feat: add solutions to lc problem: No.1395

yanglbme · yanglbme · commit 9c67122afa4b · 2023-04-12T15:02:47.000+08:00
No.1395.Count Number of Teams
diff --git a/solution/1300-1399/1395.Count Number of Teams/README.md b/solution/1300-1399/1395.Count Number of Teams/README.md
diff --git a/solution/1300-1399/1395.Count Number of Teams/README_EN.md b/solution/1300-1399/1395.Count Number of Teams/README_EN.md
diff --git a/solution/1300-1399/1395.Count Number of Teams/Solution.cpp b/solution/1300-1399/1395.Count Number of Teams/Solution.cpp
@@ -1,22 +1,53 @@
+class BinaryIndexedTree {
+public:
+    BinaryIndexedTree(int _n)
+        : n(_n)
+        , c(_n + 1) {}
+
+    void update(int x, int delta) {
+        while (x <= n) {
+            c[x] += delta;
+            x += x & -x;
+        }
+    }
+
+    int query(int x) {
+        int s = 0;
+        while (x) {
+            s += c[x];
+            x -= x & -x;
+        }
+        return s;
+    }
+
+private:
+    int n;
+    vector<int> c;
+};
+
 class Solution {
 public:
     int numTeams(vector<int>& rating) {
-        int n = rating.size(), ans = 0;
-        for (int j = 1; j < n - 1; ++j) {
-            int ia = 0, ib = 0, ka = 0, kb = 0;
-            for (int i = 0; i < j; ++i) {
-                if (rating[i] < rating[j])
-                    ++ia;
-                else if (rating[i] > rating[j])
-                    ++ib;
-            }
-            for (int k = j + 1; k < n; ++k) {
-                if (rating[j] < rating[k])
-                    ++ka;
-                else if (rating[j] > rating[k])
-                    ++kb;
-            }
-            ans += ia * ka + ib * kb;
+        vector<int> nums = rating;
+        sort(nums.begin(), nums.end());
+        nums.erase(unique(nums.begin(), nums.end()), nums.end());
+        int m = nums.size();
+        BinaryIndexedTree tree1(m);
+        BinaryIndexedTree tree2(m);
+        for (int& v : rating) {
+            int x = lower_bound(nums.begin(), nums.end(), v) - nums.begin() + 1;
+            tree2.update(x, 1);
+        }
+        int ans = 0;
+        int n = rating.size();
+        for (int i = 0; i < n; ++i) {
+            int x = lower_bound(nums.begin(), nums.end(), rating[i]) - nums.begin() + 1;
+            tree1.update(x, 1);
+            tree2.update(x, -1);
+            int l = tree1.query(x - 1);
+            int r = n - i - 1 - tree2.query(x);
+            ans += l * r;
+            ans += (i - l) * (n - i - 1 - r);
         }
         return ans;
     }
diff --git a/solution/1300-1399/1395.Count Number of Teams/Solution.go b/solution/1300-1399/1395.Count Number of Teams/Solution.go
@@ -1,22 +1,55 @@
-func numTeams(rating []int) int {
-	n, ans := len(rating), 0
-	for j := 1; j < n-1; j++ {
-		ia, ib, ka, kb := 0, 0, 0, 0
-		for i := 0; i < j; i++ {
-			if rating[i] < rating[j] {
-				ia++
-			} else if rating[i] > rating[j] {
-				ib++
-			}
-		}
-		for k := j + 1; k < n; k++ {
-			if rating[j] < rating[k] {
-				ka++
-			} else if rating[j] > rating[k] {
-				kb++
-			}
+type BinaryIndexedTree struct {
+	n int
+	c []int
+}
+
+func newBinaryIndexedTree(n int) *BinaryIndexedTree {
+	c := make([]int, n+1)
+	return &BinaryIndexedTree{n, c}
+}
+
+func (this *BinaryIndexedTree) update(x, delta int) {
+	for x <= this.n {
+		this.c[x] += delta
+		x += x & -x
+	}
+}
+
+func (this *BinaryIndexedTree) query(x int) int {
+	s := 0
+	for x > 0 {
+		s += this.c[x]
+		x -= x & -x
+	}
+	return s
+}
+
+func numTeams(rating []int) (ans int) {
+	nums := make([]int, len(rating))
+	copy(nums, rating)
+	sort.Ints(nums)
+	m := 0
+	for i, x := range nums {
+		if i == 0 || x != nums[i-1] {
+			nums[m] = x
+			m++
 		}
-		ans += ia*ka + ib*kb
 	}
-	return ans
+	nums = nums[:m]
+	tree1 := newBinaryIndexedTree(m)
+	tree2 := newBinaryIndexedTree(m)
+	for _, x := range rating {
+		tree2.update(sort.SearchInts(nums, x)+1, 1)
+	}
+	n := len(rating)
+	for i, v := range rating {
+		x := sort.SearchInts(nums, v) + 1
+		tree1.update(x, 1)
+		tree2.update(x, -1)
+		l := tree1.query(x - 1)
+		r := n - i - 1 - tree2.query(x)
+		ans += l * r
+		ans += (i - l) * (n - i - 1 - r)
+	}
+	return
 }
diff --git a/solution/1300-1399/1395.Count Number of Teams/Solution.java b/solution/1300-1399/1395.Count Number of Teams/Solution.java
@@ -1,28 +1,70 @@
+class BinaryIndexedTree {
+    private int n;
+    private int[] c;
+
+    public BinaryIndexedTree(int n) {
+        this.n = n;
+        this.c = new int[n + 1];
+    }
+
+    public void update(int x, int v) {
+        while (x <= n) {
+            c[x] += v;
+            x += x & -x;
+        }
+    }
+
+    public int query(int x) {
+        int s = 0;
+        while (x > 0) {
+            s += c[x];
+            x -= x & -x;
+        }
+        return s;
+    }
+}
+
 class Solution {
     public int numTeams(int[] rating) {
         int n = rating.length;
-        int ans = 0;
-        for (int j = 1; j < n - 1; ++j) {
-            int ia = 0;
-            int ib = 0;
-            int ka = 0;
-            int kb = 0;
-            for (int i = 0; i < j; ++i) {
-                if (rating[i] < rating[j]) {
-                    ++ia;
-                } else if (rating[i] > rating[j]) {
-                    ++ib;
-                }
-            }
-            for (int k = j + 1; k < n; ++k) {
-                if (rating[j] < rating[k]) {
-                    ++ka;
-                } else if (rating[j] > rating[k]) {
-                    ++kb;
-                }
+        int[] nums = rating.clone();
+        Arrays.sort(nums);
+        int m = 0;
+        for (int i = 0; i < n; ++i) {
+            if (i == 0 || nums[i] != nums[i - 1]) {
+                nums[m++] = nums[i];
             }
-            ans += ia * ka + ib * kb;
+        }
+        BinaryIndexedTree tree1 = new BinaryIndexedTree(m);
+        BinaryIndexedTree tree2 = new BinaryIndexedTree(m);
+        for (int v : rating) {
+            int x = search(nums, v);
+            tree2.update(x, 1);
+        }
+
+        int ans = 0;
+        for (int i = 0; i < n; ++i) {
+            int x = search(nums, rating[i]);
+            tree1.update(x, 1);
+            tree2.update(x, -1);
+            int l = tree1.query(x - 1);
+            int r = n - i - 1 - tree2.query(x);
+            ans += l * r;
+            ans += (i - l) * (n - i - 1 - r);
         }
         return ans;
     }
+
+    private int search(int[] nums, int x) {
+        int l = 0, r = nums.length;
+        while (l < r) {
+            int mid = (l + r) >> 1;
+            if (nums[mid] >= x) {
+                r = mid;
+            } else {
+                l = mid + 1;
+            }
+        }
+        return l + 1;
+    }
 }
diff --git a/solution/1300-1399/1395.Count Number of Teams/Solution.py b/solution/1300-1399/1395.Count Number of Teams/Solution.py
@@ -1,17 +1,38 @@
+class BinaryIndexedTree:
+    def __init__(self, n: int):
+        self.n = n
+        self.c = [0] * (n + 1)
+
+    def update(self, x: int, v: int):
+        while x <= self.n:
+            self.c[x] += v
+            x += x & -x
+
+    def query(self, x: int) -> int:
+        s = 0
+        while x:
+            s += self.c[x]
+            x -= x & -x
+        return s
+
+
 class Solution:
     def numTeams(self, rating: List[int]) -> int:
-        n, ans = len(rating), 0
-        for j in range(1, n - 1):
-            ia = ib = ka = kb = 0
-            for i in range(j):
-                if rating[i] < rating[j]:
-                    ia += 1
-                elif rating[i] > rating[j]:
-                    ib += 1
-            for k in range(j + 1, n):
-                if rating[j] < rating[k]:
-                    ka += 1
-                elif rating[j] > rating[k]:
-                    kb += 1
-            ans += ia * ka + ib * kb
+        nums = sorted(set(rating))
+        m = len(nums)
+        tree1 = BinaryIndexedTree(m)
+        tree2 = BinaryIndexedTree(m)
+        for v in rating:
+            x = bisect_left(nums, v) + 1
+            tree2.update(x, 1)
+        n = len(rating)
+        ans = 0
+        for i, v in enumerate(rating):
+            x = bisect_left(nums, v) + 1
+            tree1.update(x, 1)
+            tree2.update(x, -1)
+            l = tree1.query(x - 1)
+            r = n - i - 1 - tree2.query(x)
+            ans += l * r
+            ans += (i - l) * (n - i - 1 - r)
         return ans
diff --git a/solution/1300-1399/1395.Count Number of Teams/Solution.ts b/solution/1300-1399/1395.Count Number of Teams/Solution.ts
@@ -0,0 +1,67 @@
+class BinaryIndexedTree {
+    private n: number;
+    private c: number[];
+
+    constructor(n: number) {
+        this.n = n;
+        this.c = new Array(n + 1).fill(0);
+    }
+
+    public update(x: number, v: number): void {
+        while (x <= this.n) {
+            this.c[x] += v;
+            x += x & -x;
+        }
+    }
+
+    public query(x: number): number {
+        let s = 0;
+        while (x > 0) {
+            s += this.c[x];
+            x -= x & -x;
+        }
+        return s;
+    }
+}
+
+function numTeams(rating: number[]): number {
+    let nums = [...rating];
+    nums.sort((a, b) => a - b);
+    const n = rating.length;
+    let m = 0;
+    for (let i = 0; i < n; ++i) {
+        if (i === 0 || nums[i] !== nums[i - 1]) {
+            nums[m++] = nums[i];
+        }
+    }
+    nums = nums.slice(0, m);
+    const search = (x: number): number => {
+        let l = 0;
+        let r = m;
+        while (l < r) {
+            const mid = (l + r) >> 1;
+            if (nums[mid] >= x) {
+                r = mid;
+            } else {
+                l = mid + 1;
+            }
+        }
+        return l + 1;
+    };
+    let ans = 0;
+    const tree1 = new BinaryIndexedTree(m);
+    const tree2 = new BinaryIndexedTree(m);
+    for (const x of rating) {
+        tree2.update(search(x), 1);
+    }
+    for (let i = 0; i < n; ++i) {
+        const x = search(rating[i]);
+        tree1.update(x, 1);
+        tree2.update(x, -1);
+        const l = tree1.query(x - 1);
+        const r = n - i - 1 - tree2.query(x);
+        ans += l * r;
+        ans += (i - l) * (n - i - 1 - r);
+    }
+    return ans;
+}
diff --git a/solution/1300-1399/1396.Design Underground System/README.md b/solution/1300-1399/1396.Design Underground System/README.md
@@ -12,7 +12,6 @@
 
 <ul>
 	<li><code>void checkIn(int id, string stationName, int t)</code>
-
     <ul>
     	<li>通行卡 ID 等于 <code>id</code> 的乘客，在时间 <code>t</code> ，从 <code>stationName</code> 站进入</li>
     	<li>乘客一次只能从一个站进入</li>
@@ -31,7 +30,6 @@
     	<li>在调用 <code>getAverageTime</code> 之前，至少有一名乘客从 <code>startStation</code> 站到达 <code>endStation</code> 站</li>
     </ul>
     </li>
-
 </ul>
 
 <p>你可以假设对 <code>checkIn</code> 和 <code>checkOut</code> 方法的所有调用都是符合逻辑的。如果一名乘客在时间 <code>t<sub>1</sub></code> 进站、时间 <code>t<sub>2</sub></code> 出站，那么 <code>t<sub>1</sub> &lt; t<sub>2</sub></code> 。所有时间都按时间顺序发生。</p>
diff --git a/solution/1300-1399/1396.Design Underground System/README_EN.md b/solution/1300-1399/1396.Design Underground System/README_EN.md
@@ -10,7 +10,6 @@
 
 <ul>
 	<li><code>void checkIn(int id, string stationName, int t)</code>
-
     <ul>
     	<li>A customer with a card ID equal to <code>id</code>, checks in at the station <code>stationName</code> at time <code>t</code>.</li>
     	<li>A customer can only be checked into one place at a time.</li>
@@ -29,7 +28,6 @@
     	<li>There will be at least one customer that has traveled from <code>startStation</code> to <code>endStation</code> before <code>getAverageTime</code> is called.</li>
     </ul>
     </li>
-
 </ul>
 
 <p>You may assume all calls to the <code>checkIn</code> and <code>checkOut</code> methods are consistent. If a customer checks in at time <code>t<sub>1</sub></code> then checks out at time <code>t<sub>2</sub></code>, then <code>t<sub>1</sub> &lt; t<sub>2</sub></code>. All events happen in chronological order.</p>
