301. Task Arrangement 2 (advanced guide to algorithm competition, slope optimization DP)

1. Title link:

Task scheduling 2

2. The main idea of ​​the topic:

Chinese question~~

3. Analysis (drawing):

嘤嘤嘤, the first slope to optimize DP.

There are a lot of explanations on the Internet, and the big guys are also very good. I will not make wheels.

4. Code implementation:

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

typedef long long ll;

const int M = (int)3e5;
const int inf = 0x3f3f3f3f;

ll sumt[M + 5];
ll sumc[M + 5];
ll q[M + 5];
ll f[M + 5];

int main()
{
    int n, s;
    scanf("%d %d", &n, &s);
    for(int i = 1; i <= n; ++i)
    {
        scanf("%lld %lld", &sumt[i], &sumc[i]);
        sumt[i] += sumt[i - 1];
        sumc[i] += sumc[i - 1];
    }
    int l = 1, r = 0;
    q[++r] = 0;
    for(int i = 1; i <= n; ++i)
    {
        while(l < r && (f[q[l + 1]] - f[q[l]]) <= (s + sumt[i]) * (sumc[q[l + 1]] - sumc[q[l]]))    ++l;
        if(l <= r)   f[i] = f[q[l]] + sumt[i] * (sumc[i] - sumc[q[l]]) + s * (sumc[n] - sumc[q[l]]);
        while(l < r && (f[i] - f[q[r]]) * (sumc[q[r]] - sumc[q[r - 1]]) <= (f[q[r]] - f[q[r - 1]]) * (sumc[i] - sumc[q[r]]))    --r;
        q[++r] = i;
    }
    printf("%lld\n", f[n]);
    return 0;
}