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[ { "prob_id": "237e", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory", "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "202a", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }, { "prob_id": "305e", "tags": [ "Nim, Sprague-Grundy Theorem|Combinatorial Games|Advanced Mathematics" ] } ]
{ "prob_id": "607b", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }
{ "prob_id": "1303e", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "204e", "tags": [ "Suffix Array|Suffix Structures|Strings" ] }, { "prob_id": "202a", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }, { "prob_id": "528d", "tags": [ "Fast Fourier Transform (FFT)|Convolution|Math" ] } ]
{ "prob_id": "607b", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }
{ "prob_id": "476e", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "1016b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }, { "prob_id": "245h", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }, { "prob_id": "1234d", "tags": [ "Segment Tree|Trees|Data Structures" ] } ]
{ "prob_id": "1028b", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }
{ "prob_id": "1335b", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }
[ { "prob_id": "1154g", "tags": [ "Sieve, Prime Factorization and Divisors|Primes and Divisors|Number Theory" ] }, { "prob_id": "988d", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "1132g", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "796d", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }
{ "prob_id": "1272e", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }
[ { "prob_id": "36b", "tags": [ "Recursion||Preliminaries" ] }, { "prob_id": "908b", "tags": [ "All-Permutations|Complete Search|Basics" ] }, { "prob_id": "1451f", "tags": [ "Nim, Sprague-Grundy Theorem|Combinatorial Games|Advanced Mathematics" ] } ]
{ "prob_id": "1272e", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }
{ "prob_id": "769c", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }
[ { "prob_id": "152c", "tags": [ "Rule of Sum, Rule of Product|Counting|Basics" ] }, { "prob_id": "576a", "tags": [ "Prime Factorization|Number Theory|Basics" ] }, { "prob_id": "114b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] } ]
{ "prob_id": "7d", "tags": [ "String Hashing|Hashing|Strings" ] }
{ "prob_id": "727e", "tags": [ "String Hashing|Hashing|Strings" ] }
[ { "prob_id": "1203f1", "tags": [ "Exchange Argument|Greedy|Basics" ] }, { "prob_id": "1081d", "tags": [ "Minimum Spanning Tree||", "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] }, { "prob_id": "1446a", "tags": [ "Knapsack DP||" ] } ]
{ "prob_id": "488d", "tags": [ "Monotonic Queue|Miscellaneous|Data Structures (DS)" ] }
{ "prob_id": "1077f2", "tags": [ "Monotonic Queue|Miscellaneous|Data Structures (DS)" ] }
[ { "prob_id": "506d", "tags": [ "Splitting Objects into Light and Heavy / Case Processing|Square Root Decomposition|Data Structures (DS)" ] }, { "prob_id": "468b", "tags": [ "Disjoint Set Union||" ] }, { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] } ]
{ "prob_id": "1077f2", "tags": [ "Monotonic Queue|Miscellaneous|Data Structures (DS)" ] }
{ "prob_id": "488d", "tags": [ "Monotonic Queue|Miscellaneous|Data Structures (DS)" ] }
[ { "prob_id": "832d", "tags": [ "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }, { "prob_id": "875e", "tags": [ "Knapsack DP||" ] }, { "prob_id": "519e", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] } ]
{ "prob_id": "26d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "113d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
[ { "prob_id": "1408e", "tags": [ "Minimum Spanning Tree||" ] }, { "prob_id": "1093d", "tags": [ "Depth First Search (DFS)|Graph Traversal|Graph Theory" ] }, { "prob_id": "704d", "tags": [ "Flow with Lower Bounds||" ] } ]
{ "prob_id": "26d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "1418e", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
[ { "prob_id": "1103d", "tags": [ "Bit Manipulation|Bit Manipulation|Basics", "Bitmask DP|Bit Related DP|Dynamic Programming (DP)" ] }, { "prob_id": "653d", "tags": [ "Network Flows||Advanced Algorithms" ] }, { "prob_id": "700c", "tags": [ "Finding Bridges in O(N+M)|Connected components, bridges, articulations points|Graphs" ] } ]
{ "prob_id": "540d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "167b", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
[ { "prob_id": "1011e", "tags": [ "Bezout's Identity|Euclidean Algorithm|Number Theory" ] }, { "prob_id": "1010c", "tags": [ "Bézout's Lemma, Extended Euclidean Algorithm, Chinese Remainder Theorem|Number Theory|Intermediate", "Abstract Algebra||Advanced Mathematics" ] }, { "prob_id": "580e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "1096f", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "26d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
[ { "prob_id": "785e", "tags": [ "2D BIT|Binary Indexed Tree (BIT)|Data Structures (DS)" ] }, { "prob_id": "214a", "tags": [ "Iterative|Complete Search|Basics" ] }, { "prob_id": "1477d", "tags": [ "Inverse Graph|Graph Traversal|Graph Theory" ] } ]
{ "prob_id": "1525e", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "351b", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
[ { "prob_id": "535e", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "827f", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }, { "prob_id": "114b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] } ]
{ "prob_id": "540d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }
{ "prob_id": "518d", "tags": [ "Markov Chains|Probability and Expectation|Intermediate" ] }
[ { "prob_id": "700c", "tags": [ "Finding Bridges in O(N+M)|Connected components, bridges, articulations points|Graphs" ] }, { "prob_id": "212a", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] }, { "prob_id": "25c", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] } ]
{ "prob_id": "461b", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
{ "prob_id": "440d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
[ { "prob_id": "631c", "tags": [ "Combining Data Structures|Data Structure Techniques|Intermediate" ] }, { "prob_id": "193b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }, { "prob_id": "1201c", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] } ]
{ "prob_id": "311b", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] }
{ "prob_id": "631e", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] }
[ { "prob_id": "1203f1", "tags": [ "Exchange Argument|Greedy|Basics" ] }, { "prob_id": "251a", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] }, { "prob_id": "1203f2", "tags": [ "Presorting|DP Common Tricks|Intermediate" ] } ]
{ "prob_id": "550b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics", "Backtracking|Miscellaneous|Miscellaneous" ] }
{ "prob_id": "1097b", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
[ { "prob_id": "1100b", "tags": [ "Amortized Analysis||Intermediate" ] }, { "prob_id": "1295f", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }, { "prob_id": "877f", "tags": [ "Square Root Decomposition||" ] } ]
{ "prob_id": "96b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
{ "prob_id": "550b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics", "Backtracking|Miscellaneous|Miscellaneous" ] }
[ { "prob_id": "1059d", "tags": [ "Ternary Search|Search Techniques|Miscellaneous" ] }, { "prob_id": "1252l", "tags": [ "Network Flows||Advanced Algorithms" ] }, { "prob_id": "700c", "tags": [ "Finding Bridges in O(N+M)|Connected components, bridges, articulations points|Graphs" ] } ]
{ "prob_id": "815c", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
{ "prob_id": "1280d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
[ { "prob_id": "160d", "tags": [ "Biconnectivity|DFS Lowlink|Advanced Algorithms" ] }, { "prob_id": "1081d", "tags": [ "Minimum Spanning Tree||", "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] }, { "prob_id": "451e", "tags": [ "Principle of Inclusion-Exclusion|Counting|Intermediate", "Generating Functions|Polynomial|Math" ] } ]
{ "prob_id": "815c", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
{ "prob_id": "735e", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
[ { "prob_id": "816b", "tags": [ "Prefix Sum|Range Queries Without Updates|Basics", "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }, { "prob_id": "877f", "tags": [ "Square Root Decomposition||" ] }, { "prob_id": "802c", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] } ]
{ "prob_id": "1280d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
{ "prob_id": "815c", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }
[ { "prob_id": "1132g", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "1194e", "tags": [ "Sweep Line||" ] }, { "prob_id": "1042d", "tags": [ "Global Deltaing||Advanced Data Structures" ] } ]
{ "prob_id": "662a", "tags": [ "Vector Space and XOR Basis|Linear Algebra|Math" ] }
{ "prob_id": "1101g", "tags": [ "XOR Basis||" ] }
[ { "prob_id": "650d", "tags": [ "O(n lg n) Longest Monotonic Subsequence|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "729f", "tags": [ "Skip Useless States|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "576a", "tags": [ "Prime Factorization|Number Theory|Basics" ] } ]
{ "prob_id": "1101g", "tags": [ "XOR Basis||" ] }
{ "prob_id": "662a", "tags": [ "Vector Space and XOR Basis|Linear Algebra|Math" ] }
[ { "prob_id": "1012b", "tags": [ "Bipartite Graph||" ] }, { "prob_id": "237e", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory", "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "700c", "tags": [ "Finding Bridges in O(N+M)|Connected components, bridges, articulations points|Graphs" ] } ]
{ "prob_id": "11d", "tags": [ "DP on Subsets||Intermediate" ] }
{ "prob_id": "71e", "tags": [ "Bitmask DP|Bit Related DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "1137b", "tags": [ "Z algorithm|String Matching|Strings" ] }, { "prob_id": "340c", "tags": [ "Binomial Coefficients|Fundamentals|Combinatorics" ] }, { "prob_id": "776f", "tags": [ "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] } ]
{ "prob_id": "8c", "tags": [ "DP on Subsets||Intermediate" ] }
{ "prob_id": "757d", "tags": [ "Bitmask DP|Bit Related DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "761e", "tags": [ "Depth First Search|Graph traversal|Graphs" ] }, { "prob_id": "877d", "tags": [ "Grid Graphs|Graphs|Basics" ] }, { "prob_id": "827f", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] } ]
{ "prob_id": "757d", "tags": [ "Bitmask DP|Bit Related DP|Dynamic Programming (DP)" ] }
{ "prob_id": "8c", "tags": [ "DP on Subsets||Intermediate" ] }
[ { "prob_id": "930c", "tags": [ "O(n lg n) Longest Monotonic Subsequence|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "1416f", "tags": [ "Flow with Lower Bounds||" ] }, { "prob_id": "895e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "117e", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
{ "prob_id": "1109f", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
[ { "prob_id": "960e", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "1394d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "599e", "tags": [ "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] } ]
{ "prob_id": "1109f", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
{ "prob_id": "1172e", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
[ { "prob_id": "977e", "tags": [ "Depth First Search (DFS)|Graph Traversal|Graph Theory" ] }, { "prob_id": "1176e", "tags": [ "Bipartite Graph||", "Graph Traversal||" ] }, { "prob_id": "263d", "tags": [ "Cycle Detection|Cycles|Graph Theory" ] } ]
{ "prob_id": "1109f", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
{ "prob_id": "117e", "tags": [ "Link Cut Tree (LCT)|Link Cut Tree (LCT)|Data Structures (DS)" ] }
[ { "prob_id": "319c", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "193b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }, { "prob_id": "204e", "tags": [ "Suffix Array|Suffix Structures|Strings" ] } ]
{ "prob_id": "1201c", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] }
{ "prob_id": "348a", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] }
[ { "prob_id": "121a", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }, { "prob_id": "96b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }, { "prob_id": "95e", "tags": [ "Knapsack DP||" ] } ]
{ "prob_id": "52c", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }
{ "prob_id": "145e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }
[ { "prob_id": "438d", "tags": [ "Segment Tree Beats|Segment Tree|Data Structures (DS)", "Segment Tree Beats|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "1408e", "tags": [ "Minimum Spanning Tree||" ] }, { "prob_id": "402e", "tags": [ "Matrix Exponentiation|Matrices|Math" ] } ]
{ "prob_id": "1139e", "tags": [ "Bipartite Matching|Network Flows|Advanced Algorithms", "Maximum Flow / Minimum Cut|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "498c", "tags": [ "Bipartite Matching|Network Flows|Advanced Algorithms" ] }
[ { "prob_id": "788b", "tags": [ "Eulerian Path and Cycle|Eulerian Path|Graph Theory" ] }, { "prob_id": "794d", "tags": [ "Depth First Search|Graph traversal|Graphs" ] }, { "prob_id": "793d", "tags": [ "Directed Acyclic Graphs|Shortest Paths|Intermediate" ] } ]
{ "prob_id": "1140g", "tags": [ "Binary Lifting||Advanced Data Structures", "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }
{ "prob_id": "150e", "tags": [ "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] }
[ { "prob_id": "721c", "tags": [ "Directed Acyclic Graphs|Shortest Paths|Intermediate", "Rotate the Recurrence|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "715b", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }, { "prob_id": "584b", "tags": [ "Rule of Sum, Rule of Product|Counting|Basics" ] } ]
{ "prob_id": "1140g", "tags": [ "Binary Lifting||Advanced Data Structures", "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }
{ "prob_id": "833d", "tags": [ "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] }
[ { "prob_id": "727e", "tags": [ "String Hashing|Hashing|Strings" ] }, { "prob_id": "631c", "tags": [ "Combining Data Structures|Data Structure Techniques|Intermediate" ] }, { "prob_id": "1572f", "tags": [ "Segment Tree Beats|Segment Tree|Data Structures (DS)", "Segment Tree Beats|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "733f", "tags": [ "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }
{ "prob_id": "466e", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] }
[ { "prob_id": "1500b", "tags": [ "Chinese Remainder Theorem|Modular arithmetic|Algebra" ] }, { "prob_id": "623d", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }, { "prob_id": "809d", "tags": [ "Splay Trees and Treaps|Augmenting Data Structures|Advanced Data Structures" ] } ]
{ "prob_id": "1328e", "tags": [ "Binary Lifting||Advanced Data Structures" ] }
{ "prob_id": "832d", "tags": [ "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }
[ { "prob_id": "1364c", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }, { "prob_id": "1176e", "tags": [ "Bipartite Graph||", "Graph Traversal||" ] }, { "prob_id": "1272e", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] } ]
{ "prob_id": "154b", "tags": [ "Sieve of Eratosthenes|Prime numbers|Algebra" ] }
{ "prob_id": "1225d", "tags": [ "Divisibility||" ] }
[ { "prob_id": "119c", "tags": [ "DP with Solution Construction||Intermediate" ] }, { "prob_id": "1355f", "tags": [ "Interactive Problems|Interactive Problems|Miscellaneous" ] }, { "prob_id": "176e", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] } ]
{ "prob_id": "546d", "tags": [ "Fast IO||" ] }
{ "prob_id": "154b", "tags": [ "Sieve of Eratosthenes|Prime numbers|Algebra" ] }
[ { "prob_id": "1093d", "tags": [ "Depth First Search (DFS)|Graph Traversal|Graph Theory" ] }, { "prob_id": "616c", "tags": [ "Grid Graphs|Graphs|Basics" ] }, { "prob_id": "540c", "tags": [ "Grid Graphs|Graphs|Basics" ] } ]
{ "prob_id": "154b", "tags": [ "Sieve of Eratosthenes|Prime numbers|Algebra" ] }
{ "prob_id": "1561d2", "tags": [ "Sieve, Prime Factorization and Divisors|Primes and Divisors|Number Theory" ] }
[ { "prob_id": "177d2", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }, { "prob_id": "286e", "tags": [ "Fast Fourier Transform (FFT)|Convolution|Math" ] }, { "prob_id": "715c", "tags": [ "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] } ]
{ "prob_id": "154b", "tags": [ "Sieve of Eratosthenes|Prime numbers|Algebra" ] }
{ "prob_id": "222c", "tags": [ "Sieve, Prime Factorization and Divisors|Primes and Divisors|Number Theory" ] }
[ { "prob_id": "161d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "242e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] } ]
{ "prob_id": "154b", "tags": [ "Sieve of Eratosthenes|Prime numbers|Algebra" ] }
{ "prob_id": "230b", "tags": [ "Prime and Composite, Primality Testing, Prime Sieves, Finding Divisors|Number Theory|Preliminaries" ] }
[ { "prob_id": "1446a", "tags": [ "Knapsack DP||" ] }, { "prob_id": "1552i", "tags": [ "PQ Tree|More Tree Data Structures|Data Structures (DS)" ] }, { "prob_id": "1240f", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] } ]
{ "prob_id": "165e", "tags": [ "Bit Manipulation|Bit Manipulation|Basics", "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] }
{ "prob_id": "1523d", "tags": [ "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "280d", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "691e", "tags": [ "Matrix Exponentiation|Matrices|Math" ] }, { "prob_id": "272d", "tags": [ "Permutations with Repetition, Stars and Bars|Counting|Intermediate" ] } ]
{ "prob_id": "1523d", "tags": [ "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] }
{ "prob_id": "165e", "tags": [ "Bit Manipulation|Bit Manipulation|Basics", "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] }
[ { "prob_id": "1394d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "1572f", "tags": [ "Segment Tree Beats|Segment Tree|Data Structures (DS)", "Segment Tree Beats|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "1158a", "tags": [ "Greedy Sorting||", "Basic Greedy Algorithms|Greedy and Constructive|Basics" ] } ]
{ "prob_id": "600f", "tags": [ "Bipartite Matching|Network Flows|Advanced Algorithms" ] }
{ "prob_id": "1240f", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] }
[ { "prob_id": "25c", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] }, { "prob_id": "440d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "190e", "tags": [ "Inverse Graph|Graph Traversal|Graph Theory" ] } ]
{ "prob_id": "600f", "tags": [ "Bipartite Matching|Network Flows|Advanced Algorithms" ] }
{ "prob_id": "212a", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] }
[ { "prob_id": "1476a", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }, { "prob_id": "1364c", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }, { "prob_id": "1093d", "tags": [ "Depth First Search (DFS)|Graph Traversal|Graph Theory" ] } ]
{ "prob_id": "553a", "tags": [ "Permutations with Repetition, Stars and Bars|Counting|Intermediate" ] }
{ "prob_id": "1288c", "tags": [ "Stars and Bars|Basic Counting|Basics" ] }
[ { "prob_id": "850f", "tags": [ "Martingale|Probabilities and Expected Values|Math" ] }, { "prob_id": "506d", "tags": [ "Splitting Objects into Light and Heavy / Case Processing|Square Root Decomposition|Data Structures (DS)" ] }, { "prob_id": "650d", "tags": [ "O(n lg n) Longest Monotonic Subsequence|DP Optimization|Advanced Algorithms" ] } ]
{ "prob_id": "1288c", "tags": [ "Stars and Bars|Basic Counting|Basics" ] }
{ "prob_id": "553a", "tags": [ "Permutations with Repetition, Stars and Bars|Counting|Intermediate" ] }
[ { "prob_id": "778a", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] }, { "prob_id": "506d", "tags": [ "Splitting Objects into Light and Heavy / Case Processing|Square Root Decomposition|Data Structures (DS)" ] }, { "prob_id": "786c", "tags": [ "Sqrt Decomposition|Trees|Data Structures" ] } ]
{ "prob_id": "129c", "tags": [ "Direction Array|Techniques|Miscellaneous" ] }
{ "prob_id": "510b", "tags": [ "Grid Graphs|Graphs|Basics" ] }
[ { "prob_id": "1303e", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] }, { "prob_id": "237e", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory", "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "245h", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] } ]
{ "prob_id": "1312f", "tags": [ "Nim, Sprague-Grundy Theorem|Combinatorial Games|Advanced Mathematics" ] }
{ "prob_id": "305e", "tags": [ "Nim, Sprague-Grundy Theorem|Combinatorial Games|Advanced Mathematics" ] }
[ { "prob_id": "1311d", "tags": [ "Harmonic Lemma||Intermediate" ] }, { "prob_id": "1499d", "tags": [ "Divisibility||" ] }, { "prob_id": "1439b", "tags": [ "Maximum Clique|Cliques and Independent Sets|Graph Theory" ] } ]
{ "prob_id": "486a", "tags": [ "Sums and Asymptotics||Preliminaries" ] }
{ "prob_id": "1328a", "tags": [ "Big O Notation and Time and Space Complexity Analysis|Complexity Analysis|Basics" ] }
[ { "prob_id": "152c", "tags": [ "Rule of Sum, Rule of Product|Counting|Basics" ] }, { "prob_id": "825f", "tags": [ "Z algorithm|String Matching|Strings" ] }, { "prob_id": "727e", "tags": [ "String Hashing|Hashing|Strings" ] } ]
{ "prob_id": "528c", "tags": [ "Euler Tour||" ] }
{ "prob_id": "508d", "tags": [ "Euler Tour||" ] }
[ { "prob_id": "292b", "tags": [ "Basic Graph Theory|Graphs|Basics" ] }, { "prob_id": "434d", "tags": [ "Network Flows||Advanced Algorithms" ] }, { "prob_id": "631d", "tags": [ "Knuth Morris Pratt (KMP) and Prefix Automaton|String Matching|Strings" ] } ]
{ "prob_id": "508d", "tags": [ "Euler Tour||" ] }
{ "prob_id": "528c", "tags": [ "Euler Tour||" ] }
[ { "prob_id": "629e", "tags": [ "Binary Lifting||Advanced Data Structures" ] }, { "prob_id": "1083a", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "319c", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] } ]
{ "prob_id": "808f", "tags": [ "Maximum Flow / Minimum Cut|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "653d", "tags": [ "Network Flows||Advanced Algorithms" ] }
[ { "prob_id": "506d", "tags": [ "Splitting Objects into Light and Heavy / Case Processing|Square Root Decomposition|Data Structures (DS)" ] }, { "prob_id": "704e", "tags": [ "Heavy Light Decomposition (HLD) ft Subtrees and Path Query|Heavy Light Decomposition (HLD)|Data Structures (DS)" ] }, { "prob_id": "484e", "tags": [ "Persistent Segment Tree|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "708d", "tags": [ "Flow with Lower Bounds||" ] }
{ "prob_id": "704d", "tags": [ "Flow with Lower Bounds||" ] }
[ { "prob_id": "479e", "tags": [ "Knapsack DP||" ] }, { "prob_id": "1381a2", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }, { "prob_id": "1446a", "tags": [ "Knapsack DP||" ] } ]
{ "prob_id": "818g", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "1510b", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
[ { "prob_id": "868f", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming", "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }, { "prob_id": "863d", "tags": [ "Splay Trees and Treaps|Augmenting Data Structures|Advanced Data Structures" ] }, { "prob_id": "1176e", "tags": [ "Bipartite Graph||", "Graph Traversal||" ] } ]
{ "prob_id": "818g", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "280d", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
[ { "prob_id": "802j", "tags": [ "Depth First Search (DFS)|Graph Traversal|Graph Theory" ] }, { "prob_id": "587e", "tags": [ "Vector Space and XOR Basis|Linear Algebra|Math" ] }, { "prob_id": "599e", "tags": [ "Sum Over Subsets DP (SOS DP)|Bit Related DP|Dynamic Programming (DP)" ] } ]
{ "prob_id": "818g", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "802c", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
[ { "prob_id": "486e", "tags": [ "O(n lg n) Longest Monotonic Subsequence|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "868f", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming", "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }, { "prob_id": "577b", "tags": [ "Counting with DP||Intermediate" ] } ]
{ "prob_id": "1510b", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "818g", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
[ { "prob_id": "825f", "tags": [ "Z algorithm|String Matching|Strings" ] }, { "prob_id": "900e", "tags": [ "Knapsack DP||" ] }, { "prob_id": "1303e", "tags": [ "Interval DP / Range DP / Matrix Chain Multiplication (MCM)|Classic DP|Dynamic Programming (DP)" ] } ]
{ "prob_id": "818g", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
{ "prob_id": "884f", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }
[ { "prob_id": "343d", "tags": [ "Small to Large||", "Tree Flattening||Advanced Data Structures" ] }, { "prob_id": "587e", "tags": [ "Vector Space and XOR Basis|Linear Algebra|Math" ] }, { "prob_id": "689b", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] } ]
{ "prob_id": "920g", "tags": [ "Mobius Function and Mobius Inversion|Multiplicative Functions|Number Theory" ] }
{ "prob_id": "547c", "tags": [ "Möbius Inversion||Advanced Mathematics", "Principle of Inclusion-Exclusion|Counting|Intermediate" ] }
[ { "prob_id": "1175d", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }, { "prob_id": "1006c", "tags": [ "Two Pointers|Leveraging Monotonicity|Basics" ] }, { "prob_id": "1101g", "tags": [ "XOR Basis||" ] } ]
{ "prob_id": "321e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
{ "prob_id": "1527e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
[ { "prob_id": "295b", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] }, { "prob_id": "689b", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }, { "prob_id": "177c2", "tags": [ "Depth-First Traversal, Connectivity, Cycle Detection|Graphs|Basics" ] } ]
{ "prob_id": "1527e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
{ "prob_id": "321e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
[ { "prob_id": "833e", "tags": [ "Sweep Line||" ] }, { "prob_id": "707b", "tags": [ "Single Source|Shortest Paths|Intermediate" ] }, { "prob_id": "793a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] } ]
{ "prob_id": "1527e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
{ "prob_id": "833b", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming", "Knapsack DP||" ] }
[ { "prob_id": "280d", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "446a", "tags": [ "Classic Problems with Twists|DP|Intermediate" ] }, { "prob_id": "877f", "tags": [ "Square Root Decomposition||" ] } ]
{ "prob_id": "321e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
{ "prob_id": "868f", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }
[ { "prob_id": "1513d", "tags": [ "Minimum Spanning Tree||" ] }, { "prob_id": "1513b", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "1270c", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] } ]
{ "prob_id": "514d", "tags": [ "Sparse Table|Sparse Table|Data Structures (DS)" ] }
{ "prob_id": "1547f", "tags": [ "Sparse Table|Sparse Table|Data Structures (DS)" ] }
[ { "prob_id": "1245d", "tags": [ "Minimum Spanning Tree||" ] }, { "prob_id": "1240f", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] }, { "prob_id": "1277e", "tags": [ "DFS Tree|Graph Traversal|Graph Theory" ] } ]
{ "prob_id": "453e", "tags": [ "Segment Tree Beats|Segment Tree|Data Structures (DS)" ] }
{ "prob_id": "1572f", "tags": [ "Segment Tree Beats|Segment Tree|Data Structures (DS)" ] }
[ { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "348c", "tags": [ "Square-Root Discrimination||Intermediate" ] }, { "prob_id": "295b", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] } ]
{ "prob_id": "816b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics", "Prefix Sum|Range Queries Without Updates|Basics" ] }
{ "prob_id": "296c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
[ { "prob_id": "1000e", "tags": [ "Articulation Bridges and Bridge Tree|Graph Connectivity|Graph Theory" ] }, { "prob_id": "1100b", "tags": [ "Amortized Analysis||Intermediate" ] }, { "prob_id": "340c", "tags": [ "Binomial Coefficients|Fundamentals|Combinatorics" ] } ]
{ "prob_id": "843d", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }
{ "prob_id": "827f", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }
[ { "prob_id": "506d", "tags": [ "Splitting Objects into Light and Heavy / Case Processing|Square Root Decomposition|Data Structures (DS)" ] }, { "prob_id": "891c", "tags": [ "Disjoint Set Union||", "Offline Deletion||" ] }, { "prob_id": "293e", "tags": [ "Centroid Decomposition|Centroid Decomposition|Data Structures (DS)" ] } ]
{ "prob_id": "827f", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }
{ "prob_id": "843d", "tags": [ "Dijkstra's Algorithm|Shortest Paths|Graph Theory" ] }
[ { "prob_id": "786a", "tags": [ "Winning and Losing Positions, Strategy Stealing|Combinatorial Games|Advanced Algorithms" ] }, { "prob_id": "363b", "tags": [ "Prefix Sum|Range Queries Without Updates|Basics" ] }, { "prob_id": "546e", "tags": [ "Network Flows||Advanced Algorithms" ] } ]
{ "prob_id": "837g", "tags": [ "Persistent Segment Tree|Segment Tree|Data Structures (DS)" ] }
{ "prob_id": "786c", "tags": [ "Sqrt Decomposition|Trees|Data Structures" ] }
[ { "prob_id": "212a", "tags": [ "Edge Coloring of Bipartite Graph|Graph Coloring|Graph Theory" ] }, { "prob_id": "191c", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] }, { "prob_id": "440d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] } ]
{ "prob_id": "33b", "tags": [ "Floyd Warshall|Shortest Paths|Graph Theory" ] }
{ "prob_id": "25c", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] }
[ { "prob_id": "706c", "tags": [ "Common Patterns|DP|Intermediate" ] }, { "prob_id": "279b", "tags": [ "Two Pointers|Leveraging Monotonicity|Basics" ] }, { "prob_id": "30e", "tags": [ "Suffix Array|Suffix Structures|Strings" ] } ]
{ "prob_id": "25c", "tags": [ "All-Pairs|Shortest Paths|Intermediate" ] }
{ "prob_id": "33b", "tags": [ "Floyd Warshall|Shortest Paths|Graph Theory" ] }
[ { "prob_id": "204e", "tags": [ "Suffix Array|Suffix Structures|Strings" ] }, { "prob_id": "808b", "tags": [ "Sliding Window|Data Structure Techniques|Intermediate" ] }, { "prob_id": "191c", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] } ]
{ "prob_id": "346b", "tags": [ "Knuth Morris Pratt (KMP) and Prefix Automaton|String Matching|Strings", "Substring DP|Dp on Different Structures|Dynamic Programming (DP)" ] }
{ "prob_id": "808g", "tags": [ "Knuth Morris Pratt (KMP) and Prefix Automaton|String Matching|Strings" ] }
[ { "prob_id": "1446a", "tags": [ "Knapsack DP||" ] }, { "prob_id": "1552i", "tags": [ "PQ Tree|More Tree Data Structures|Data Structures (DS)" ] }, { "prob_id": "727e", "tags": [ "String Hashing|Hashing|Strings" ] } ]
{ "prob_id": "486a", "tags": [ "Sums and Asymptotics||Preliminaries" ] }
{ "prob_id": "82a", "tags": [ "Sums and Asymptotics||Preliminaries" ] }
[ { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "204a", "tags": [ "DP on Digits||Intermediate" ] }, { "prob_id": "96b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] } ]
{ "prob_id": "486a", "tags": [ "Sums and Asymptotics||Preliminaries" ] }
{ "prob_id": "318a", "tags": [ "Sums and Asymptotics||Preliminaries" ] }
[ { "prob_id": "822e", "tags": [ "Dynamic Programming||", "Hashing||" ] }, { "prob_id": "1245f", "tags": [ "DP on Digits||Intermediate" ] }, { "prob_id": "961e", "tags": [ "BIT / Fenwick Tree|Binary Indexed Tree (BIT)|Data Structures (DS)" ] } ]
{ "prob_id": "527a", "tags": [ "Greatest Common Divisor and Least Common Multiple|Number Theory|Basics" ] }
{ "prob_id": "822a", "tags": [ "Greatest Common Divisor and Least Common Multiple|Number Theory|Basics" ] }
[ { "prob_id": "47d", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }, { "prob_id": "152c", "tags": [ "Rule of Sum, Rule of Product|Counting|Basics" ] }, { "prob_id": "895e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] } ]
{ "prob_id": "822a", "tags": [ "Greatest Common Divisor and Least Common Multiple|Number Theory|Basics" ] }
{ "prob_id": "527a", "tags": [ "Greatest Common Divisor and Least Common Multiple|Number Theory|Basics" ] }
[ { "prob_id": "468d", "tags": [ "Bipartite Matching|Network Flows|Advanced Algorithms" ] }, { "prob_id": "802c", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "547b", "tags": [ "Stack||", "Stacks||" ] } ]
{ "prob_id": "375a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
{ "prob_id": "284a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
[ { "prob_id": "729f", "tags": [ "Skip Useless States|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "1154e", "tags": [ "Lists, Stacks, Queues|Basic Data Structures|Basics" ] }, { "prob_id": "1151c", "tags": [ "Sums and Asymptotics||Preliminaries" ] } ]
{ "prob_id": "742a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
{ "prob_id": "793a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
[ { "prob_id": "494b", "tags": [ "Knuth Morris Pratt (KMP) and Prefix Automaton|String Matching|Strings" ] }, { "prob_id": "507d", "tags": [ "Counting with DP||Intermediate" ] }, { "prob_id": "214a", "tags": [ "Iterative|Complete Search|Basics" ] } ]
{ "prob_id": "375a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
{ "prob_id": "495b", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }
[ { "prob_id": "204e", "tags": [ "Suffix Array|Suffix Structures|Strings" ] }, { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "455d", "tags": [ "Splay Trees and Treaps|Augmenting Data Structures|Advanced Data Structures" ] } ]
{ "prob_id": "18c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
{ "prob_id": "276c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics", "Prefix Sum|Range Queries Without Updates|Basics" ] }
[ { "prob_id": "877f", "tags": [ "Square Root Decomposition||" ] }, { "prob_id": "815c", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] }, { "prob_id": "587e", "tags": [ "Vector Space and XOR Basis|Linear Algebra|Math" ] } ]
{ "prob_id": "18c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
{ "prob_id": "816b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics", "Prefix Sum|Range Queries Without Updates|Basics" ] }
[ { "prob_id": "464b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous", "All-Permutations|Complete Search|Basics" ] }, { "prob_id": "817c", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] }, { "prob_id": "849b", "tags": [ "Basics|Geometry|Basics" ] } ]
{ "prob_id": "816b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics", "Prefix Sum|Range Queries Without Updates|Basics" ] }
{ "prob_id": "18c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
[ { "prob_id": "149e", "tags": [ "Z algorithm|String Matching|Strings" ] }, { "prob_id": "884f", "tags": [ "Min Cost Max Flow (MCMF)|Flow and Min Cut|Graph Theory" ] }, { "prob_id": "825f", "tags": [ "Z algorithm|String Matching|Strings" ] } ]
{ "prob_id": "983b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
{ "prob_id": "877b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
[ { "prob_id": "679c", "tags": [ "Sliding Window|Data Structure Techniques|Intermediate" ] }, { "prob_id": "60b", "tags": [ "Grid Graphs|Graphs|Basics" ] }, { "prob_id": "377a", "tags": [ "Grid Graphs|Graphs|Basics" ] } ]
{ "prob_id": "983b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
{ "prob_id": "611c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
[ { "prob_id": "1270c", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "1176e", "tags": [ "Bipartite Graph||", "Graph Traversal||" ] }, { "prob_id": "1513d", "tags": [ "Minimum Spanning Tree||" ] } ]
{ "prob_id": "877b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
{ "prob_id": "983b", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }
[ { "prob_id": "821e", "tags": [ "Matrix Exponentiation|Matrices|Math" ] }, { "prob_id": "689b", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }, { "prob_id": "1083a", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] } ]
{ "prob_id": "131c", "tags": [ "Binomial Coefficients|Fundamentals|Combinatorics" ] }
{ "prob_id": "340c", "tags": [ "Binomial Coefficients|Fundamentals|Combinatorics" ] }
[ { "prob_id": "467d", "tags": [ "Depth-First Traversal, Connectivity, Cycle Detection|Graphs|Basics" ] }, { "prob_id": "387e", "tags": [ "Square-Root Decomposition, Segment Trees, Binary-Indexed Trees|Range Queries|Intermediate" ] }, { "prob_id": "348a", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] } ]
{ "prob_id": "893b", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
{ "prob_id": "467b", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
[ { "prob_id": "1176e", "tags": [ "Bipartite Graph||", "Graph Traversal||" ] }, { "prob_id": "1446a", "tags": [ "Knapsack DP||" ] }, { "prob_id": "1439b", "tags": [ "Maximum Clique|Cliques and Independent Sets|Graph Theory" ] } ]
{ "prob_id": "424c", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
{ "prob_id": "988d", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
[ { "prob_id": "193b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }, { "prob_id": "242e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "691e", "tags": [ "Matrix Exponentiation|Matrices|Math" ] } ]
{ "prob_id": "988d", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
{ "prob_id": "424c", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
[ { "prob_id": "193b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }, { "prob_id": "296c", "tags": [ "Prefix Sums and Difference Arrays|Range Queries|Basics" ] }, { "prob_id": "371c", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] } ]
{ "prob_id": "484a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
{ "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }
[ { "prob_id": "242e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "243a", "tags": [ "Bit Manipulation|Bit Manipulation|Basics" ] }, { "prob_id": "348a", "tags": [ "Binary Search|Leveraging Monotonicity|Basics" ] } ]
{ "prob_id": "47d", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }
{ "prob_id": "193b", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }
[ { "prob_id": "659a", "tags": [ "Divisibility, Modular Arithmetic|Number Theory|Basics" ] }, { "prob_id": "895e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "576a", "tags": [ "Prime Factorization|Number Theory|Basics" ] } ]
{ "prob_id": "292c", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }
{ "prob_id": "47d", "tags": [ "Backtracking|Miscellaneous|Miscellaneous" ] }
[ { "prob_id": "535e", "tags": [ "Convex Hull Trick|DP Optimization|Advanced Algorithms" ] }, { "prob_id": "547c", "tags": [ "Principle of Inclusion-Exclusion|Counting|Intermediate", "Möbius Inversion||Advanced Mathematics" ] }, { "prob_id": "95e", "tags": [ "Knapsack DP||" ] } ]
{ "prob_id": "550b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics", "Backtracking|Miscellaneous|Miscellaneous" ] }
{ "prob_id": "535b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
[ { "prob_id": "1100b", "tags": [ "Amortized Analysis||Intermediate" ] }, { "prob_id": "1295f", "tags": [ "Probabilities and Expected Values|Probabilities and Expected Values|Math" ] }, { "prob_id": "877f", "tags": [ "Square Root Decomposition||" ] } ]
{ "prob_id": "535b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
{ "prob_id": "550b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics", "Backtracking|Miscellaneous|Miscellaneous" ] }
[ { "prob_id": "294c", "tags": [ "Permutations with Repetition, Stars and Bars|Counting|Intermediate" ] }, { "prob_id": "821d", "tags": [ "Breadth First Search|Graph traversal|Graphs" ] }, { "prob_id": "147b", "tags": [ "Matrix Exponentiation|Matrices|Math" ] } ]
{ "prob_id": "96b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
{ "prob_id": "812b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
[ { "prob_id": "895e", "tags": [ "Segment Tree with Lazy Propagation|Segment Tree|Data Structures (DS)" ] }, { "prob_id": "107b", "tags": [ "Basics|Probability and Expectation|Basics" ] }, { "prob_id": "727e", "tags": [ "String Hashing|Hashing|Strings" ] } ]
{ "prob_id": "244b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
{ "prob_id": "114b", "tags": [ "All-Subsets / Binary Choice|Complete Search|Basics" ] }
[ { "prob_id": "832d", "tags": [ "Lowest Common Ancestor|Lowest common ancestor|Graphs" ] }, { "prob_id": "321e", "tags": [ "Divide and Conquer DP|DP optimizations|Dynamic Programming", "Divide and Conquer DP|DP optimizations|Dynamic Programming" ] }, { "prob_id": "191c", "tags": [ "Level Ancestors and Lowest Common Ancestors||Advanced Data Structures" ] } ]
{ "prob_id": "124b", "tags": [ "All-Permutations|Complete Search|Basics" ] }
{ "prob_id": "431b", "tags": [ "All-Permutations|Complete Search|Basics" ] }
[ { "prob_id": "377a", "tags": [ "Grid Graphs|Graphs|Basics" ] }, { "prob_id": "1063b", "tags": [ "0/1 BFS|Shortest Paths|Graph Theory" ] }, { "prob_id": "1394d", "tags": [ "DP on Trees and DAGs|Dp on Different Structures|Dynamic Programming (DP)" ] } ]
{ "prob_id": "431b", "tags": [ "All-Permutations|Complete Search|Basics" ] }
{ "prob_id": "908b", "tags": [ "All-Permutations|Complete Search|Basics" ] }
[ { "prob_id": "1476a", "tags": [ "Basic Constructive Algorithms|Greedy and Constructive|Basics" ] }, { "prob_id": "1096g", "tags": [ "Fast Fourier Transform (FFT)|Convolution|Math" ] }, { "prob_id": "1439b", "tags": [ "Maximum Clique|Cliques and Independent Sets|Graph Theory" ] } ]
{ "prob_id": "431b", "tags": [ "All-Permutations|Complete Search|Basics" ] }
{ "prob_id": "124b", "tags": [ "All-Permutations|Complete Search|Basics" ] }