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ZJ12. 编程题2

描述

给定一个数组序列, 需要求选出一个区间, 使得该区间是所有区间中经过如下计算的值最大的一个：

区间中的最小数 * 区间所有数的和最后程序输出经过计算后的最大值即可，不需要输出具体的区间。如给定序列  [6 2 1]则根据上述公式, 可得到所有可以选定各个区间的计算值:

 

[6] = 6 * 6 = 36;

[2] = 2 * 2 = 4;

[1] = 1 * 1 = 1;

[6,2] = 2 * 8 = 16;

[2,1] = 1 * 3 = 3;

[6, 2, 1] = 1 * 9 = 9;

 

从上述计算可见选定区间 [6] ，计算值为 36， 则程序输出为 36。

区间内的所有数字都在[0, 100]的范围内;

输入描述

第一行输入数组序列长度n，第二行输入数组序列。 对于 50%的数据, 1 <= n <= 10000; 对于 100%的数据, 1 <= n <= 500000;

输出描述

输出数组经过计算后的最大值。

示例1

输入: 

3
6 2 1

输出: 

36

原站题解

C++ 解法, 执行用时: 16ms, 内存消耗: 4224KB, 提交时间: 2021-08-17 

#include <iostream>
#include <cstdio>
#include <vector>

using namespace std;

inline int getint(){
    int x=0;
    char ch=getchar();
    while (!isdigit(ch)) ch=getchar();
    while (isdigit(ch)){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x;
}
   
int main(){
    int n; cin>>n;
    vector<int> a(n+1, 0);
    vector<int> s(n+1, 0);
    for (int i=1; i<=n; i++){
        a[i]=getint();
        s[i]=s[i-1]+a[i];
    }
       
    vector<int> stack;
       
    int result=a[1]*a[1];
    stack.push_back(1);
    for (int i=2; i<=n; i++){
        int top=stack.back();
        while (a[top]>=a[i]){
            int st=(stack.size()>=2)?stack[stack.size()-2]:0;
            result=max(result, a[top]*(s[i-1]-s[st]));
            stack.pop_back();
            if (stack.size()==0) break;
            else top=stack.back();
        }
        if (stack.size()==0) result=max(result, a[i]*s[i]);
        else result=max(result, a[i]*(s[i]-s[top]));
        stack.push_back(i);
    }
    while (stack.size()>0){
        int top=stack.back();
        int st=(stack.size()>=2)?stack[stack.size()-2]:0;
        result=max(result, a[top]*(s[n]-s[st]));
        stack.pop_back();
    }
       
    cout<<result<<endl;
       
    return 0;
}

C++ 解法, 执行用时: 19ms, 内存消耗: 5752KB, 提交时间: 2020-10-29 

#include <iostream>
#include <cstdio>
#include <vector>
   
using namespace std;
   
inline int getint(){
    int x=0;
    char ch=getchar();
    while (!isdigit(ch)) ch=getchar();
    while (isdigit(ch)){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x;
}
   
int main(){
    int n; cin>>n;
    vector<int> a(n+1, 0);
    vector<int> s(n+1, 0);
    for (int i=1; i<=n; i++){
        a[i]=getint();
        s[i]=s[i-1]+a[i];
    }
       
    vector<int> stack;
       
    int result=a[1]*a[1];
    stack.push_back(1);
    for (int i=2; i<=n; i++){
        int top=stack.back();
        while (a[top]>=a[i]){
            int st=(stack.size()>=2)?stack[stack.size()-2]:0;
            result=max(result, a[top]*(s[i-1]-s[st]));
            stack.pop_back();
            if (stack.size()==0) break;
            else top=stack.back();
        }
        if (stack.size()==0) result=max(result, a[i]*s[i]);
        else result=max(result, a[i]*(s[i]-s[top]));
        stack.push_back(i);
    }
    while (stack.size()>0){
        int top=stack.back();
        int st=(stack.size()>=2)?stack[stack.size()-2]:0;
        result=max(result, a[top]*(s[n]-s[st]));
        stack.pop_back();
    }
       
    cout<<result<<endl;
       
    return 0;
}

C++ 解法, 执行用时: 19ms, 内存消耗: 5764KB, 提交时间: 2020-10-29 

#include <iostream>
#include <cstdio>
#include <vector>
   
using namespace std;
   
inline int getint(){
    int x=0;
    char ch=getchar();
    while (!isdigit(ch)) ch=getchar();
    while (isdigit(ch)){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x;
}
   
int main(){
    int n; cin>>n;
    vector<int> a(n+1, 0);
    vector<int> s(n+1, 0);
    for (int i=1; i<=n; i++){
        a[i]=getint();
        s[i]=s[i-1]+a[i];
    }
       
    vector<int> stack;
       
    int result=a[1]*a[1];
    stack.push_back(1);
    for (int i=2; i<=n; i++){
        int top=stack.back();
        while (a[top]>=a[i]){
            int st=(stack.size()>=2)?stack[stack.size()-2]:0;
            result=max(result, a[top]*(s[i-1]-s[st]));
            stack.pop_back();
            if (stack.size()==0) break;
            else top=stack.back();
        }
        if (stack.size()==0) result=max(result, a[i]*s[i]);
        else result=max(result, a[i]*(s[i]-s[top]));
        stack.push_back(i);
    }
    while (stack.size()>0){
        int top=stack.back();
        int st=(stack.size()>=2)?stack[stack.size()-2]:0;
        result=max(result, a[top]*(s[n]-s[st]));
        stack.pop_back();
    }
       
    cout<<result<<endl;
       
    return 0;
}

C++ 解法, 执行用时: 20ms, 内存消耗: 4544KB, 提交时间: 2020-10-29 

#include <iostream>
#include <cstdio>
#include <vector>
   
using namespace std;
   
inline int getint(){
    int x=0;
    char ch=getchar();
    while (!isdigit(ch)) ch=getchar();
    while (isdigit(ch)){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x;
}
   
int main(){
    int n; cin>>n;
    vector<int> a(n+1, 0);
    vector<int> s(n+1, 0);
    for (int i=1; i<=n; i++){
        a[i]=getint();
        s[i]=s[i-1]+a[i];
    }
       
    vector<int> stack;
       
    int result=a[1]*a[1];
    stack.push_back(1);
    for (int i=2; i<=n; i++){
        int top=stack.back();
        while (a[top]>=a[i]){
            int st=(stack.size()>=2)?stack[stack.size()-2]:0;
            result=max(result, a[top]*(s[i-1]-s[st]));
            stack.pop_back();
            if (stack.size()==0) break;
            else top=stack.back();
        }
        if (stack.size()==0) result=max(result, a[i]*s[i]);
        else result=max(result, a[i]*(s[i]-s[top]));
        stack.push_back(i);
    }
    while (stack.size()>0){
        int top=stack.back();
        int st=(stack.size()>=2)?stack[stack.size()-2]:0;
        result=max(result, a[top]*(s[n]-s[st]));
        stack.pop_back();
    }
       
    cout<<result<<endl;
       
    return 0;
}

C++ 解法, 执行用时: 20ms, 内存消耗: 5644KB, 提交时间: 2020-07-30 

#include <iostream>
#include <cstdio>
#include <vector>
    
using namespace std;
    
inline int getint(){
    int x=0;
    char ch=getchar();
    while (!isdigit(ch)) ch=getchar();
    while (isdigit(ch)){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x;
}
    
int main(){
    int n; cin>>n;
    vector<int> a(n+1, 0);
    vector<int> s(n+1, 0);
    for (int i=1; i<=n; i++){
        a[i]=getint();
        s[i]=s[i-1]+a[i];
    }
        
    vector<int> stack;
        
    int result=a[1]*a[1];
    stack.push_back(1);
    for (int i=2; i<=n; i++){
        int top=stack.back();
        while (a[top]>=a[i]){
            int st=(stack.size()>=2)?stack[stack.size()-2]:0;
            result=max(result, a[top]*(s[i-1]-s[st]));
            stack.pop_back();
            if (stack.size()==0) break;
            else top=stack.back();
        }
        if (stack.size()==0) result=max(result, a[i]*s[i]);
        else result=max(result, a[i]*(s[i]-s[top]));
        stack.push_back(i);
    }
    while (stack.size()>0){
        int top=stack.back();
        int st=(stack.size()>=2)?stack[stack.size()-2]:0;
        result=max(result, a[top]*(s[n]-s[st]));
        stack.pop_back();
    }
        
    cout<<result<<endl;
        
    return 0;
}

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