6）贪心.

文章目录

---

区间问题

区间选点

#include<iostream>
#include<algorithm>

using namespace std;

const int N = 100010;

int n;
struct Range{
  
  int l, r;
  bool operator < (const Range & W) const{
      
      return r < W.r;
  }
}range[N];

int main(){
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++) scanf("%d%d", &range[i].l, &range[i].r);
    
    sort(range, range + n);
    
    int res = 0, ed = -2e9;
    
    for(int i = 0; i < n; i++){
        
        if(range[i].l > ed){
            
            res++;
            ed = range[i].r;
        }
    }
    
    printf("%d\n", res);
    
    return 0;
}

最大不相交区间数量

#include<iostream>
#include<algorithm>

using namespace std;

const int N = 100010;

int n;
struct Range{
  
  int l, r;
  bool operator < (const Range & W) const{
    
        return r < W.r;
  }
}range[N];

int main(){
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++) scanf("%d%d", &range[i].l, &range[i].r);
    
    sort(range, range + n);
    
    int res = 0, ed = -2e9;
    
    for(int i = 0; i < n; i++){
        
        if(ed < range[i].l){
            
            res++;
            ed = range[i].r;
        }
    }
    
    printf("%d\n", res);
    
    return 0;
}

区间分组

#include<iostream>
#include<algorithm>
#include<queue>

using namespace std;

const int N = 100010;

int n;
struct Range{
    
    int l, r;
    bool operator < (const Range & W) const{
        return l < W.l;
    }
}range[N];

int main(){
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++){
        
        int l, r;
        scanf("%d%d", &l, &r);
        range[i] = {l, r};
    }
    
    sort(range, range + n);
    
    priority_queue<int, vector<int>, greater<int>> heap;
    
    for(int i = 0; i < n; i++){
        
        auto r = range[i];
        if(heap.empty() || heap.top() >= r.l) heap.push(r.r);
        else{
            
            heap.pop();
            heap.push(r.r);
        }
    }
    
    printf("%d\n", heap.size());
    
    return 0;
}

区间覆盖

#include<iostream>
#include<algorithm>

using namespace std;

const int N = 100010;

int n;
struct Range{
    
    int l, r;
    bool operator < (const Range & W) const{
        
        return l < W.l;
    }
}range[N];

int main(){
    
    int st, ed;
    
    scanf("%d%d", &st, &ed);
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++){
        
        int l, r;
        scanf("%d%d", &l, &r);
        range[i] = {l, r};
    }
    
    sort(range, range + n);
    
    int res = 0;
    bool success = false;
    
    for(int i = 0; i < n; i++){
        
        int j = i, r = -2e9;
        
        // 双指针扫描
        while(j < n && range[j].l <= st){
            
            r = max(r, range[j].r);
            j++;
        }
        
        if(r < st){
            
            res = -1;
            break;
        }
        
        res++;
        
        if(r >= ed){
            
            success = true;
            break;
        }
        
        st = r;
        i = j - 1;
    }
    
    if(!success) res = -1;
    printf("%d\n", res);
    
    return 0;
}

Huffman树

合并果子

#include<iostream>
#include<algorithm>
#include<queue>

using namespace std;

int main(){
    
    int n;
    scanf("%d", &n);
    
    priority_queue<int, vector<int>, greater<int>> heap;
    
    while(n--){
        
        int x;
        scanf("%d", &x);
        heap.push(x);
    }
    
    int res = 0;
    while(heap.size() > 1){
        
        int a = heap.top(); heap.pop();
        int b = heap.top(); heap.pop();
        res += a + b;
        heap.push(a + b);
    }
    
    printf("%d\n", res);
    
    return 0;
}

排序不等式

排队打水

#include<iostream>
#include<algorithm>

using namespace std;

typedef long long ll;

const int N = 100010;

int n;
int t[N];

int main(){
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++) scanf("%d", &t[i]);
    
    sort(t, t + n);
    
    ll res = 0;
    
    for(int i = 0; i < n; i++) res += t[i] * (n - i - 1);
    
    printf("%lld\n", res);
    
    return 0;
}

绝对值不等式

货仓选址

#include<iostream>
#include<algorithm>

using namespace std;

const int N = 100010;

int n;
int q[N];

int main(){
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++) scanf("%d", &q[i]);
    
    sort(q, q + n);
    
    int res = 0;
    for(int i = 0; i < n; i++) res += abs(q[i] - q[n / 2]);
    
    printf("%d\n", res);
    
    return 0;
}

推公式

耍杂技的牛

#include<iostream>
#include<algorithm>

using namespace std;

typedef pair<int, int> PII;

const int N = 50010;

int n;
PII cow[N];

int main(){
    
    scanf("%d", &n);
    for(int i = 0; i < n; i++){
        
        int s, w;
        scanf("%d%d", &w, &s);
        cow[i] = {w + s, w};
    }
    
    sort(cow, cow + n);
    
    int res = -2e9, sum = 0;
    for(int i = 0; i < n; i++){
        
        int s = cow[i].first - cow[i].second, w = cow[i].second;
        res = max(res, sum - s);
        sum += w;
    }
    
    printf("%d\n", res);
    
    return 0;
}