 1 < n and nums.at(i + 1) != x: i += 1 else: i += bisect_left(range(i, n), True, key=lambda j: nums.at(j) != x) return ans
2,936
Number of Equal Numbers Blocks
Medium
<p>You are given a <strong>0-indexed</strong> array of integers, <code>nums</code>. The following property holds for <code>nums</code>:</p> <ul> <li>All occurrences of a value are adjacent. In other words, if there are two indices <code>i &lt; j</code> such that <code>nums[i] == nums[j]</code>, then for every index <code>k</code> that <code>i &lt; k &lt; j</code>, <code>nums[k] == nums[i]</code>.</li> </ul> <p>Since <code>nums</code> is a very large array, you are given an instance of the class <code>BigArray</code> which has the following functions:</p> <ul> <li><code>int at(long long index)</code>: Returns the value of <code>nums[i]</code>.</li> <li><code>void size()</code>: Returns <code>nums.length</code>.</li> </ul> <p>Let&#39;s partition the array into <strong>maximal</strong> blocks such that each block contains <strong>equal values</strong>. Return<em> the number of these blocks.</em></p> <p><strong>Note</strong> that if you want to test your solution using a custom test, behavior for tests with <code>nums.length &gt; 10</code> is undefined.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [3,3,3,3,3] <strong>Output:</strong> 1 <strong>Explanation:</strong> There is only one block here which is the whole array (because all numbers are equal) and that is: [<u>3,3,3,3,3</u>]. So the answer would be 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [1,1,1,3,9,9,9,2,10,10] <strong>Output:</strong> 5 <strong>Explanation:</strong> There are 5 blocks here: Block number 1: [<u>1,1,1</u>,3,9,9,9,2,10,10] Block number 2: [1,1,1,<u>3</u>,9,9,9,2,10,10] Block number 3: [1,1,1,3,<u>9,9,9</u>,2,10,10] Block number 4: [1,1,1,3,9,9,9,<u>2</u>,10,10] Block number 5: [1,1,1,3,9,9,9,2,<u>10,10</u>] So the answer would be 5.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [1,2,3,4,5,6,7] <strong>Output:</strong> 7 <strong>Explanation:</strong> Since all numbers are distinct, there are 7 blocks here and each element representing one block. So the answer would be 7. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= nums.length &lt;= 10<sup>15</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li> <li>The input is generated such that all equal values are adjacent.</li> <li>The sum of the elements of&nbsp;<code>nums</code>&nbsp;is at most&nbsp;<code>10<sup>15</sup></code>.</li> </ul>
Array; Binary Search; Interactive
TypeScript
/** * Definition for BigArray. * class BigArray { * constructor(elements: number[]); * public at(index: number): number; * public size(): number; * } */ function countBlocks(nums: BigArray | null): number { const n = nums.size(); const search = (l: number): number => { let r = n; const x = nums.at(l); while (l < r) { const mid = l + Math.floor((r - l) / 2); if (nums.at(mid) !== x) { r = mid; } else { l = mid + 1; } } return l; }; let ans = 0; for (let i = 0; i < n; ++ans) { i = search(i); } return ans; }
2,937
Make Three Strings Equal
Easy
<p>You are given three strings: <code>s1</code>, <code>s2</code>, and <code>s3</code>. In one operation you can choose one of these strings and delete its <strong>rightmost</strong> character. Note that you <strong>cannot</strong> completely empty a string.</p> <p>Return the <em>minimum number of operations</em> required to make the strings equal<em>. </em>If it is impossible to make them equal, return <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;abc&quot;, s2 = &quot;abb&quot;, s3 = &quot;ab&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">2</span></p> <p><strong>Explanation:&nbsp;</strong>Deleting the rightmost character from both <code>s1</code> and <code>s2</code> will result in three equal strings.</p> </div> <p><strong class="example">Example 2:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;dac&quot;, s2 = &quot;bac&quot;, s3 = &quot;cac&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">-1</span></p> <p><strong>Explanation:</strong> Since the first letters of <code>s1</code> and <code>s2</code> differ, they cannot be made equal.</p> </div> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= s1.length, s2.length, s3.length &lt;= 100</code></li> <li><font face="monospace"><code>s1</code>,</font> <code><font face="monospace">s2</font></code><font face="monospace"> and</font> <code><font face="monospace">s3</font></code> consist only of lowercase English letters.</li> </ul>
String
C++
class Solution { public: int findMinimumOperations(string s1, string s2, string s3) { int s = s1.size() + s2.size() + s3.size(); int n = min({s1.size(), s2.size(), s3.size()}); for (int i = 0; i < n; ++i) { if (!(s1[i] == s2[i] && s2[i] == s3[i])) { return i == 0 ? -1 : s - 3 * i; } } return s - 3 * n; } };
2,937
Make Three Strings Equal
Easy
<p>You are given three strings: <code>s1</code>, <code>s2</code>, and <code>s3</code>. In one operation you can choose one of these strings and delete its <strong>rightmost</strong> character. Note that you <strong>cannot</strong> completely empty a string.</p> <p>Return the <em>minimum number of operations</em> required to make the strings equal<em>. </em>If it is impossible to make them equal, return <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;abc&quot;, s2 = &quot;abb&quot;, s3 = &quot;ab&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">2</span></p> <p><strong>Explanation:&nbsp;</strong>Deleting the rightmost character from both <code>s1</code> and <code>s2</code> will result in three equal strings.</p> </div> <p><strong class="example">Example 2:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;dac&quot;, s2 = &quot;bac&quot;, s3 = &quot;cac&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">-1</span></p> <p><strong>Explanation:</strong> Since the first letters of <code>s1</code> and <code>s2</code> differ, they cannot be made equal.</p> </div> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= s1.length, s2.length, s3.length &lt;= 100</code></li> <li><font face="monospace"><code>s1</code>,</font> <code><font face="monospace">s2</font></code><font face="monospace"> and</font> <code><font face="monospace">s3</font></code> consist only of lowercase English letters.</li> </ul>
String
Go
func findMinimumOperations(s1 string, s2 string, s3 string) int { s := len(s1) + len(s2) + len(s3) n := min(len(s1), len(s2), len(s3)) for i := range s1[:n] { if !(s1[i] == s2[i] && s2[i] == s3[i]) { if i == 0 { return -1 } return s - 3*i } } return s - 3*n }
2,937
Make Three Strings Equal
Easy
<p>You are given three strings: <code>s1</code>, <code>s2</code>, and <code>s3</code>. In one operation you can choose one of these strings and delete its <strong>rightmost</strong> character. Note that you <strong>cannot</strong> completely empty a string.</p> <p>Return the <em>minimum number of operations</em> required to make the strings equal<em>. </em>If it is impossible to make them equal, return <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;abc&quot;, s2 = &quot;abb&quot;, s3 = &quot;ab&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">2</span></p> <p><strong>Explanation:&nbsp;</strong>Deleting the rightmost character from both <code>s1</code> and <code>s2</code> will result in three equal strings.</p> </div> <p><strong class="example">Example 2:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;dac&quot;, s2 = &quot;bac&quot;, s3 = &quot;cac&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">-1</span></p> <p><strong>Explanation:</strong> Since the first letters of <code>s1</code> and <code>s2</code> differ, they cannot be made equal.</p> </div> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= s1.length, s2.length, s3.length &lt;= 100</code></li> <li><font face="monospace"><code>s1</code>,</font> <code><font face="monospace">s2</font></code><font face="monospace"> and</font> <code><font face="monospace">s3</font></code> consist only of lowercase English letters.</li> </ul>
String
Java
class Solution { public int findMinimumOperations(String s1, String s2, String s3) { int s = s1.length() + s2.length() + s3.length(); int n = Math.min(Math.min(s1.length(), s2.length()), s3.length()); for (int i = 0; i < n; ++i) { if (!(s1.charAt(i) == s2.charAt(i) && s2.charAt(i) == s3.charAt(i))) { return i == 0 ? -1 : s - 3 * i; } } return s - 3 * n; } }
2,937
Make Three Strings Equal
Easy
<p>You are given three strings: <code>s1</code>, <code>s2</code>, and <code>s3</code>. In one operation you can choose one of these strings and delete its <strong>rightmost</strong> character. Note that you <strong>cannot</strong> completely empty a string.</p> <p>Return the <em>minimum number of operations</em> required to make the strings equal<em>. </em>If it is impossible to make them equal, return <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;abc&quot;, s2 = &quot;abb&quot;, s3 = &quot;ab&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">2</span></p> <p><strong>Explanation:&nbsp;</strong>Deleting the rightmost character from both <code>s1</code> and <code>s2</code> will result in three equal strings.</p> </div> <p><strong class="example">Example 2:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;dac&quot;, s2 = &quot;bac&quot;, s3 = &quot;cac&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">-1</span></p> <p><strong>Explanation:</strong> Since the first letters of <code>s1</code> and <code>s2</code> differ, they cannot be made equal.</p> </div> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= s1.length, s2.length, s3.length &lt;= 100</code></li> <li><font face="monospace"><code>s1</code>,</font> <code><font face="monospace">s2</font></code><font face="monospace"> and</font> <code><font face="monospace">s3</font></code> consist only of lowercase English letters.</li> </ul>
String
Python
class Solution: def findMinimumOperations(self, s1: str, s2: str, s3: str) -> int: s = len(s1) + len(s2) + len(s3) n = min(len(s1), len(s2), len(s3)) for i in range(n): if not s1[i] == s2[i] == s3[i]: return -1 if i == 0 else s - 3 * i return s - 3 * n
2,937
Make Three Strings Equal
Easy
<p>You are given three strings: <code>s1</code>, <code>s2</code>, and <code>s3</code>. In one operation you can choose one of these strings and delete its <strong>rightmost</strong> character. Note that you <strong>cannot</strong> completely empty a string.</p> <p>Return the <em>minimum number of operations</em> required to make the strings equal<em>. </em>If it is impossible to make them equal, return <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;abc&quot;, s2 = &quot;abb&quot;, s3 = &quot;ab&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">2</span></p> <p><strong>Explanation:&nbsp;</strong>Deleting the rightmost character from both <code>s1</code> and <code>s2</code> will result in three equal strings.</p> </div> <p><strong class="example">Example 2:</strong></p> <div class="example-block" style="border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;"> <p><strong>Input: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">s1 = &quot;dac&quot;, s2 = &quot;bac&quot;, s3 = &quot;cac&quot;</span></p> <p><strong>Output: </strong><span class="example-io" style="font-family: Menlo,sans-serif; font-size: 0.85rem;">-1</span></p> <p><strong>Explanation:</strong> Since the first letters of <code>s1</code> and <code>s2</code> differ, they cannot be made equal.</p> </div> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= s1.length, s2.length, s3.length &lt;= 100</code></li> <li><font face="monospace"><code>s1</code>,</font> <code><font face="monospace">s2</font></code><font face="monospace"> and</font> <code><font face="monospace">s3</font></code> consist only of lowercase English letters.</li> </ul>
String
TypeScript
function findMinimumOperations(s1: string, s2: string, s3: string): number { const s = s1.length + s2.length + s3.length; const n = Math.min(s1.length, s2.length, s3.length); for (let i = 0; i < n; ++i) { if (!(s1[i] === s2[i] && s2[i] === s3[i])) { return i === 0 ? -1 : s - 3 * i; } } return s - 3 * n; }
2,938
Separate Black and White Balls
Medium
<p>There are <code>n</code> balls on a table, each ball has a color black or white.</p> <p>You are given a <strong>0-indexed</strong> binary string <code>s</code> of length <code>n</code>, where <code>1</code> and <code>0</code> represent black and white balls, respectively.</p> <p>In each step, you can choose two adjacent balls and swap them.</p> <p>Return <em>the <strong>minimum</strong> number of steps to group all the black balls to the right and all the white balls to the left</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = &quot;101&quot; <strong>Output:</strong> 1 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;011&quot;. Initially, 1s are not grouped together, requiring at least 1 step to group them to the right.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = &quot;100&quot; <strong>Output:</strong> 2 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;010&quot;. - Swap s[1] and s[2], s = &quot;001&quot;. It can be proven that the minimum number of steps needed is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = &quot;0111&quot; <strong>Output:</strong> 0 <strong>Explanation:</strong> All the black balls are already grouped to the right. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li> </ul>
Greedy; Two Pointers; String
C++
class Solution { public: long long minimumSteps(string s) { long long ans = 0; int cnt = 0; int n = s.size(); for (int i = n - 1; i >= 0; --i) { if (s[i] == '1') { ++cnt; ans += n - i - cnt; } } return ans; } };
2,938
Separate Black and White Balls
Medium
<p>There are <code>n</code> balls on a table, each ball has a color black or white.</p> <p>You are given a <strong>0-indexed</strong> binary string <code>s</code> of length <code>n</code>, where <code>1</code> and <code>0</code> represent black and white balls, respectively.</p> <p>In each step, you can choose two adjacent balls and swap them.</p> <p>Return <em>the <strong>minimum</strong> number of steps to group all the black balls to the right and all the white balls to the left</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = &quot;101&quot; <strong>Output:</strong> 1 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;011&quot;. Initially, 1s are not grouped together, requiring at least 1 step to group them to the right.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = &quot;100&quot; <strong>Output:</strong> 2 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;010&quot;. - Swap s[1] and s[2], s = &quot;001&quot;. It can be proven that the minimum number of steps needed is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = &quot;0111&quot; <strong>Output:</strong> 0 <strong>Explanation:</strong> All the black balls are already grouped to the right. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li> </ul>
Greedy; Two Pointers; String
Go
func minimumSteps(s string) (ans int64) { n := len(s) cnt := 0 for i := n - 1; i >= 0; i-- { if s[i] == '1' { cnt++ ans += int64(n - i - cnt) } } return }
2,938
Separate Black and White Balls
Medium
<p>There are <code>n</code> balls on a table, each ball has a color black or white.</p> <p>You are given a <strong>0-indexed</strong> binary string <code>s</code> of length <code>n</code>, where <code>1</code> and <code>0</code> represent black and white balls, respectively.</p> <p>In each step, you can choose two adjacent balls and swap them.</p> <p>Return <em>the <strong>minimum</strong> number of steps to group all the black balls to the right and all the white balls to the left</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = &quot;101&quot; <strong>Output:</strong> 1 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;011&quot;. Initially, 1s are not grouped together, requiring at least 1 step to group them to the right.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = &quot;100&quot; <strong>Output:</strong> 2 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;010&quot;. - Swap s[1] and s[2], s = &quot;001&quot;. It can be proven that the minimum number of steps needed is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = &quot;0111&quot; <strong>Output:</strong> 0 <strong>Explanation:</strong> All the black balls are already grouped to the right. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li> </ul>
Greedy; Two Pointers; String
Java
class Solution { public long minimumSteps(String s) { long ans = 0; int cnt = 0; int n = s.length(); for (int i = n - 1; i >= 0; --i) { if (s.charAt(i) == '1') { ++cnt; ans += n - i - cnt; } } return ans; } }
2,938
Separate Black and White Balls
Medium
<p>There are <code>n</code> balls on a table, each ball has a color black or white.</p> <p>You are given a <strong>0-indexed</strong> binary string <code>s</code> of length <code>n</code>, where <code>1</code> and <code>0</code> represent black and white balls, respectively.</p> <p>In each step, you can choose two adjacent balls and swap them.</p> <p>Return <em>the <strong>minimum</strong> number of steps to group all the black balls to the right and all the white balls to the left</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = &quot;101&quot; <strong>Output:</strong> 1 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;011&quot;. Initially, 1s are not grouped together, requiring at least 1 step to group them to the right.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = &quot;100&quot; <strong>Output:</strong> 2 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;010&quot;. - Swap s[1] and s[2], s = &quot;001&quot;. It can be proven that the minimum number of steps needed is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = &quot;0111&quot; <strong>Output:</strong> 0 <strong>Explanation:</strong> All the black balls are already grouped to the right. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li> </ul>
Greedy; Two Pointers; String
Python
class Solution: def minimumSteps(self, s: str) -> int: n = len(s) ans = cnt = 0 for i in range(n - 1, -1, -1): if s[i] == '1': cnt += 1 ans += n - i - cnt return ans
2,938
Separate Black and White Balls
Medium
<p>There are <code>n</code> balls on a table, each ball has a color black or white.</p> <p>You are given a <strong>0-indexed</strong> binary string <code>s</code> of length <code>n</code>, where <code>1</code> and <code>0</code> represent black and white balls, respectively.</p> <p>In each step, you can choose two adjacent balls and swap them.</p> <p>Return <em>the <strong>minimum</strong> number of steps to group all the black balls to the right and all the white balls to the left</em>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = &quot;101&quot; <strong>Output:</strong> 1 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;011&quot;. Initially, 1s are not grouped together, requiring at least 1 step to group them to the right.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = &quot;100&quot; <strong>Output:</strong> 2 <strong>Explanation:</strong> We can group all the black balls to the right in the following way: - Swap s[0] and s[1], s = &quot;010&quot;. - Swap s[1] and s[2], s = &quot;001&quot;. It can be proven that the minimum number of steps needed is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = &quot;0111&quot; <strong>Output:</strong> 0 <strong>Explanation:</strong> All the black balls are already grouped to the right. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li> </ul>
Greedy; Two Pointers; String
TypeScript
function minimumSteps(s: string): number { const n = s.length; let [ans, cnt] = [0, 0]; for (let i = n - 1; ~i; --i) { if (s[i] === '1') { ++cnt; ans += n - i - cnt; } } return ans; }
2,939
Maximum Xor Product
Medium
<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p> <p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p> <p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> a = 12, b = 5, n = 4 <strong>Output:</strong> 98 <strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. It can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style="font-size: 10.8333px;">.</span> </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> a = 6, b = 7 , n = 5 <strong>Output:</strong> 930 <strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930. It can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> a = 1, b = 6, n = 3 <strong>Output:</strong> 12 <strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12. It can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li> <li><code>0 &lt;= n &lt;= 50</code></li> </ul>
Greedy; Bit Manipulation; Math
C++
class Solution { public: int maximumXorProduct(long long a, long long b, int n) { const int mod = 1e9 + 7; long long ax = (a >> n) << n, bx = (b >> n) << n; for (int i = n - 1; ~i; --i) { int x = a >> i & 1, y = b >> i & 1; if (x == y) { ax |= 1LL << i; bx |= 1LL << i; } else if (ax < bx) { ax |= 1LL << i; } else { bx |= 1LL << i; } } ax %= mod; bx %= mod; return ax * bx % mod; } };
2,939
Maximum Xor Product
Medium
<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p> <p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p> <p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> a = 12, b = 5, n = 4 <strong>Output:</strong> 98 <strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. It can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style="font-size: 10.8333px;">.</span> </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> a = 6, b = 7 , n = 5 <strong>Output:</strong> 930 <strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930. It can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> a = 1, b = 6, n = 3 <strong>Output:</strong> 12 <strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12. It can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li> <li><code>0 &lt;= n &lt;= 50</code></li> </ul>
Greedy; Bit Manipulation; Math
Go
func maximumXorProduct(a int64, b int64, n int) int { const mod int64 = 1e9 + 7 ax := (a >> n) << n bx := (b >> n) << n for i := n - 1; i >= 0; i-- { x, y := (a>>i)&1, (b>>i)&1 if x == y { ax |= 1 << i bx |= 1 << i } else if ax < bx { ax |= 1 << i } else { bx |= 1 << i } } ax %= mod bx %= mod return int(ax * bx % mod) }
2,939
Maximum Xor Product
Medium
<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p> <p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p> <p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> a = 12, b = 5, n = 4 <strong>Output:</strong> 98 <strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. It can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style="font-size: 10.8333px;">.</span> </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> a = 6, b = 7 , n = 5 <strong>Output:</strong> 930 <strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930. It can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> a = 1, b = 6, n = 3 <strong>Output:</strong> 12 <strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12. It can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li> <li><code>0 &lt;= n &lt;= 50</code></li> </ul>
Greedy; Bit Manipulation; Math
Java
class Solution { public int maximumXorProduct(long a, long b, int n) { final int mod = (int) 1e9 + 7; long ax = (a >> n) << n; long bx = (b >> n) << n; for (int i = n - 1; i >= 0; --i) { long x = a >> i & 1; long y = b >> i & 1; if (x == y) { ax |= 1L << i; bx |= 1L << i; } else if (ax < bx) { ax |= 1L << i; } else { bx |= 1L << i; } } ax %= mod; bx %= mod; return (int) (ax * bx % mod); } }
2,939
Maximum Xor Product
Medium
<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p> <p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p> <p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> a = 12, b = 5, n = 4 <strong>Output:</strong> 98 <strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. It can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style="font-size: 10.8333px;">.</span> </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> a = 6, b = 7 , n = 5 <strong>Output:</strong> 930 <strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930. It can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> a = 1, b = 6, n = 3 <strong>Output:</strong> 12 <strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12. It can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li> <li><code>0 &lt;= n &lt;= 50</code></li> </ul>
Greedy; Bit Manipulation; Math
Python
class Solution: def maximumXorProduct(self, a: int, b: int, n: int) -> int: mod = 10**9 + 7 ax, bx = (a >> n) << n, (b >> n) << n for i in range(n - 1, -1, -1): x = a >> i & 1 y = b >> i & 1 if x == y: ax |= 1 << i bx |= 1 << i elif ax > bx: bx |= 1 << i else: ax |= 1 << i return ax * bx % mod
2,939
Maximum Xor Product
Medium
<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p> <p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p> <p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> a = 12, b = 5, n = 4 <strong>Output:</strong> 98 <strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. It can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style="font-size: 10.8333px;">.</span> </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> a = 6, b = 7 , n = 5 <strong>Output:</strong> 930 <strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930. It can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> a = 1, b = 6, n = 3 <strong>Output:</strong> 12 <strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12. It can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li> <li><code>0 &lt;= n &lt;= 50</code></li> </ul>
Greedy; Bit Manipulation; Math
TypeScript
function maximumXorProduct(a: number, b: number, n: number): number { const mod = BigInt(1e9 + 7); let ax = (BigInt(a) >> BigInt(n)) << BigInt(n); let bx = (BigInt(b) >> BigInt(n)) << BigInt(n); for (let i = BigInt(n - 1); ~i; --i) { const x = (BigInt(a) >> i) & 1n; const y = (BigInt(b) >> i) & 1n; if (x === y) { ax |= 1n << i; bx |= 1n << i; } else if (ax < bx) { ax |= 1n << i; } else { bx |= 1n << i; } } ax %= mod; bx %= mod; return Number((ax * bx) % mod); }
2,940
Find Building Where Alice and Bob Can Meet
Hard
<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p> <p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i &lt; j</code> and <code>heights[i] &lt; heights[j]</code>.</p> <p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p> <p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]] <strong>Output:</strong> [2,5,-1,5,2] <strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] &lt; heights[2] and heights[1] &lt; heights[2]. In the second query, Alice and Bob can move to building 5 since heights[0] &lt; heights[5] and heights[3] &lt; heights[5]. In the third query, Alice cannot meet Bob since Alice cannot move to any other building. In the fourth query, Alice and Bob can move to building 5 since heights[3] &lt; heights[5] and heights[4] &lt; heights[5]. In the fifth query, Alice and Bob are already in the same building. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]] <strong>Output:</strong> [7,6,-1,4,6] <strong>Explanation:</strong> In the first query, Alice can directly move to Bob&#39;s building since heights[0] &lt; heights[7]. In the second query, Alice and Bob can move to building 6 since heights[3] &lt; heights[6] and heights[5] &lt; heights[6]. In the third query, Alice cannot meet Bob since Bob cannot move to any other building. In the fourth query, Alice and Bob can move to building 4 since heights[3] &lt; heights[4] and heights[0] &lt; heights[4]. In the fifth query, Alice can directly move to Bob&#39;s building since heights[1] &lt; heights[6]. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= heights.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= heights.length - 1</code></li> </ul>
Stack; Binary Indexed Tree; Segment Tree; Array; Binary Search; Monotonic Stack; Heap (Priority Queue)
C++
class BinaryIndexedTree { private: int inf = 1 << 30; int n; vector<int> c; public: BinaryIndexedTree(int n) { this->n = n; c.resize(n + 1, inf); } void update(int x, int v) { while (x <= n) { c[x] = min(c[x], v); x += x & -x; } } int query(int x) { int mi = inf; while (x > 0) { mi = min(mi, c[x]); x -= x & -x; } return mi == inf ? -1 : mi; } }; class Solution { public: vector<int> leftmostBuildingQueries(vector<int>& heights, vector<vector<int>>& queries) { int n = heights.size(), m = queries.size(); for (auto& q : queries) { if (q[0] > q[1]) { swap(q[0], q[1]); } } vector<int> idx(m); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), [&](int i, int j) { return queries[j][1] < queries[i][1]; }); vector<int> s = heights; sort(s.begin(), s.end()); s.erase(unique(s.begin(), s.end()), s.end()); vector<int> ans(m); int j = n - 1; BinaryIndexedTree tree(n); for (int i : idx) { int l = queries[i][0], r = queries[i][1]; while (j > r) { int k = s.end() - lower_bound(s.begin(), s.end(), heights[j]) + 1; tree.update(k, j); --j; } if (l == r || heights[l] < heights[r]) { ans[i] = r; } else { int k = s.end() - lower_bound(s.begin(), s.end(), heights[l]); ans[i] = tree.query(k); } } return ans; } };
2,940
Find Building Where Alice and Bob Can Meet
Hard
<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p> <p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i &lt; j</code> and <code>heights[i] &lt; heights[j]</code>.</p> <p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p> <p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]] <strong>Output:</strong> [2,5,-1,5,2] <strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] &lt; heights[2] and heights[1] &lt; heights[2]. In the second query, Alice and Bob can move to building 5 since heights[0] &lt; heights[5] and heights[3] &lt; heights[5]. In the third query, Alice cannot meet Bob since Alice cannot move to any other building. In the fourth query, Alice and Bob can move to building 5 since heights[3] &lt; heights[5] and heights[4] &lt; heights[5]. In the fifth query, Alice and Bob are already in the same building. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]] <strong>Output:</strong> [7,6,-1,4,6] <strong>Explanation:</strong> In the first query, Alice can directly move to Bob&#39;s building since heights[0] &lt; heights[7]. In the second query, Alice and Bob can move to building 6 since heights[3] &lt; heights[6] and heights[5] &lt; heights[6]. In the third query, Alice cannot meet Bob since Bob cannot move to any other building. In the fourth query, Alice and Bob can move to building 4 since heights[3] &lt; heights[4] and heights[0] &lt; heights[4]. In the fifth query, Alice can directly move to Bob&#39;s building since heights[1] &lt; heights[6]. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= heights.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= heights.length - 1</code></li> </ul>
Stack; Binary Indexed Tree; Segment Tree; Array; Binary Search; Monotonic Stack; Heap (Priority Queue)
Go
const inf int = 1 << 30 type BinaryIndexedTree struct { n int c []int } func NewBinaryIndexedTree(n int) BinaryIndexedTree { c := make([]int, n+1) for i := range c { c[i] = inf } return BinaryIndexedTree{n: n, c: c} } func (bit *BinaryIndexedTree) update(x, v int) { for x <= bit.n { bit.c[x] = min(bit.c[x], v) x += x & -x } } func (bit *BinaryIndexedTree) query(x int) int { mi := inf for x > 0 { mi = min(mi, bit.c[x]) x -= x & -x } if mi == inf { return -1 } return mi } func leftmostBuildingQueries(heights []int, queries [][]int) []int { n, m := len(heights), len(queries) for _, q := range queries { if q[0] > q[1] { q[0], q[1] = q[1], q[0] } } idx := make([]int, m) for i := range idx { idx[i] = i } sort.Slice(idx, func(i, j int) bool { return queries[idx[j]][1] < queries[idx[i]][1] }) s := make([]int, n) copy(s, heights) sort.Ints(s) ans := make([]int, m) tree := NewBinaryIndexedTree(n) j := n - 1 for _, i := range idx { l, r := queries[i][0], queries[i][1] for ; j > r; j-- { k := n - sort.SearchInts(s, heights[j]) + 1 tree.update(k, j) } if l == r || heights[l] < heights[r] { ans[i] = r } else { k := n - sort.SearchInts(s, heights[l]) ans[i] = tree.query(k) } } return ans }
2,940
Find Building Where Alice and Bob Can Meet
Hard
<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p> <p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i &lt; j</code> and <code>heights[i] &lt; heights[j]</code>.</p> <p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p> <p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]] <strong>Output:</strong> [2,5,-1,5,2] <strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] &lt; heights[2] and heights[1] &lt; heights[2]. In the second query, Alice and Bob can move to building 5 since heights[0] &lt; heights[5] and heights[3] &lt; heights[5]. In the third query, Alice cannot meet Bob since Alice cannot move to any other building. In the fourth query, Alice and Bob can move to building 5 since heights[3] &lt; heights[5] and heights[4] &lt; heights[5]. In the fifth query, Alice and Bob are already in the same building. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]] <strong>Output:</strong> [7,6,-1,4,6] <strong>Explanation:</strong> In the first query, Alice can directly move to Bob&#39;s building since heights[0] &lt; heights[7]. In the second query, Alice and Bob can move to building 6 since heights[3] &lt; heights[6] and heights[5] &lt; heights[6]. In the third query, Alice cannot meet Bob since Bob cannot move to any other building. In the fourth query, Alice and Bob can move to building 4 since heights[3] &lt; heights[4] and heights[0] &lt; heights[4]. In the fifth query, Alice can directly move to Bob&#39;s building since heights[1] &lt; heights[6]. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= heights.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= heights.length - 1</code></li> </ul>
Stack; Binary Indexed Tree; Segment Tree; Array; Binary Search; Monotonic Stack; Heap (Priority Queue)
Java
class BinaryIndexedTree { private final int inf = 1 << 30; private int n; private int[] c; public BinaryIndexedTree(int n) { this.n = n; c = new int[n + 1]; Arrays.fill(c, inf); } public void update(int x, int v) { while (x <= n) { c[x] = Math.min(c[x], v); x += x & -x; } } public int query(int x) { int mi = inf; while (x > 0) { mi = Math.min(mi, c[x]); x -= x & -x; } return mi == inf ? -1 : mi; } } class Solution { public int[] leftmostBuildingQueries(int[] heights, int[][] queries) { int n = heights.length; int m = queries.length; for (int i = 0; i < m; ++i) { if (queries[i][0] > queries[i][1]) { queries[i] = new int[] {queries[i][1], queries[i][0]}; } } Integer[] idx = new Integer[m]; for (int i = 0; i < m; ++i) { idx[i] = i; } Arrays.sort(idx, (i, j) -> queries[j][1] - queries[i][1]); int[] s = heights.clone(); Arrays.sort(s); int[] ans = new int[m]; int j = n - 1; BinaryIndexedTree tree = new BinaryIndexedTree(n); for (int i : idx) { int l = queries[i][0], r = queries[i][1]; while (j > r) { int k = n - Arrays.binarySearch(s, heights[j]) + 1; tree.update(k, j); --j; } if (l == r || heights[l] < heights[r]) { ans[i] = r; } else { int k = n - Arrays.binarySearch(s, heights[l]); ans[i] = tree.query(k); } } return ans; } }
2,940
Find Building Where Alice and Bob Can Meet
Hard
<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p> <p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i &lt; j</code> and <code>heights[i] &lt; heights[j]</code>.</p> <p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p> <p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]] <strong>Output:</strong> [2,5,-1,5,2] <strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] &lt; heights[2] and heights[1] &lt; heights[2]. In the second query, Alice and Bob can move to building 5 since heights[0] &lt; heights[5] and heights[3] &lt; heights[5]. In the third query, Alice cannot meet Bob since Alice cannot move to any other building. In the fourth query, Alice and Bob can move to building 5 since heights[3] &lt; heights[5] and heights[4] &lt; heights[5]. In the fifth query, Alice and Bob are already in the same building. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]] <strong>Output:</strong> [7,6,-1,4,6] <strong>Explanation:</strong> In the first query, Alice can directly move to Bob&#39;s building since heights[0] &lt; heights[7]. In the second query, Alice and Bob can move to building 6 since heights[3] &lt; heights[6] and heights[5] &lt; heights[6]. In the third query, Alice cannot meet Bob since Bob cannot move to any other building. In the fourth query, Alice and Bob can move to building 4 since heights[3] &lt; heights[4] and heights[0] &lt; heights[4]. In the fifth query, Alice can directly move to Bob&#39;s building since heights[1] &lt; heights[6]. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= heights.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= heights.length - 1</code></li> </ul>
Stack; Binary Indexed Tree; Segment Tree; Array; Binary Search; Monotonic Stack; Heap (Priority Queue)
Python
class BinaryIndexedTree: __slots__ = ["n", "c"] def __init__(self, n: int): self.n = n self.c = [inf] * (n + 1) def update(self, x: int, v: int): while x <= self.n: self.c[x] = min(self.c[x], v) x += x & -x def query(self, x: int) -> int: mi = inf while x: mi = min(mi, self.c[x]) x -= x & -x return -1 if mi == inf else mi class Solution: def leftmostBuildingQueries( self, heights: List[int], queries: List[List[int]] ) -> List[int]: n, m = len(heights), len(queries) for i in range(m): queries[i] = [min(queries[i]), max(queries[i])] j = n - 1 s = sorted(set(heights)) ans = [-1] * m tree = BinaryIndexedTree(n) for i in sorted(range(m), key=lambda i: -queries[i][1]): l, r = queries[i] while j > r: k = n - bisect_left(s, heights[j]) + 1 tree.update(k, j) j -= 1 if l == r or heights[l] < heights[r]: ans[i] = r else: k = n - bisect_left(s, heights[l]) ans[i] = tree.query(k) return ans
2,940
Find Building Where Alice and Bob Can Meet
Hard
<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p> <p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i &lt; j</code> and <code>heights[i] &lt; heights[j]</code>.</p> <p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p> <p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]] <strong>Output:</strong> [2,5,-1,5,2] <strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] &lt; heights[2] and heights[1] &lt; heights[2]. In the second query, Alice and Bob can move to building 5 since heights[0] &lt; heights[5] and heights[3] &lt; heights[5]. In the third query, Alice cannot meet Bob since Alice cannot move to any other building. In the fourth query, Alice and Bob can move to building 5 since heights[3] &lt; heights[5] and heights[4] &lt; heights[5]. In the fifth query, Alice and Bob are already in the same building. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]] <strong>Output:</strong> [7,6,-1,4,6] <strong>Explanation:</strong> In the first query, Alice can directly move to Bob&#39;s building since heights[0] &lt; heights[7]. In the second query, Alice and Bob can move to building 6 since heights[3] &lt; heights[6] and heights[5] &lt; heights[6]. In the third query, Alice cannot meet Bob since Bob cannot move to any other building. In the fourth query, Alice and Bob can move to building 4 since heights[3] &lt; heights[4] and heights[0] &lt; heights[4]. In the fifth query, Alice can directly move to Bob&#39;s building since heights[1] &lt; heights[6]. For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet. For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= heights.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li> <li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</sup></code></li> <li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li> <li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= heights.length - 1</code></li> </ul>
Stack; Binary Indexed Tree; Segment Tree; Array; Binary Search; Monotonic Stack; Heap (Priority Queue)
TypeScript
class BinaryIndexedTree { private n: number; private c: number[]; private inf: number = 1 << 30; constructor(n: number) { this.n = n; this.c = Array(n + 1).fill(this.inf); } update(x: number, v: number): void { while (x <= this.n) { this.c[x] = Math.min(this.c[x], v); x += x & -x; } } query(x: number): number { let mi = this.inf; while (x > 0) { mi = Math.min(mi, this.c[x]); x -= x & -x; } return mi === this.inf ? -1 : mi; } } function leftmostBuildingQueries(heights: number[], queries: number[][]): number[] { const n = heights.length; const m = queries.length; for (const q of queries) { if (q[0] > q[1]) { [q[0], q[1]] = [q[1], q[0]]; } } const idx: number[] = Array(m) .fill(0) .map((_, i) => i); idx.sort((i, j) => queries[j][1] - queries[i][1]); const tree = new BinaryIndexedTree(n); const ans: number[] = Array(m).fill(-1); const s = [...heights]; s.sort((a, b) => a - b); const search = (x: number) => { let [l, r] = [0, n]; while (l < r) { const mid = (l + r) >> 1; if (s[mid] >= x) { r = mid; } else { l = mid + 1; } } return l; }; let j = n - 1; for (const i of idx) { const [l, r] = queries[i]; while (j > r) { const k = n - search(heights[j]) + 1; tree.update(k, j); --j; } if (l === r || heights[l] < heights[r]) { ans[i] = r; } else { const k = n - search(heights[l]); ans[i] = tree.query(k); } } return ans; }
2,941
Maximum GCD-Sum of a Subarray
Hard
<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p> <p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p> <ul> <li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li> <li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li> <li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li> </ul> <p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2 <strong>Output:</strong> 48 <strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48. It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [7,3,9,4], k = 1 <strong>Output:</strong> 81 <strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81. It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == nums.length</code></li> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= k &lt;= n</code></li> </ul>
Array; Math; Binary Search; Number Theory
C++
class Solution { public: long long maxGcdSum(vector<int>& nums, int k) { int n = nums.size(); long long s[n + 1]; s[0] = 0; for (int i = 1; i <= n; ++i) { s[i] = s[i - 1] + nums[i - 1]; } vector<pair<int, int>> f; long long ans = 0; for (int i = 0; i < n; ++i) { vector<pair<int, int>> g; for (auto [j, x] : f) { int y = gcd(x, nums[i]); if (g.empt() || g.back().second != y) { g.emplace_back(j, y); } } f = move(g); f.emplace_back(i, nums[i]); for (auto [j, x] : f) { if (i - j + 1 >= k) { ans = max(ans, (s[i + 1] - s[j]) * x); } } } return ans; } };
2,941
Maximum GCD-Sum of a Subarray
Hard
<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p> <p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p> <ul> <li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li> <li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li> <li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li> </ul> <p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2 <strong>Output:</strong> 48 <strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48. It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [7,3,9,4], k = 1 <strong>Output:</strong> 81 <strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81. It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == nums.length</code></li> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= k &lt;= n</code></li> </ul>
Array; Math; Binary Search; Number Theory
Go
func maxGcdSum(nums []int, k int) int64 { n := len(nums) s := make([]int64, n+1) s[0] = 0 for i, x := range nums { s[i+1] = s[i] + int64(x) } type pair [2]int var f []pair var ans int64 for i := 0; i < n; i++ { var g []pair for _, p := range f { j, x := p[0], p[1] y := int(gcd(int(x), nums[i])) if len(g) == 0 || g[len(g)-1][1] != y { g = append(g, pair{j, y}) } } f = g f = append(f, pair{i, nums[i]}) for _, p := range f { j, x := p[0], p[1] if i-j+1 >= k { ans = max(ans, (s[i+1]-s[j])*int64(x)) } } } return ans } func gcd(a, b int) int { if b == 0 { return a } return gcd(b, a%b) }
2,941
Maximum GCD-Sum of a Subarray
Hard
<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p> <p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p> <ul> <li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li> <li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li> <li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li> </ul> <p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2 <strong>Output:</strong> 48 <strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48. It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [7,3,9,4], k = 1 <strong>Output:</strong> 81 <strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81. It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == nums.length</code></li> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= k &lt;= n</code></li> </ul>
Array; Math; Binary Search; Number Theory
Java
class Solution { public long maxGcdSum(int[] nums, int k) { int n = nums.length; long[] s = new long[n + 1]; for (int i = 1; i <= n; ++i) { s[i] = s[i - 1] + nums[i - 1]; } List<int[]> f = new ArrayList<>(); long ans = 0; for (int i = 0; i < n; ++i) { List<int[]> g = new ArrayList<>(); for (var e : f) { int j = e[0], x = e[1]; int y = gcd(x, nums[i]); if (g.isEmpty() || g.get(g.size() - 1)[1] != y) { g.add(new int[] {j, y}); } } f = g; f.add(new int[] {i, nums[i]}); for (var e : f) { int j = e[0], x = e[1]; if (i - j + 1 >= k) { ans = Math.max(ans, (s[i + 1] - s[j]) * x); } } } return ans; } private int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } }
2,941
Maximum GCD-Sum of a Subarray
Hard
<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p> <p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p> <ul> <li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li> <li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li> <li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li> </ul> <p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2 <strong>Output:</strong> 48 <strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48. It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [7,3,9,4], k = 1 <strong>Output:</strong> 81 <strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81. It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == nums.length</code></li> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= k &lt;= n</code></li> </ul>
Array; Math; Binary Search; Number Theory
Python
class Solution: def maxGcdSum(self, nums: List[int], k: int) -> int: s = list(accumulate(nums, initial=0)) f = [] ans = 0 for i, v in enumerate(nums): g = [] for j, x in f: y = gcd(x, v) if not g or g[-1][1] != y: g.append((j, y)) f = g f.append((i, v)) for j, x in f: if i - j + 1 >= k: ans = max(ans, (s[i + 1] - s[j]) * x) return ans
2,941
Maximum GCD-Sum of a Subarray
Hard
<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p> <p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p> <ul> <li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li> <li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li> <li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li> </ul> <p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2 <strong>Output:</strong> 48 <strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48. It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [7,3,9,4], k = 1 <strong>Output:</strong> 81 <strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81. It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>n == nums.length</code></li> <li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li> <li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li> <li><code>1 &lt;= k &lt;= n</code></li> </ul>
Array; Math; Binary Search; Number Theory
TypeScript
function maxGcdSum(nums: number[], k: number): number { const n: number = nums.length; const s: number[] = Array(n + 1).fill(0); for (let i = 1; i <= n; i++) { s[i] = s[i - 1] + nums[i - 1]; } let f: [number, number][] = []; let ans: number = 0; for (let i = 0; i < n; ++i) { const g: [number, number][] = []; for (const [j, x] of f) { const y: number = gcd(x, nums[i]); if (g.length === 0 || g.at(-1)[1] !== y) { g.push([j, y]); } } f = g; f.push([i, nums[i]]); for (const [j, x] of f) { if (i - j + 1 >= k) { ans = Math.max(ans, (s[i + 1] - s[j]) * x); } } } return ans; } function gcd(a: number, b: number): number { return b === 0 ? a : gcd(b, a % b); }
2,942
Find Words Containing Character
Easy
<p>You are given a <strong>0-indexed</strong> array of strings <code>words</code> and a character <code>x</code>.</p> <p>Return <em>an <strong>array of indices</strong> representing the words that contain the character </em><code>x</code>.</p> <p><strong>Note</strong> that the returned array may be in <strong>any</strong> order.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> words = [&quot;leet&quot;,&quot;code&quot;], x = &quot;e&quot; <strong>Output:</strong> [0,1] <strong>Explanation:</strong> &quot;e&quot; occurs in both words: &quot;l<strong><u>ee</u></strong>t&quot;, and &quot;cod<u><strong>e</strong></u>&quot;. Hence, we return indices 0 and 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;a&quot; <strong>Output:</strong> [0,2] <strong>Explanation:</strong> &quot;a&quot; occurs in &quot;<strong><u>a</u></strong>bc&quot;, and &quot;<u><strong>aaaa</strong></u>&quot;. Hence, we return indices 0 and 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;z&quot; <strong>Output:</strong> [] <strong>Explanation:</strong> &quot;z&quot; does not occur in any of the words. Hence, we return an empty array. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= words.length &lt;= 50</code></li> <li><code>1 &lt;= words[i].length &lt;= 50</code></li> <li><code>x</code> is a lowercase English letter.</li> <li><code>words[i]</code> consists only of lowercase English letters.</li> </ul>
Array; String
C++
class Solution { public: vector<int> findWordsContaining(vector<string>& words, char x) { vector<int> ans; for (int i = 0; i < words.size(); ++i) { if (words[i].find(x) != string::npos) { ans.push_back(i); } } return ans; } };
2,942
Find Words Containing Character
Easy
<p>You are given a <strong>0-indexed</strong> array of strings <code>words</code> and a character <code>x</code>.</p> <p>Return <em>an <strong>array of indices</strong> representing the words that contain the character </em><code>x</code>.</p> <p><strong>Note</strong> that the returned array may be in <strong>any</strong> order.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> words = [&quot;leet&quot;,&quot;code&quot;], x = &quot;e&quot; <strong>Output:</strong> [0,1] <strong>Explanation:</strong> &quot;e&quot; occurs in both words: &quot;l<strong><u>ee</u></strong>t&quot;, and &quot;cod<u><strong>e</strong></u>&quot;. Hence, we return indices 0 and 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;a&quot; <strong>Output:</strong> [0,2] <strong>Explanation:</strong> &quot;a&quot; occurs in &quot;<strong><u>a</u></strong>bc&quot;, and &quot;<u><strong>aaaa</strong></u>&quot;. Hence, we return indices 0 and 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;z&quot; <strong>Output:</strong> [] <strong>Explanation:</strong> &quot;z&quot; does not occur in any of the words. Hence, we return an empty array. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= words.length &lt;= 50</code></li> <li><code>1 &lt;= words[i].length &lt;= 50</code></li> <li><code>x</code> is a lowercase English letter.</li> <li><code>words[i]</code> consists only of lowercase English letters.</li> </ul>
Array; String
Go
func findWordsContaining(words []string, x byte) (ans []int) { for i, w := range words { for _, c := range w { if byte(c) == x { ans = append(ans, i) break } } } return }
2,942
Find Words Containing Character
Easy
<p>You are given a <strong>0-indexed</strong> array of strings <code>words</code> and a character <code>x</code>.</p> <p>Return <em>an <strong>array of indices</strong> representing the words that contain the character </em><code>x</code>.</p> <p><strong>Note</strong> that the returned array may be in <strong>any</strong> order.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> words = [&quot;leet&quot;,&quot;code&quot;], x = &quot;e&quot; <strong>Output:</strong> [0,1] <strong>Explanation:</strong> &quot;e&quot; occurs in both words: &quot;l<strong><u>ee</u></strong>t&quot;, and &quot;cod<u><strong>e</strong></u>&quot;. Hence, we return indices 0 and 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;a&quot; <strong>Output:</strong> [0,2] <strong>Explanation:</strong> &quot;a&quot; occurs in &quot;<strong><u>a</u></strong>bc&quot;, and &quot;<u><strong>aaaa</strong></u>&quot;. Hence, we return indices 0 and 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;z&quot; <strong>Output:</strong> [] <strong>Explanation:</strong> &quot;z&quot; does not occur in any of the words. Hence, we return an empty array. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= words.length &lt;= 50</code></li> <li><code>1 &lt;= words[i].length &lt;= 50</code></li> <li><code>x</code> is a lowercase English letter.</li> <li><code>words[i]</code> consists only of lowercase English letters.</li> </ul>
Array; String
Java
class Solution { public List<Integer> findWordsContaining(String[] words, char x) { List<Integer> ans = new ArrayList<>(); for (int i = 0; i < words.length; ++i) { if (words[i].indexOf(x) != -1) { ans.add(i); } } return ans; } }
2,942
Find Words Containing Character
Easy
<p>You are given a <strong>0-indexed</strong> array of strings <code>words</code> and a character <code>x</code>.</p> <p>Return <em>an <strong>array of indices</strong> representing the words that contain the character </em><code>x</code>.</p> <p><strong>Note</strong> that the returned array may be in <strong>any</strong> order.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> words = [&quot;leet&quot;,&quot;code&quot;], x = &quot;e&quot; <strong>Output:</strong> [0,1] <strong>Explanation:</strong> &quot;e&quot; occurs in both words: &quot;l<strong><u>ee</u></strong>t&quot;, and &quot;cod<u><strong>e</strong></u>&quot;. Hence, we return indices 0 and 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;a&quot; <strong>Output:</strong> [0,2] <strong>Explanation:</strong> &quot;a&quot; occurs in &quot;<strong><u>a</u></strong>bc&quot;, and &quot;<u><strong>aaaa</strong></u>&quot;. Hence, we return indices 0 and 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;z&quot; <strong>Output:</strong> [] <strong>Explanation:</strong> &quot;z&quot; does not occur in any of the words. Hence, we return an empty array. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= words.length &lt;= 50</code></li> <li><code>1 &lt;= words[i].length &lt;= 50</code></li> <li><code>x</code> is a lowercase English letter.</li> <li><code>words[i]</code> consists only of lowercase English letters.</li> </ul>
Array; String
Python
class Solution: def findWordsContaining(self, words: List[str], x: str) -> List[int]: return [i for i, w in enumerate(words) if x in w]
2,942
Find Words Containing Character
Easy
<p>You are given a <strong>0-indexed</strong> array of strings <code>words</code> and a character <code>x</code>.</p> <p>Return <em>an <strong>array of indices</strong> representing the words that contain the character </em><code>x</code>.</p> <p><strong>Note</strong> that the returned array may be in <strong>any</strong> order.</p> <p>&nbsp;</p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> words = [&quot;leet&quot;,&quot;code&quot;], x = &quot;e&quot; <strong>Output:</strong> [0,1] <strong>Explanation:</strong> &quot;e&quot; occurs in both words: &quot;l<strong><u>ee</u></strong>t&quot;, and &quot;cod<u><strong>e</strong></u>&quot;. Hence, we return indices 0 and 1. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;a&quot; <strong>Output:</strong> [0,2] <strong>Explanation:</strong> &quot;a&quot; occurs in &quot;<strong><u>a</u></strong>bc&quot;, and &quot;<u><strong>aaaa</strong></u>&quot;. Hence, we return indices 0 and 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> words = [&quot;abc&quot;,&quot;bcd&quot;,&quot;aaaa&quot;,&quot;cbc&quot;], x = &quot;z&quot; <strong>Output:</strong> [] <strong>Explanation:</strong> &quot;z&quot; does not occur in any of the words. Hence, we return an empty array. </pre> <p>&nbsp;</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 &lt;= words.length &lt;= 50</code></li> <li><code>1 &lt;= words[i].length &lt;= 50</code></li> <li><code>x</code> is a lowercase English letter.</li> <li><code>words[i]</code> consists only of lowercase English letters.</li> </ul>
Array; String
Rust
impl Solution { pub fn find_words_containing(words: Vec<String>, x: char) -> Vec<i32> { words .into_iter() .enumerate() .filter_map(|(i, w)| w.contains(x).then(|| i as i32)) .collect() } }