Volume of Histogram


Imagine a histogram (bar graph). Design an algorithm to compute the volume of water it could hold if someone poured water across the top. You can assume that each histogram bar has width 1.

/* Go through each bar and compute the volume of water above it. 
 * Volume of water at a bar =
 *   height - min(tallest bar on left, tallest bar on right)
 *   [where above equation is positive]
 * Compute the left max in the first sweep, then sweep again to 
 * compute the right max, minimum of the bar heights, and the 
 * delta. */
public static int computeHistogramVolume(int[] histo) {
/* Get left max */
int[] leftMaxes = new int[histo.length];
int leftMax = histo[0];
for (int i = 0; i < histo.length; i++) {
leftMax = Math.max(leftMax, histo[i]);
leftMaxes[i] = leftMax;
}
int sum = 0;
/* Get right max */
int rightMax = histo[histo.length - 1];
for (int i = histo.length - 1; i >= 0; i--) {
rightMax = Math.max(rightMax, histo[i]);
int secondTallest = Math.min(rightMax, leftMaxes[i]);
/* If there are taller things on the left and right side, then there is 
* water above this bar. Compute the volume and add to the sum. */
if (secondTallest > histo[i]) { 
sum += secondTallest - histo[i];
}
}
return sum;
}

O(N)
public static int borderedVolume(HistogramData[] data, int start, int end) {
if (start >= end) return 0;
int min = Math.min(data[start].getHeight(), data[end].getHeight());
int sum = 0;
for (int i = start + 1; i < end; i++) {
sum += min - data[i].getHeight();
}
return sum;
}

public static int subgraphVolume(HistogramData[] histogram, int start, int end, boolean isLeft) {
if (start >= end) return 0;
int sum = 0;
if (isLeft) {
int max = histogram[end - 1].getLeftMaxIndex();
sum += borderedVolume(histogram, max, end);
sum += subgraphVolume(histogram, start, max, isLeft);
} else {
int max = histogram[start + 1].getRightMaxIndex();
sum += borderedVolume(histogram, start, max);
sum += subgraphVolume(histogram, max, end, isLeft);
}
return sum;
}

public static HistogramData[] createHistogramData(int[] histo) {
HistogramData[] histogram = new HistogramData[histo.length];
for (int i = 0; i < histo.length; i++) {
histogram[i] = new HistogramData(histo[i]);
}
/* Set left max index. */
int maxIndex = 0;
for (int i = 0; i < histo.length; i++) {
if (histo[maxIndex] < histo[i]) {
maxIndex = i;
}
histogram[i].setLeftMaxIndex(maxIndex);
}
/* Set right max index. */
maxIndex = histogram.length - 1;
for (int i = histogram.length - 1; i >= 0; i--) {
if (histo[maxIndex] < histo[i]) {
maxIndex = i;
}
histogram[i].setRightMaxIndex(maxIndex);
}
return histogram;
}

public static int computeHistogramVolume(int[] histogram) {
int start = 0;
int end = histogram.length - 1;
HistogramData[] data = createHistogramData(histogram);
int max = data[0].getRightMaxIndex();
int leftVolume =  subgraphVolume(data, start, max, true);
int rightVolume = subgraphVolume(data, max, end, false);
return leftVolume + rightVolume;
}


O(N^2)
public class HistogramData {

private int height;
private int leftMaxIndex = -1;
private int rightMaxIndex = -1;
public HistogramData(int v) {
height = v;
}
}
public static int findIndexOfMax(int[] histogram, int start, int end) {
int indexOfMax = start;
for (int i = start + 1; i <= end; i++) {
if (histogram[i] > histogram[indexOfMax]) {
indexOfMax = i;
}
}
return indexOfMax;
}

public static int borderedVolume(int[] histogram, int start, int end) {
if (start >= end) return 0;
int min = Math.min(histogram[start], histogram[end]);
int sum = 0;
for (int i = start + 1; i < end; i++) {
sum += min - histogram[i];
}
return sum;
}

public static int subgraphVolume(int[] histogram, int start, int end, boolean isLeft) {
if (start >= end) return 0;
int sum = 0;
if (isLeft) {
int max = findIndexOfMax(histogram, start, end - 1);
sum += borderedVolume(histogram, max, end);
sum += subgraphVolume(histogram, start, max, isLeft);
} else {
int max = findIndexOfMax(histogram, start + 1, end);
sum += borderedVolume(histogram, start, max);
sum += subgraphVolume(histogram, max, end, isLeft);
return sum;
}

public static int computeHistogramVolume(int[] histogram) {
int start = 0;
int end = histogram.length - 1;
int max = findIndexOfMax(histogram, start, end);
int leftVolume =  subgraphVolume(histogram, start, max, true);
int rightVolume = subgraphVolume(histogram, max, end, false);
return leftVolume + rightVolume;
}




Labels

LeetCode (1432) GeeksforGeeks (1122) LeetCode - Review (1067) Review (882) Algorithm (668) to-do (609) Classic Algorithm (270) Google Interview (237) Classic Interview (222) Dynamic Programming (220) DP (186) Bit Algorithms (145) POJ (141) Math (137) Tree (132) LeetCode - Phone (129) EPI (122) Cracking Coding Interview (119) DFS (115) Difficult Algorithm (115) Lintcode (115) Different Solutions (110) Smart Algorithm (104) Binary Search (96) BFS (91) HackerRank (90) Binary Tree (86) Hard (79) Two Pointers (78) Stack (76) Company-Facebook (75) BST (72) Graph Algorithm (72) Time Complexity (69) Greedy Algorithm (68) Interval (63) Company - Google (62) Geometry Algorithm (61) Interview Corner (61) LeetCode - Extended (61) Union-Find (60) Trie (58) Advanced Data Structure (56) List (56) Priority Queue (53) Codility (52) ComProGuide (50) LeetCode Hard (50) Matrix (50) Bisection (48) Segment Tree (48) Sliding Window (48) USACO (46) Space Optimization (45) Company-Airbnb (41) Greedy (41) Mathematical Algorithm (41) Tree - Post-Order (41) ACM-ICPC (40) Algorithm Interview (40) Data Structure Design (40) Graph (40) Backtracking (39) Data Structure (39) Jobdu (39) Random (39) Codeforces (38) Knapsack (38) LeetCode - DP (38) Recursive Algorithm (38) String Algorithm (38) TopCoder (38) Sort (37) Introduction to Algorithms (36) Pre-Sort (36) Beauty of Programming (35) Must Known (34) Binary Search Tree (33) Follow Up (33) prismoskills (33) Palindrome (32) Permutation (31) Array (30) Google Code Jam (30) HDU (30) Array O(N) (29) Logic Thinking (29) Monotonic Stack (29) Puzzles (29) Code - Detail (27) Company-Zenefits (27) Microsoft 100 - July (27) Queue (27) Binary Indexed Trees (26) TreeMap (26) to-do-must (26) 1point3acres (25) GeeksQuiz (25) Merge Sort (25) Reverse Thinking (25) hihocoder (25) Company - LinkedIn (24) Hash (24) High Frequency (24) Summary (24) Divide and Conquer (23) Proof (23) Game Theory (22) Topological Sort (22) Lintcode - Review (21) Tree - Modification (21) Algorithm Game (20) CareerCup (20) Company - Twitter (20) DFS + Review (20) DP - Relation (20) Brain Teaser (19) DP - Tree (19) Left and Right Array (19) O(N) (19) Sweep Line (19) UVA (19) DP - Bit Masking (18) LeetCode - Thinking (18) KMP (17) LeetCode - TODO (17) Probabilities (17) Simulation (17) String Search (17) Codercareer (16) Company-Uber (16) Iterator (16) Number (16) O(1) Space (16) Shortest Path (16) itint5 (16) DFS+Cache (15) Dijkstra (15) Euclidean GCD (15) Heap (15) LeetCode - Hard (15) Majority (15) Number Theory (15) Rolling Hash (15) Tree Traversal (15) Brute Force (14) Bucket Sort (14) DP - Knapsack (14) DP - Probability (14) Difficult (14) Fast Power Algorithm (14) Pattern (14) Prefix Sum (14) TreeSet (14) Algorithm Videos (13) Amazon Interview (13) Basic Algorithm (13) Codechef (13) Combination (13) Computational Geometry (13) DP - Digit (13) LCA (13) LeetCode - DFS (13) Linked List (13) Long Increasing Sequence(LIS) (13) Math-Divisible (13) Reservoir Sampling (13) mitbbs (13) Algorithm - How To (12) Company - Microsoft (12) DP - Interval (12) DP - Multiple Relation (12) DP - Relation Optimization (12) LeetCode - Classic (12) Level Order Traversal (12) Prime (12) Pruning (12) Reconstruct Tree (12) Thinking (12) X Sum (12) AOJ (11) Bit Mask (11) Company-Snapchat (11) DP - Space Optimization (11) Dequeue (11) Graph DFS (11) MinMax (11) Miscs (11) Princeton (11) Quick Sort (11) Stack - Tree (11) 尺取法 (11) 挑战程序设计竞赛 (11) Coin Change (10) DFS+Backtracking (10) Facebook Hacker Cup (10) Fast Slow Pointers (10) HackerRank Easy (10) Interval Tree (10) Limited Range (10) Matrix - Traverse (10) Monotone Queue (10) SPOJ (10) Starting Point (10) States (10) Stock (10) Theory (10) Tutorialhorizon (10) Kadane - Extended (9) Mathblog (9) Max-Min Flow (9) Maze (9) Median (9) O(32N) (9) Quick Select (9) Stack Overflow (9) System Design (9) Tree - Conversion (9) Use XOR (9) Book Notes (8) Company-Amazon (8) DFS+BFS (8) DP - States (8) Expression (8) Longest Common Subsequence(LCS) (8) One Pass (8) Quadtrees (8) Traversal Once (8) Trie - Suffix (8) 穷竭搜索 (8) Algorithm Problem List (7) All Sub (7) Catalan Number (7) Cycle (7) DP - Cases (7) Facebook Interview (7) Fibonacci Numbers (7) Flood fill (7) Game Nim (7) Graph BFS (7) HackerRank Difficult (7) Hackerearth (7) Inversion (7) Kadane’s Algorithm (7) Manacher (7) Morris Traversal (7) Multiple Data Structures (7) Normalized Key (7) O(XN) (7) Radix Sort (7) Recursion (7) Sampling (7) Suffix Array (7) Tech-Queries (7) Tree - Serialization (7) Tree DP (7) Trie - Bit (7) 蓝桥杯 (7) Algorithm - Brain Teaser (6) BFS - Priority Queue (6) BFS - Unusual (6) Classic Data Structure Impl (6) DP - 2D (6) DP - Monotone Queue (6) DP - Unusual (6) DP-Space Optimization (6) Dutch Flag (6) How To (6) Interviewstreet (6) Knapsack - MultiplePack (6) Local MinMax (6) MST (6) Minimum Spanning Tree (6) Number - Reach (6) Parentheses (6) Pre-Sum (6) Probability (6) Programming Pearls (6) Rabin-Karp (6) Reverse (6) Scan from right (6) Schedule (6) Stream (6) Subset Sum (6) TSP (6) Xpost (6) n00tc0d3r (6) reddit (6) AI (5) Abbreviation (5) Anagram (5) Art Of Programming-July (5) Assumption (5) Bellman Ford (5) Big Data (5) Code - Solid (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Convex Hull (5) Crazyforcode (5) DFS - Multiple (5) DFS+DP (5) DP - Multi-Dimension (5) DP-Multiple Relation (5) Eulerian Cycle (5) Graph - Unusual (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Java (5) LogN (5) Manhattan Distance (5) Matrix Chain Multiplication (5) N Queens (5) Pre-Sort: Index (5) Quick Partition (5) Quora (5) Randomized Algorithms (5) Resources (5) Robot (5) SPFA(Shortest Path Faster Algorithm) (5) Shuffle (5) Sieve of Eratosthenes (5) Strongly Connected Components (5) Subarray Sum (5) Sudoku (5) Suffix Tree (5) Swap (5) Threaded (5) Tree - Creation (5) Warshall Floyd (5) Word Search (5) jiuzhang (5)

Popular Posts