Dynamic Programming21 sections · 915 units
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Jobs and Deadlines - Problem Statement

Scheduling variant

nn jobs with processing times and deadlines. Schedule to reduce total tardiness (lateness past deadline). Sort jobs by deadline (EDD rule).

Process in this order. dp[i][t]dp[i][t] = min tardiness for first ii jobs finishing at time tt. Transition: dp[i][t]=dp[i−1][t−pi]+max⁡(0,t−di)dp[i][t] = dp[i-1][t - p_i] + \max(0, t - d_i). The max⁡\max term is piecewise linear. Slope Trick applies: maintain the DP function as breakpoints. Each job adds a new breakpoint at its deadline.